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I III. II. KOMI. H iloVt'AK!) 

.slloKIIIAMX ()|.l.l.( HON 

l'li<( n.Asl.l) I OK 

nil. .NI.W VOKK I'l hl.K I IhK.AKY 

hV MM. 

NAIION.AI. .MIOKIHAM) Kr.l'OKII.K.V 

AS.SOC lAllo.N .\NI) nil. I.II'.KNKV 

I '>.'•» 



f *' 






I 



•* 



% 




lif 






1^ 



«. - 



ACCOMPLISHED TUTOR; 



Olt, 










OF 



LIBERAL EDUCATION: 

CONTAINING THE 

MOST DIPROFED THEORY AND PRACTICE 

or THE 

FOLLOWING SUBJECTS : 



1. ED^ilh Cnmmvy 

and Elocutioa. 

2. Pe rmin fbip, and 

Short Haad. 

3. Arithmetic, Vulpar 

aod DecrtnaL 

4. Stod:-ht>Mmg:« and 
MettfaaQtsAcoofDpts 



5- Mcrfurat OX-, and 

Archi*o6tuic. 
^. OJuic^. 

7. Alcrbra- 

8. Dortrinc'crf' Aimnities 
y. Trirtmomrtry. 

ic Lomriihins. 
1 1 . Ceopraphy. 



1 , *\.ftronomr. 



'■"<. 



T-^. H>c: 

u. Dra^nmc..' . .rav'mj, 
and Pa-utiug. 



AND OTHEK USFFUL MATTET- 



E.mhdl:JktdwiihT'Viaiiy Copper 'plates anJSlxl*lr.:.^. \fc:'' cv^avcd. 



By THOMAS HODSOX. 



SE. OND EDJTJvS 



IN TWO VOLUN'LS:. 



VOL. 1. 



L o y D O A : 

fILIIITED rO£ H. D. SYMONDi>, PATIKhOf^'R KOW ; AND 



l8'.2. 



iv vnr.rst v.. 

f{ i'-riM i< tfiMtilr.H n|»oii llii;; lul/ji rJ;, in nrdrr to render 
it innu p'rffurMoim, 

Iff A(\\ of til** oth»r (!ll»'|^/•^s, I hav^. ntailH rl thrifif.* 
prtrti ' '"i* li H|»p(Hn.(l !/; hii \)v irK/fl 'frrnfr I, ;mi(I 
rfj( ('t 'I the Imj/ rfln/ijij* : ,i . lilirifr niyf* If of* fli'* lHl/f;iirf» 
of fitli^rs on in; \\ of tlir ^ihjt'Os ; llioii/li I hnvo not 
ijuofrd pvrry author 5 «» Ifiat would he rttcitl^d vifli 
more diflK ulty Uinn inifrjit hr, at lirH oxjifrtrd, nrid 
parlakt: ol a iirccifcufffi luiiH-t '(Hiry in lli<; pre fin t v/ork# 

It may lio projWT fo mnitioti, Oiat I havt rrrdira* 
vourrd hi inff-rt all the mo<l(rji liii|Frf»v(*mcnt«», in farh 
(if ihc fuhjrtts, that, flppran-d of any confidrrahlft 
utility. Tlu! errors unnvoidahl" in works of thift nftturr, 
KlxMinding with inhuhitom, I have, aji far tt9 they 
mU'Uffvt] to me, corrected in this '-dition. The eAridoor 
iVith which the fortt»er editiori (»f this work wfl» 
received, is at haft fofne argnmrnt iti favour of it;i 
tttility^ fls alff? emifohi^iofi to it# author } ftnd temli to 
ilteviate in aflli/ting difprfifiition of Hivitie l'r(;videneci 
Atid rend'^r t/denhle ati uninferrupfed eonfinenient to 
his room, which has turn (otitiiiticd tipwardft of 
eighteen years. 

MM/r 7'm/fiff 
jfToi. 




CONTENTS 



FIRST I'OLV ME, 



CHAP, I. 

Or«N<SUSH OltAMMAh. 

tier. I. Of tht mitttwi MdSmnd tf tMHM 
I. OrSyllnUn 

3. 01 the Nine Tarti of Spwch 

4. Of Synlnx . 

5. Of hm^iiation 

(>. OfElgculiuii , 



f 
« 



CHAP. It. 

Of PKNMANStltl". 

Skct. I. Riileifbrllie AllHinincnlot iheArlofWrliing 6i| 
I. Of 5«n:i Wming . . '74 

J. Of E)iillt>l.iry Wiidii^;, hikI Siipci fci iptioii 

ofLrtWt^ . ■ , '11 

4. Tlia An of Sttiiogi gi[ilij', or Slioti U«ml , 9) 



iu'-uUM IrfiiiifcB mum iliis ful)ji-^t), in order In render 
it ni'irc jK-rfpiciiiius, 

In .-ach (if the other fuhjr^K, I have rctniiiL'd thofc 
.parts "'liih agvpiiircd to inl ihe mod ((rtiiti-l, and 
rcjct-t.'l the fiiii-.r(liiriiis: a.iiling niyfclf of the labinirs 
of Dtlitra on cacli of the fiibjcOn; ihoii^'i 1 have i)»t 
i]uotL'd every Jitthor ; u th^it would \i<: cltctii!cLl with 
more di({ii.nliy than might be at lirtl cxi>cet>.'d, and 
pvlakc o( u j.rccifeiiers uiineccfTary in the [iri^lcnt wiirk. 

It liiay lie |iropcr lo mention, that I have rmluai 
Vonrcd ((I tiiftTt all (he modcni improtctncnts, in each 
c^ tbe fiihjrcts, that appeared of any coiiRderah?6 
utility. Till- I rrorit unavoidable in works of (hi» nature, 
tbounditig vtiili calciilations, I have, as far a* they 
occutTrd tn inr , coiTedcd In thii edition. The eandoar 
*ilh which the ftmner edition of this work .wai 
received, is al leift fome argument in favour of ity 
ntility, a^ nlfo eonfolatinn to its author ; and tendi to 
aTtevialc an iiffliftingdifpenfiiliiin of Divine Providence: 
and rcndir ti»lcnblc an uninterrupted confinement to 
his room, which has ndw continued upwards tjf 
tighXeen yciirH. 

MM'' TemfUf 
■ Boi. . 



1 



CONTENTS 



or TBS 



FIRST VOLUME. 



UBIi 



^•Am. 



CHAP. !• 
Op ENGLISH CRAMMAft* 



SscT. X. Of the IMvifioa and Sooiid •£ 
ft. Of Syllables 
3.. Of the Nine Parts of Speech 

4. Of Syntax • 

5. Of Punduation 

6. Of Elocution 



I 

4 
S 

4» 
5S 



CHAP* IT. 
Op penmanship. 

Sect. i. Rules for the Attainment ot the Art of Writing 69 

2. Of Secret Writing . . .74 

3. Of Epiftolary Writinc;, and Superfcription 

of Letters . . -77 

4« The Art of Steiiogi aphy, or Short Hand . 93. 



CH 



*l COJITK!»T». 




CHAP. III. 




Or VtXGAK AIinilMETIC. 






fv 


Act. I. NMUIon of Nuinb«i 


tt» 


J. Of Aiiiiiv.n 


Hi 


3. Of SubtrtA^/n 


140 




U5 


;. Of Dni&n 


• iS» 


A. OfRedu^ioii 


|£6 


;. OfOuRukofTbin TKnO, Cncle 


■74 


1. Of ihe >iil< of Thicc loicrfc, lioik 


■79 


9. Of the Kiil« of Thrtc Dircfi. (U.ubl« 


■•j 


10. Of ttir Rule M Three Inrerfe, double 


•>7 


■ 1. Of Kellowlliip, fitijcle and double 


■•9 


It. or AlliK>iiuii. rncd Ml aixl altcrnale 


■9» 


1). Of Viilgir fia^hun*. Rcduaiiin, AiMiiion 




S\Allr'Ak,ii, MultiplkariOD, Divifioo, ind 




the Kide of Three 


•03 


.4. 0( Kra^lKe 


• It 


15. Of B«iicr 


••7 


16. Off r.dn.ii, 


•«9 


1 7. Of hjjuMion of PitynKnli 


•31 


a. Of ihe Role of fjf., finale iiul dooUe 


•33 


19. Ol tix-hange 


.36 


M. Ot the Relation of Number* 


.46 



■ I. OfiiicEativaivnofRooo.SquareaiwlCubic f{S 



CHAP. IV. 
Or DECIMAL AKITHMETIC. 



h^ 



If CT. I. Of ReJuflion of Decimil FraAloni 
s. Of Addiiion ui diito ■ 



) 



w 



% 



SscT* 3* C^Subtradioii of Dedmal Fradions • 

4. df Multiplication of ditto « • s6( 

5. Of Divifioa of ditto • • 



CHAP. V. 
Op STOCK.HOLDING. 

Sect. i. The Nature of the Public Stpdn • s6t 

a. Of Simpfie and Compoaiid Inaereft • S70 

3. Of DiibooQt and ReverfioQ • • 



CHAP* VI, 

Op merchants ACCOMPTS. 

SscT. I. Of Book-keqiioj^ the Italian Waj^ or hf 

Double Eotij . • • • tS|. 

s. Fkecedenta of RecdpCs, Promiflbry Nofiet, 
Bills of Exchange, Bills of Debt, Bilk 
of Lading, Bills of Parcels, &c. with the 
Laws cooceniing them • • jo^ 



CHAP. VII. 

Op mensuration. 

Sect, i* Of Superficial Meafure, with the Method 
of meafuring Mafon's, Bricklayer's, Car- 
penter's, Sawyer's, Plafterer*s, l^lumber's^ 
Painter's, and Glazier's Work, and the 
Price of each. Alfo, the Price of each 
Commodity, and the Wages of Journey- 
men • • • • 3^1 
ft SEer* 



«w.' 



• ••m 

tm €X)19TRNTS< 




SftCT. 2. Of meafuring Land • • 

3. Of ^oltd Meafurr, meafuring Tim$r, 

D.j^^ing, ;»nd Gauging • 

4« The Ddt.i iption aiid Ufc of the Carpenter*! 
Rule, (ill liter's Line, and Cog^elhairi 
Sh'lin^Rulc • • • 397 

$• A View of the Five Orders of Arclute^ture 407 



< A 



CHAP. VIII. 
Of optics. 



8«CT. I. Of Vifion . . . . , 414 

•• Of Single, CbmpoAi^d, and Soiar Micro- 

3. Of Refraaing, Refleding, and Solar Tele- 

fcopes • . • 434 

i* Dr. Herfchers Improved Tcleicope « 45$ 






T«* 






• 



r. 







..' 



ACCOMPLISHED TUTOR 



m • 



CHAP. I. 



••V • Op ENGLISH GRAMMAR. 



SECT, I. 

^* ■• 

• ■ OP THE DIVISION AND SOUND OP LETTERS 

)• 

•*• /In the early ages of antiqiiit}r» before alptudxts were in- 
';^ : vented, mankiody feofible of their want oi focce means of 
/ ■ recording hifbrical events and fcientifical dHcofcries, had re- 
' ycourfe to various arts for tbefe purpofes ; the firil of which 
^ ^Vas painting. That partiality for pidures, fo evident in all 
*'•* ages and countries, afforded our ancients a method of per- 
'* petuating their trania&ions. To commemorate that, one 
« * nuui4iad killed anocber, they painted the figure of a dead 
; ' 3^a|i^ with anochcr man ftanding over him, having an hoiiile 
^^' ' wewbo in his hand. On the firft difcovery of America^ this 
>» was the only kind of writing uftd by the Mexicans. 

'- Td« firft improvement made by opr ancefiors in the art of 
writ^tg (if it might then be called an art) was by the intro* 
d«idiCa of hicroglyphical charadert. Thcfe coofifted cf 

A certaui 



'fi. 



M 







or I.NOMSn (JrtAMMA^I 



I 

. s 

I ■ 



rertiiiii iymUnU^ whuli wcir inndr to tT)irciM99ilPM)i*niy/-, 

flbk nbjf'^ti, to witif li, in foiiir )}:iilii tilin, fii(i|^th)UllV5{rff 

ftip|Mlr<l in hmv Uuur. rr:lriii1il.iii( r. An r'yr \S7ifi<|lir iyifjHil 

of knnwWify^c ; n mrlr, of rtrrnlly, im linviii;r-tiiflirr hrj^tn- 

Jiitiff nor Airl. Thr lif;)iiri of Miiini.iln wf^H* tiUiriiliiK h l?IQ« 

ptfjyccl in thii kind ot writinj;, on ircoiint o^ ('oiiir '(|bMKty . '•Ir'j! 

with which thry wcic iii|i|iofc(l to he cndowrd, ;ind iti whU h 

thry rcfcirihk'd ihr olijcA ftj'jiihrd. Thus irn|irii(U'iirc: w»« 






:* 



*tw\ J t««|Vlliiril«I| liir «#lfj«,l.il llf'^llltll.llf • lllf<| III ll/l ll«lt III «■ VTH« I • ■ I 

rcprckiiicTd hy m fly; wtfdom hy an :inr ( mid victory hy ii' ^ > ^' 'a 
hawk, ^riicfti hicniy,)y)diir0 floutinicd iiioH iiiniKirnt l'Ky(*| ^'^"f j'^Z 
(flA did fill (fthrr hTHi inn^ a\ ih.it iiiiir), wlicir llir kMr»wlrd/j;f V*.^> ^ 




coiitiifcd Mild prrplrxrd \\n iiioft fkilful iirolrn'orB* •'<^ *.^ 

In a frw liiucrdio/j aj/.^'S hicioyjyjdiim g;ivc plarc to.'- /*'^ 
hmplc iirhitiitiy iri.irkr., vvliif It wrir iiitrorlnrrd fo rrjirrfont , \ ' • 
nlijc^R, without )i:ivttifr the Innf^ rdicmtdntH-r. (m afNiiity tc^ * 
ihn ohjcAi icprclriitcd. 'Mir Chinrfr Hill nfr (hai'a/>ciH qf-"' * )#V' 
thii fiafiirc : they hjivc no jd|ih;il»ct of Irtti-iH, bill rvrry '*• '! 
linglc mnrk or ch.ira/.tcr rtf^riifirfi our pnfr/t idra or ohjr/t, ^*?fcl 




" ' vyr >-r.* 

c!rmirti(m ri^.iitff), i, «, '^^ 4, &< , afford iii an rxartipic of ifhr?.*. 'jf * .j* 

kNTof wridiifr ; whrrc ra» h fi^'iirc or cli.ira/.^r.r c'oiivcys 'th« "'' ,j 

iOrauf Iho nimdiri f^r wlmli it (l;iffd« a<>rlr:trly niid iiitrfh-^ , «*' 

• ' • 

|(i|y|y :A fhu wuid* tlmnfi'lvcs niir, |wr», tlirrr, &r, **Q(n * f '■' 

«lFlien imirki or rliarn^tnt roiiir to he ttfcd f<tr all our i|fcn»i' ,- V . ' 

iil«Mfl1fion to an alph.d»rt ni lrttn% tiiry thrn, froiir|nrlf * •! ; » 

finitibrr. lircomc irii.oiiveni«.ni« T* *•''. 

Tli«?lMxt improvriiirnt in thr art of wriini;; wa« I«y4hf*, j . ~ 

invrntlmi o| ii)#n« nr n1«^k«, vvhich (food, not dirr^iHf for '*; 

'li^ nbj^Ai (ii6iYilcIvr>, bnt ii)t' tlic wfrWi or ««w#i ifhttl'f . ^* - 

■ Uicy 



OF BNnr.isn okammaii. 3 

^^ ■y— i—— — —■— ■— ^1— —I— — 11^1— Mi^— 

they were diftinji^iirtiecl. Thin \«*ai nti nlph^hti •/ (rliaMr*, 
An alphabet of rhi« kind U ftill in iifc in ^'.thiopb, and feme 
countriei of India. 

jBut the nohic and fiiWiiiir dift-overy of an Afpf^ahrf ttfkttetf 
fuiKHcdcd every other impmveiiK'Ht in this art. Who wat 
the Arft in this invention U nnrerrain. An alphnhet of letters 
w;is, hinvcvcr, hniii|(ht into Greece liy Catlmii«i. thePWtenl- 
cian, who wa« cotrmporary with kin|( David. Thti alpliahci 
ronfidcd of only fixtrrn Icitcrii : the rc(l weiv aiided after- 
«vardi, an (if^na for pnYfwr feunda were found to be want In g. 
The Phccnician, Hebrew, (tirrk, and Rnman alphnbet^ are 
ib much alike in the fl);**c^' ^^^^ nainei of the letters, ns 
filainly to evince thry were ori^iniUy derived from the Ikine. 
By the life of the alphabet, we are now, therefore, enabled 
to exprrfs our idcai with the fame <teanie1'i and preclfioiii 
as in converfatiotu 

The F.nglilh alphabet confifti of twenry^fia Ictterp, A, a ; 
fli b ; C, c ; D, d j K, c ; F, U O, g: H. h ; 1, i : J, j \ 
K, k; L| W M, m; N, n; O, o ; P, p; Q, q t R, r ; S, f, t ; 
T, t ; U, « ; V, V ; W, w i X, K ; Y, y i 7., f i and ii di- 
vidrd into vowrU and ronlorMnts, niutm and trmi'ViuvcU. 

Tlie nautm of the twenty- lix letters :irc ns follow : n, bcr, 
cec, doc, r, cf, j^rc, aitth, i, j:i, ka, tl, cn», en, o. pic, iiic, ar, 
cfs tee, «, vrc, double 11, ex, y, yail. 

The voweli arc lix in numlvr, vir. •!. r, 1, /», », > i all 
ilic rcrt are confonantn. 

The imitc« are iUt)fr let torn wliich arc brj;\in, whrn they 
avc Iprllcd, hv a cnnittnaul : as, /•, hrc ; « , %ft ; •/% //rr, A:o. ; 
thole which are bepwn with a vowtl arc called ll nii-vowcli : 
as, /, «•/; w, em : n, r» ; r, iir; /, rfs, ^i . ; /, »f, «, r, are 
alfo called lifjnitlii. 

When two voweU meet toj^cihcr, they arc called a diph- 
thon;; ; urthel'e there arc thirteen, vir. tit\ fi\ «n\ uiy iiw, eu^ 
«ar, rr« <h», r^, r^, #<f, acui /r. 

V\ hen three vowels meet, tliey arc called a tiiphthonp : as 
in tlie word btauty. 

A ft Wiih 



or BNOLISR ORAMMAR. 



With regard to the found of thefc double voweU , there are 
M nikiy that can he given, which will hold good in all cafei, 
•• wordf are founded according to the caprice or affcdation 
of the age, or the fpeakers : a knowledge of them nmftf 
tbereforei be acquired by experience and obfervation. 

And concerning the found of Angle lettcrii the feHowing 
nikf are all that can (afeiy be depended upon. 

C it prooouncid hard like i, before «, #» «; and foft like /, 
before #» /« and^. 

O is alfo (bunded hard before iff,#,ar i fometimet hard, and 
foonetimei foft, befer^/ and^^ ; and generally foft before #• 

fi it moftly filent at the end of a word { but in that cafo k 
Itngthcni the foregoing iFOwel i at, M^ biJe ; and that fome* 
timet in the middle of a woiti ; at ungrate/ml. But fometimet 
It only foftent a preceding g^ at in Udgif judge. 

H it only an afpiratioo of the breath, and fometimet at the 
beginning of a word it not foumled at all : at, an i#irr, an 
kmffi man. 

W it either a rowel or a diphthong : itt proper found it the 
fiime at u In the Italian, §u in the French, or #^ in the Englifli* 
Sometimet it it not founded at all after #, fometimet like mm. 

X it a double confenant, compofed of a hard c or i, and / y 
and at the beginning of a word moftly founded like z. 

Y hat exactly the fame found at / ; and it only a fubftitute 
for it at the end of a word, or before i ; at, ery, Jfying, It it 
a perfeA vowel : and when ufed at a confonant at the begin* 
ning of a word, it anfwert to the ancient Saxon i .- at, yew^ 
inu ; youngf iong* 

Z it a double confonant ; it foundt at much coarfor and 
thicker than /, at v docs than /• 

J and vp though confounded by fome old writert with 
and IV, are entirely different lettert ; the former having the 
found of a foft g^ and the latter that of a coarfer /• Tlie 
former it calledy'tf, and the latter vee. 



t 



SECT. 



OP KWatlllR QKAMMAII. 



SECT. 11. 

OF SVI.LAin.HS. 

A lYLLABLi 11 a conftitucnt part of a word, or a tvliole 
^'ord i it Qonfifts of o«e or more letters, and is forntcd by m 
finglc impulfe of the voice. 

Spelling is the art of rightly naming the letters fingly that 
conftitute a vrord, and dividing them into i^'lUblcs. 

The art of fpelltng perfe^ly is not to Im acquired (parti- 
cularly in the EagJiOi) but by pradtice ; but a few rulck for 
Che dividing of fyllables may polfibly be of lirrvicc. 

I. A fyllable in the beginning, or middle, of a word ends 
in a vowel, except fuch vowel Ik followed by .r, or two or 
niore confonants : as in rr*/i*ji^i>#ff« 

m* When two or more oonfonaitts follow a \ owe?, which it 
pronounced (hort, they mull be (ieparatcd ; and one, at Icall^ 
always belongs to the preceding fyllable : ai in tth-jli menK-r. 

3. Wlien two or more confonants follow a vowel » which 
is pronounced lung, they fometimes belong to the following 
fv I lablc : as, M-grrfs. 

4. A particle, thouj;li placed imnicdi.itcly bolorc a vi)\\t!^ 
IS Icldom divided : as, utft-tjM^tl, 

5. A nuUc with a li(|uid loilowing aiT IcKloin diviJcd; but 
.1 li(]uid or a mute, with a mute follow iti;;, aiv inollly divided. 

6. When It or r< follow ;i luutc thcv air urvcr diviiU-d. 
Thclc arc the t'undaiiuMUal lulcs ior the divivhii); ot' i)l- 

i.\Mcs ; but fonic gramm.u iaus trv-otiuiKiui tbciu to be di- 
vided as they are founded in ;i juil pmnum uuion. 



SKCT. in. 

or TiiK KIM. pvuis or smiv'ji. 

When mankind had arrived at loine prrfd^titMi in th<* ait 
ijf writing, they loon diliovercd the prv4)ii(t\ nt iv(hi.-in<r 

1 »"«;uaj;e 



OF XNOLISH OILAMMAR. 



language into different forms of vvordi ; or, as tliey are com* 
WKn\\y called, parts of fpeech* 

In Englifh we have nine forms of words, or parts of fpeech. 

1. The Articlr— placed before nouns to helptodcter- 
0ime their iigniBcarion : as, a nnan, the man, 

s. The Substantive, or noun— which Is the name ol 
any objed whatever, of which we have any idea : as, a «r<r«, 
a hor/ef a fpirit^ S^'^A ^f* 

3. The Pronoun — ufed as a fubfiitnte for the noun : as, 
&, Jbe^ //• 

4. The Adjective — added to the noun to denote itj 
quality : ai, an bonrft man, a white horfe, an evil fpirit. 

5. The VERt — which'fignifies a ftate of etiftence, aAing 
or fuffcring : as, '• the centinels Jlept^ the enemy enter eJ^ and 
the fort was taim,** 

6. The Adver b — ufed to qualify or enforce the meaning 
«f other words. It is added fometimes to a verb : as, he readi 
lA^eil, Sometimes to an adjedive: as,"anr.r.,vr<//>^high n>oun< 
tain." Sometimes to another adverb: as, ^^ m^Ji divinely fair.** 

7. The Preposition — placed between words to conned) 
them together : as, ** the path /^ fame lies /^^a;^/^ the rrtad 
to danger.** 

8. The Coy JUNCTION — ufed to conne^fentences, as pre* 
pofitions connc(fl words : as, ** fear God ami honour the King." 

9. The Intlr jscTioN — ufed to exprefs the furprife 01 
afFcdlion of the fpealcer : ^jOf alas f 

Thefe are the nine parts of fpeech in the Englifli tongue j 
every word in which is reducible to one of ihcfe parts. 

The ARTICLE is placed before fubftantives 10 fliew how 
far their fignificatioo extends. 

There are ia Engiifli only two articles; a and the. ji\\ 
called the indefinite, and the the definite article. 

The indefinite article a is changed into an when the nexl 
word begins with a vowel, or a filent h before the vowel i 
except fuch vowel be y or w. This article, as its name im- 
ports, is ufed in an indefinite and undetermined fcnfe : as, i 

maa. 



Of SNOLISII QIAMMAS, 7 

^wmmmf^ms!^msmmamsmfP''^^'9fr^tmte^- ■ -lj . .■ it j 

MVdNv, moani one mniif without deecrtnining who in pariicuUi ; 
ieavtnf that eo be expl<iioed, if neceflkry, by the other purii 
of the leiitencc. 

Tiiii irticle can, therefore^ be joined to fubftantivci in tlie 
Angular number only, except it coiue before che adjedivee 
f^v and nNnty f nny 4iffw iLtvs^ ti (jc'^^*) many mem \ or before 
the complete numerical adjedtives, a eUuett^ a f'^^re^ «« ^w*- 
iireJ^ n th0nj\iHJ^ a miiihn^ ti myriad: as, a t^tzrn p^un^^ s 

The definite article r/«^ detcnuine* which pxrticular.thing 
is n^eanri or of many which they are i this it therefore em- 
p\o}td both with Angular and plural nount : as *^ f^ fi^rk 
in Mf htmHui^^ 

It is alio ufed fometimei hr fore adverbs in the comparative 
and fuptrlativc degrees ; at, the m^rt^ the better^ /'v ^e^%/t ^ of all.) 

The SUBSTANTIVE h the ftame of any ohje^ whato-cr 
of which we have aay idea. 

There arc two font of fnbftantlves, Proper and Common, 
Pi*oper names are fiich at belong to individual object, whether 
animate or inanimate , but not to evn y individual or ohjcft 
of the fame lort or Iprcica : thus, John is the name ot :i man, 
but iH)t the name <>f every man ; CVmv.v n^iy be the name <>( 
a dog, but it is not il>e name uf every il(»jj ; LomJoh the name 
of a city, but not of every city. Thefo uie lhercft)ie |)ro|)cr 
jiaines ; but man^ Jo-^^ and city are conuv.on iuui>cs : fi^r man 
i» the common name of every man ; i/^.s the c(mmu)u name 
4»r every dv>j{; and c/Vv, the conmion name of every city, 

Vropcr names have no articles nor pluial number, unlefs by 
a metapnoi : as wlun a cruel ryiai.t is called .1 AV»i>; or when 
a comux^n iian:e is> uiulcrft.uxl, as ihe (ftnp) R^\\\i!Gior^e\ or 
whrn there arc nuny of the lame name, as tf^- twc Ive Car/Ins, 

There arc three attributes bclonj;inj^ to an tnglilh noun, 
viz. number, genvhr, juui cafe. 

The nvnnber is either finguhr or plural. The lingular 
number expretVe? one object : as, a kiitv • the plural, two or 
iWre, ati kin^i, 

Th« 



I 



8 or umauhii guamuam. 

The plural number ii moAl/ formed, m Knglifli, by sIm 
Virion of i or /j ; iiy If^f Lcyi ; g0aty j^^ois ; fpx^ f^xtt. 

Some chanj;e the /into v : ai, af//>, ii/ity/ ; /r/#/i ieaveim 
, I S'^me pi u rail end io /« ; a^ ^jt, ^;ir//i j chiU^ chiidrm ; /w^i/r 

M#/!i ; hrothn^ hrtthren^ in the Utter, and (bme ocheri, iIm 
# in t!k: fir (I fylUblc ii changed into /• This form ii thi 
re iiiainv of the Teutonic languagCy and the folkMviog of th< 
baxon ; loHfe^l'ut\ moufe^ mice \ t§4th^ teeth, 

o/itnc nouni cfuling in y^ change it into i ; af, ^iiy^ eitses ; 
^alUrj/f galUriet* 

Some nounft liave no plural : as, efn^g^Utf pitchy lUth^ &c 
And otheri no ftn^^ukir numberi ; at, annmli, beiUwi^/ciffan, 
lkn7U &c. The words Jberp aud Jeer hare no variatioD o 
uuinl>er* 

All fubflantivei in Englidi, whether common or proper 
arc conftdcred with relation to gtnder, at being either of tb 
mafculinc, feminine* or neuter gender. That ii, either i^ 
the male or female fex, or neither. 

The mafculine or feminine gcndcri are applied to the nama 
of nnimali only, and fuch whofe fcx is obvious : as, mmi, 
Ifwrnat^cx^ which arc the mnfculine gender : Mary, wpmaw. 
hm^ ccvjt which are the feminine gender. Thofe whofe (b 
n not evident, with all inanimate objei^s, arc of tlic neutei 
grnd.r : a«, oxfler^ njj^rm^ houfr^ tree ; except in J^octry, aiv; 
the clcgint fpcciei of conipofition, where inanimate obje6t!»| 
and the human p.ifHons, are perfoniiicd into men and women, 
and confcqucntly have their genders. 
, A few i'ubftantives arc maikcd by their tcrminationt : a9, 

prince^ prlnce/t ; //>», lione/t ; ii(.7#r, aSirefi, 

'^rhc chief ufe of gender is to agree with the pronoun. 

In Kngtifli there are three different cafes of the noun : thi 
noiiiuiativc, polfcflive, and objc^ive cafe. 

The nominative cafe is the (imple name of the oonn, 
without relation to other objects : as, ** Jobn.'*^ 

Tlic polTeiiivc ligniHes the relation of poflTeflion : as, ^^J^Bm'^ 
book,** and was formerly written ^^Jphms book,'' and not**7#^a 
Lii book/* as is vulgaily written. It may alfo be exprefled by 

3 inverting 







Inttmf f'tfimc 



J^mi 






^hc J ^ rmmia' ^ifhw wtniitiiMi" ti^ 



f tcr«tM«l»i3 ^ 



' •" 



«'ii 



#K^ /-r^^MA 






yW' 



14:: 



^ •^^f 



\^^'l 



to or BMOUtH OMimiAli^ 

< lEaBmBsaeaaxmmmmsmammmmmi 



: 7Um. in all kt cufti, gencndly givci pbfit lo >#»t •icfit|pl 
in • very folemn ftylc, and in addrciToi to the Daily* 

Al the peribiial pronoun is a fobflilitte for the ooynt t$ it 
hai the (iime nature ki^granmiatical conAni^U^ and It capa^ 
Ue of forming a flfn^^nca without ihc aid of rho Aibftandfof 
ai, ** /thai fpcak unto thee am^ [Chrittl." John, W.a6# . 
' But there are otiier prooouoiv of the nature of adjodiret, 
and, like adjeAivcf » require foAa fubfliUiCivc tofaeioinadwitlft 
theni, which is either cxprcHed or undi^riUiodt Tkoiiil.art 
therefore called Pronominal AdjeAivet. /Of theft lhafif« re 
fmir ibrtsi poilH&M^ dafinitifiBai ralatlfvii a^ddiOributtvea*! 
i The poAeAives arey m^^ #^71 ^t/ff pm%^^iUiri aod arvoiH 
tirelydiflermt words from the polbffive^onoiinaiiifiiar»ii/iMV 
Ut» In theie the liibAantivc is fometimaa ttlifkrftood iivithouc 
being eMpreiTed : anfr^jJbeJXmme tejfm/n y' . vbt paaSt to t^ff: 
the fiibftantive IbouJd bo added t 4M| ^^ify pt0pk Jkmllit mf 

The definiijya irei tUh ^U ^^hifi^^% ftmH ^t^% ^^$0^^ 
Thefcdeline, or limiti tbe meaning of |lic fubfiantiM iiit 
Hfbich they refert or 9re joinod. Tbo jhree firftliava4ha p^al 
number : as, //^, ih/ft iibtri* 7 bit tvfcr» to the latter terni 
or fitntenee, that to tbo former: as, *^th^( are definitiveif tkt^ 
(mentioned l>cfott) are po(leffivesi*'-p/Arr Isuied in the piur4 
form only, when the /ubilantivc bflon^^ing fo it \% not ex- 
prcfTed, as is fcmiethncs tlie cafe in d#fiAi|ivci : •tlnr and av 
liave alfo the po^ci&v^ Ciiia ; ^9 '* this is oihtn' property/' 
and *Mt flartlcs ^«/j apprelienlion i*' oneU alio uicd in an 
indefinite fcnre» as *^ont thinlii." Thcfe are all the vaiiu* 
tion« defiDitivcs admit of. ' 

Tiic rclati.ves arc, nxjho^ wbtcL that, TheCe rrfcr to fomo 
fubdMntive or prooouo going before, which is lliercfure called 
the antecedent t as, ** I am //v L9rd thai niaketb till things 
that flretchcth forth the heavens alone." liaiah, xliif. %^. 
They tlio coiuiedl the foliowitf; and foregoing parts of a feti* 
fence to[;cther. Who is varied to exprtfl the three cafes : 
aS| *\^hOi nijljojt^ nuhfifu \ thcfc relatives refer to all the tliree 

pcrfiMis, 



I 

Ol^'fiMGtfSH ORAMlfJfS. II 

'feiiont, whereat the other praooaiiiial adje^et beloi^ only 
to the third pciribo. Wl^^ nMcls «u&c^y are called interro- 
f^tiTet, when they are ufed in a queftum. "■ 

EmA^ mtfy^ ikher, are called diftribtnWet, becaufe tbcy 
relate to objcds or peribni taken ieptnitely. • 

Befidcs the foregoing pronominal adje^tivef, there are two 
othen : #c(ffi, and fil/^ m the plural fehtim Both of ibem 
expreis empbafis, or oj:jxyfition, and are .joined to the pof> 
felfivety and ici form a compound pronominal adjedive : at, 

Omrfilf^ the plural prononnml adjcdive, with the finguhir 
fnbAantive, belongs to the regal AyJe. 

AH fubftantives belong to the third perfon, except when 
an addieft b made to a perfon, then the fubftantive is of the 
fecond perfbn. . . ^ 

An ADJECTIVE it a word added to a fubflantive, to 
exprefs the quality of it| or fome other property : a% « g$9d 
moM^ am iniMdrtd p§imJi^ s hnmiug m»Mmimm* 

Adjedif et have no variatiooy except the three degrees of 
companion : pofitire, comparative) and fuperlative. 

Mod qualitiei confift of different degrees, or of m^re or Ufs. 
Thus, when a quality is fimply exprefled, without reference 
to a greater or lefs degree of the fame, it is called the pofttive 
degree : as, large^Jhmt. When it is expreifed with relation to 
a lefs degree^ it is called the comparative degree : as, largery 
Jh&rier. When it is exprefled as being of the higheft degree 
iu its quality, it b called the fuperlative : as, Imrgeft^Jborteft. 

There are two ways of forming the comparative and fuper- 
lative degrees ; the firft is by adding r or er to the poiitive 
degree, which forms the comparative ; and by adding sf or est 
to the poiitive, and fo forming the fuperlative degree ; as in 
the !au example. Mod n^onofyllablcs are compared in this 
manner; and dinyilablcs ending in^ ; as, happy; and k^ when 
rhcy aie loll owed by a mute : as, a&U ; or when they are ac- 
fcr/cH oil ih* !ail fyllabJc : as, gmtceU But others, and words 

B2 ot 



' ta or tftSLtiin okammar* 

w^ m m SI > m 1 1 

of mort thio two fyiUblcn, feldotn idnik of tb^fe terming- 
tion»i but ire comptred atioettling to tbc following rule* 

The fcrond method of lbmitn[|[thc eompumtive and fiipct^ 
litlvedcgrceiof cofrifMfirnni li by pUoIng the ndvfrbt i»#r» 
or ri#/P before the «djeAi«e of iIm pnfitivt degrct s as Mff 

The fuperlativo It, iti a few wordii formed by adding the 
•dvtrb mpjl to the end of thtlii t ai| neibirm^^ /^nm^/l^ 
m/ferw99^^ tmJtrm$fi^ Ice* 

The four following adjei^ives are irragylar in the ibrnMi* 
tion of the degrcei of eomfiarUiMi in tiMl laitguagci i ji|[»#f/, 
hutr^hjl\ Mftver/f.mmt^^ MHh^i^,hmJI\ mmh^tiMmx^ 

Double companttret and faperiativei are improper in 
grammar t ai, the m0rt gremtrr^ or the mjlgrrmffix exeqit 
The M#/ M/*c|f , a phnfe uAmI <n tho Pftiklif of David| and it 
properly apptioaUle to the Sopretfio Biing only. 

The VERB iia word whieh figniaot an aAlon, or « Ihti 
or condition of hHng t and U eltlier ae^l^e, palRve, or oettter. 

A verb aatve ekprefTea an aAlon In iti natural ordcr» 
thnt is when 'Che agtnt ii>phifed Rr((> and the objeft lafti 
ftS " J»^n r^tti'lh h^k^ Here y$^ \% called the agent, 
iTfcatife hf pcrformn the aAlon, whK'h h /^, and which ia 
*thc terh i and Hwl U the objeA, upon which the action htvo 
-11 exercHcd. 

A Vcrli'paiRre ^xpttlRi an aAkm, but in an InveHevI onkr t 
that 1% whtrn'Hie objeA hplaced flrtt, and theaf^t kft : at, 
^ the Iwok /I /aw*/ by John." Here may be fiecn the ufe 
t<f the cafeic^f nouni and pronounii: for when the\xrbli 
a^lvr, fl\c agent ii pljiced Hrft, and li In the nondnaiHfe cafct 
•fti, •« r lo\*c //"cr." When the verb li pdfflve, the objcrt 
Uing pla(*ed flrft, muft be in the nominative rafeiand the ngetit 
bilnglaftmnft be in the objeAlvc cafe, accompanied with 
a prcpofiilon \ and the vcfb artVimei a dllTerent form : an, 
•• iif§m ArtiH*f4 h wf/' Tluii nn bAIvc verb may be tranC 
formed Into a paffiye, or a palltve verb Into an aaive vci b. 

Aveili 



or «KaLtSK eiUMMAII. 13 

A vcib neuter cx|M*cirei a iUte» or ccuiiUion, of beii^ 
oMly« and coufequcntly liai no objeft to be aAed upon 1 boc 
AD tgent only ; w^ ImMli^ J^^ I dtesmJ, iifiii^Jhe mr^. 
Tte verb neuter it ctlLed alio the ititnuifitive verb* and the 
verbadive tranfitive. 

Mnuy vcrbt are uiSed ia Englifli both in an adive and 
neuter tigfdfication ; their form ilemonflrating of «rhich kind 
they are* 

The verb it varied^ fiift, to coireCjxMid with the ihrao 
diftrtnt perfont of the pronoun i fecondlji to ^rce with 
the number lingular or plural ; thirdly, to cxpicfi ibc three 
.principal fradilioM of timci— prtfiint, p»i, and future; 
liiftly» to flicw the mode or manner in which the aAion or 
ftate of being it expreflcd. 

. In a verb arci thorefere» thcfe four attributes < perCm, 
-nuinbcri tinie» and mode. 

To agict with (ht three perfonal pronount, though ^f tho 
Suae numbcTi the vetb it varied : at^ J knu^ ib$u /tvc/'i ^ 
kvtibofhvcu 

Alfo to agree with tho two difEerent numbcrt of the (ame 
prrl'on : a9, thou Uvr/}^ yc /oa/# ; he h¥fth^ tliey /rrr • 

Ltkcwifr, to exprcfi the different tiincR in which the A^ion 
it repreCcnted : as, 1 i^*f^ I l«vcti^ 1 have lovcJ* To cxprefs 
the different time% other verbs are often ufed, called auxi- 
liaries, AS will be fcen hcrclfrrr. 

The verb is moreover vtried acoording to the different 
mtiMiro^ cxprefling thea^^ion or being i whidi variationt 
arc called its modes ; of which tliere arc generally reckontd 
fbur» lyefidcs the prticiplc : the indicative, imperative, fub* 
jmu^lve, anl infitiitivc. 

When a rircumftancc is Hmply declared, or when a qneAion 
is nikcd, the veil) en)|)loyed on thcfc occafions is ot the indi» 
cntivc mode : as, I lovt^ he lovfs^ Iwcft Uiou ? When any 
thing is romiDatuIcd, or folicited, or rcqucfted to be doi)c, be 
it to a ftiperior or inferior, the verb employed \\\ the fen- 
tci'cc k ot* the imperative mode; aS| /#vr thoui •• O Thou 

my 



f4 ^^ e^OUsH OtAWMAI. 

tof foke m/ptre .'*' — l*cpc. When any thing it exprefted ia 
sdMbcMoiamxr, or imifer a co»diuofi« or Co ppofitkin, or 
the like ; or when tt if liibjotCKrd at the coi or drigo ; or 
mAiktm it tf exprefied io the form of • triii ; it ■, is maj ^i 
tbtic cifcif and m nizny othcrt, tlie fiJUJttnAive mode of the 
verbr at , / I /#tRr« *^ th^ggb be >Cff aie;» )rct will I ^«uc 
my trtii io bim.^' Job, xitL i $. ^ toog wf be UvtJ* Tbt 
▼erb in thii floode gcoer^Jiy dtptodt co iiwrie otiier icfb, 
'«0d bat a coojuoAion before it : at, ^ Th^uf^b after my fM, 
wonm iE^nr; tbii bod)-, yet io my llcfli tell i fit God/* 
Job, abt. t6. 

Here jt mwtt be noted, that when an application i» made, 
•f tbe future of a rcqued, tlie verb is of tiie unpe/atiwe 
mode: ai, *^ fx>rd/i',< mc/' M<tCt. xiv. Wbrokisof the 
natorc of a wiib, the verb h tA the lubjun^.remode : at, 
^ O Kingf //V^ for ever/' Dan. iii* IVheo the vtrb » c»» 
preilcd '^hout any fetrrenoa to peribo or n«mber/jt it 
caUtd the iufiiiitive mode : ae, to i^ve ; aod vrben tt it 
pi eiTed in iudi a iVrin, thar it may be joined toai 
it H called the panicipte, aod baa fomcwbat of tbe native at 
an adje^ime : as, i^vAf^t iW///« 

To espteff the different timet of the verb, in En^ifhf It ia 
often neoeDary to m^ke ufeof otLicr \et\Hf called tberefoce 
jtmitiarief, ^jt helperi ;. of which there ire nine : h^ have^ /#, 
Utj may, mvft^ can^JhaU^ iv-ll. The two firft are chiefly itkd 
for forfuing tbe dilTereot timo ol tbe verb : it if, therefore, 
neceflary to imow how to declme tbeo) according to jftriom^ 
fliNnber, time, and mode* 

TO HAVE. 

Ikricative Mode.— Pr^/r/ Timf. 
lingular NuwUr. Plural KumlaCx 

ri.Ihave, Wc "^ 

fcrfoni* < «. Thou haft^ Ye Vhare. 

1 3. He bath, or luH 4 They J 



Of KKOkMfl tMIAMMAlU 



«5 



m 



f^fi Tiwr, 



Hertei. V •• Thou HmIR, 
lichacji 






We ^ 

Yd >h«L 



rti'funi. 



f.I flialUnr will x 
t.Tliouflmlr.ur (^| 



wilt I 

.>H« Dull, or will J 



►ha\T 



We 

'I'hry 



(^Hull, or 



J 



Fcifoni. 




iMI'hHATlVK MoDB. 

I. Let mr luive^ 
I. Have thon. ur do 



I rt \iA Imvr. 
H.i\c Yc, or ilo )«c 

luivo. 
Lrt ti^iD have. 



IVrfonii 



SuBjUNCTivic Mode.- Piftu Tiwi-, 

(i.lffor ^ lU.ui thouKliix 
though. 1 J W> 

••ILor I If, or though, ' 
tftough, Vu.,.^. Yo !.,_ 

Thou ;"-*^<^» f"'^^<^ 



Thou 
3.11", or 
thougji. 
He 



lf,oi tho\ii»li, 
TUcv 



IWjtHt^ To \\A\t\ /*/!//, To Ir.ivc hail. 

iVvM Having ;— iV.ViV, llaih, - r7*.i>V, lla\ iiu'. li.ul. 

As the •^ilunil proiutua v**u U nu>ftlv empli»ynl iullrnl i»f 
the (in^\)bu //*«», ir Duut, thcivforr, liavt- the pluuil \ril); 
ai, iv« /a^iv, y0h Lut^ \vu \\.\ft' ; and iu>t vai, Ai^, m'^t '''.i.'A 
ii/i^ ;4*t«4. Whii'h Utt in lui ti roneitvi^i lolniliii, luuii; tli<* 
l^liiial prouumi of thcfcioiu) pciUiu, placed m a^nctiuMU 
A\\\\ the llii\ or thiiil perloii fiit^iilai of the \c\U ; mi\U 
V tuh cirivr wriicru ot thr tirft eminrnry li.i\c (.oumut&i»(J# 

J- 



* 

Iti thtt third iHsifon AnguUri prc(f nl timci itivllcntiyc mmlf» 
th« itmkiiitloa of the vurb ii gtn«iiilly In #1, loAtrnd of «fr or 
f#/»i In tht polUe Antl fumUtar ftyl« i u^ h« iiti» inftfatl of 
htikoAi ft« lM¥fi for h« AmiA* B«il In tho vdy fohRM 
ttnd fei ioui ftyk the ttrndnntbn (1 in i^% 

TO BE. * 

iNOICATtVtt MoDk«-»/VVt«ti TVntTi 

t.lHmi Wo *i 

P«rfoni. ^ i« Thnu (irt» Y« >irt. 



rt.iHmi 
u < i« Thnu H 
V3» He li I 



They J 



were. 



P^l/I Tim. . 

A« Thou wafti Yo > 

;)»Hcw«i) ThryJ 

PofontJ *.ThouftMlr»orwilr, Vie) Yo V^^i^ 



TliriltATIVR Moi>i» 

I. Let mr be, Ltiuibc* 

F«rroni% ^ i% Be thoiu ov do thou bt| Be yt| or do ye be« 

Let him be | Let them be. 



fi.Lel 
4i«Be 

I J. Let 



tulil •! tfwe ") 

Piirroiu. V A. If thovi Vbe ) U ye Vbe « 

l).Ifho J Uihey J 



ftarCbni, ^ t. Thou wkrt| Ye > wi-e^ 

He were j They J 






lirrtNtTtvBMontt 
i*lff;^il^ To be)-«IV^» To htive bMO. 

PAlTimrLU 

^t^>^^ Being J— ?#i/i^, lleeni^r«(/f| Hivtng been. 

1 Tk 



OP BNOttlR n^AMMAIt. 




Number, Time, and M9di. 

TO LOVE. 
iKntCATIVl MoDi.«*Av#«# f/nvf. 



Ye Movt. 

They/ 



} 



r tJ love, 
Pcifons. < ft. Thou lovefti 

V3« He lovethi or lovei i 

P^ Tim. 

Perroni. < t. Ttion lovedftf 
Ij.Heiovedi 

rt.IfluUiorwili, ^ 
Perfoni, < t. Thou flitlti or wilt. Viove t 
I3. He Aftll, or will, J 

iMPtRATivK Modi* 

r I. Let me love, Let ui love* 

Perfoni. < t. Love thou, or do thou love, I.QVcyc^ordojretoive. 
13. Lit him love \ Im tntm lovt. 

SvijVNCTiYft MoDi.-nPr^/ Ttmt* 



We 

Ye 

TKey 

We 1 
Ye I 
TheyJ 



Ikftll or 
wttllovf. 



IVrfoni 






Thou Move I 
3. He J 



r I.I may "> 
Pfcrfoni.X ft.Tluiu mty ^love; 



Pi^rfoni. 



3. He may J 

rt. I might ^ 

< ft. Thou mighteft ^love) 



3* He might 



i^. 



We ^ 

Ye Vlovt. 

ThcyJ 

We ^ may love 1 
Ye } and 
They J have loved. 

We T might love j 
Ye V and 
They J have ioved 



I I. J could, fliotiid, 1 

or would I 

a.Thoucouldcft, I 

(houkkl^, or > 



Vou I 



wouldeft 

3, He could* (hould, 

or would 

C 



We 1 

I could, 
Ye I fliould« or 
> would love{ 

'^'*'^« They have""oved^ 



love I 

and 
hnve 



* 

vnd pc;rf«(ft UiiH« arc put together* 1 lie verb \i\ th« pnu 

tiinfii of tbi« nu>i|tf| irtiiwi\)i\y b;iV4; s future iignidc^tion ( aif 
'* //be ^rr/V# i\\ti\^^htr) wc (Imtl i^i w#ll'»" *♦ if bii /j'/:'»//f, 
fif'W0i0UUin\6 (lumonow)v I migh$^ nmitld^ f0uM^ of JhoM 
\\)ciiV to bim/' Tb<! fiuxWiaiM Jh0i4l(l mi wouU^ \n ibe psft 
m^fiM^ 4rt alfo iift/i to exprnf^ tt)e tbree fptcics of tbi^e, 
)H«r«nrf |H)((» iind futuK^ ; m«, ^' it // my <te({re tbut ii« ^»A/ 
«f fUifivM ^of»# (OMW, or to-n)ofiow)| mA it <^tf^fny dcArt 
tbiit b« JbouldQX 'Would QQWin (y«Aerd»y)«'' Tb«r«fore| in 
tbif modc^ tbo tii|)« i)f tb« verb i» kiiowM n)o(tly by tl»e nature 
i»f ibc font«H^<$* 

Thir tbrM gfAtid divifioni of tiiiui, iota |)r«feHt9 p^fti iOif 
futur^f are f All«d iiidi^ftHitf^y of MHdfiU^nni/mt^ (i(P# { but cicb 
of tlusfe Are fulMUvid<:4 into im|)«ifiL<^ ai(4 perfi^i^r tifnci wbicb 
<ub4M^i<iMfi if «fitl«4 iltfbiiiu or ii(;^4(fii)iii(e;4 tifrn. 

Deflnitt 0r thttr mined Timi, 

Atu^fi S/ciU, l^uHiytVtih N«ui#rV«ri 

Prejinf ImptrffH. 

I am (mw) bnriiyjty 1 am lov^df • 1 nm «nt«rlf»f . 

I Imyc (uow) lov^4 ^ '^'^^^ ^^^^^ lovftd^ I bftve «ntcreil* 
i WM (tti«o) toving^ I wi* lovtfd, I w4i enwUip 

\ bail (tbcn) lovedi I biut luftfi \W0A% I li«4 «i)Urt4. 

/^4^/«r# lmp$rf$fl. 
I 0mU (tb^n) be lovingf I fliall be lovidi \ 0Mli b« «ntiri«if| 

/^»/»r# PtrfeH. 
ilk»U (tlMfi;biyfftov«4y l(b(ilili»vfl»M|il«rfd# l0iil|l»tVf«iiifM4. 



# 



t%f 1(Nnt.Tftlf OnAMMAUT 1^ 

*.<. . M. . . . 

tt U utu ncorlT;)!'}* to yivr (hr v,inA(k)ni nf the tlcllintrt 
iimri, A]i tlirv «if f'oin»r\l only hy thr pn)|)rr vniiiulnhft of 
t hr ;tiiMlifi nrn, joincil totlir pirfnit or |H*itW> panUMplc. 

In X^w f.Mrt\MiUm (»t* ihclt* ilrlSnlci* time*, \\w Af\\\t «iul 
nfuirv vci'b* s^ir «liVo ; ihr p.itRvc vfil> tllflVr* Irom \\yt 
AO^vi»| only in h.ivin^ \\\r \\r\\'cc\ |wriuiplr inllrnil o1' the 
prrfrnt in thr ln>|H?iiCiM tuntt j :4nil Hiivlnj( ih<* p« rfro^ p.n'- 
(Wlpl« il^^n In (hv |)«i tV^'t time K. 

Thr pAlRvp vn'U U foimtii ihron^h all iti v.uloiitni i»f 
|>n(m)| Mwwbcr, liiuc, nfiil i««m\«% hy m\\\\\\% ihr pnfr»M, or 
|MtUvc |Htiihiplf (h«nh which dir ihr Unir, :n\il iu i«\l tr^u- 
Ui vcihx rhc lAmc ai ihc iildclSnttc p^ll Innc AOttvr) in ihr 
AuxihAiy vnh /i» A^, chmiij^h aW iti Vrtimutuu i «»| / dw /#«««/• 
/ tiMi /^Vf/, / y^it// A^ /ihWi //mit iff#7 /ttivi/^ &i . ; thr ohjtVt 
is plAcrd Ivfoir the vcih. aiuI i« in the numuuiivr \t<\r^ a\\\\ 
thr A^cm |«)lto\vii thr v«lh. nn<t in in tho nhjoMivr rnfr, m** 
com^Muicd wiih a prcjMtltuou ; as / ^m hvtti \hm* llcir 
thr pi^^noun h'm \^ the n|;rnt, ai he |)cttoini« iho ACtioiH vi/,. 
1nv4| aiuI i« pUcril iu the ohjoMivc caIc) aiuI ihr priUmnl 
pinnonn / i« the nhjci^, Ami i* pUvcil liiU« aiu! I« hi tlic 
nouunAtivr cilW 

The nmtn vrth i» t'oiiurvi ihtougli aH Iin YAUdiion> like 
thr AO\(vrvrih; Init Ai h tloch mil cxpirU any AOlion nr 
|m(litmi but only a \\a\c w conMwow o( hcuiK, lU oinlnpirntW, 
«Viii hn^T no ohjrii to Ik* aOW(1 upon : ii ihrirtoic hAk only 
AO -^Ktoi, An«l ih;0 AlM'Ayn ni thr noiuiiutivc kaU \ a«| / ttm^ 
I jf.ff^y Ihit in foior InANnirN ihc nrntri vcih Imi a pAitlvo 
Ixirm \ \\\\t u in lontr vrih« which h|;infv a loit ol uiotion, 
or «'hAni;r ^t plAvc or civiulitiim : a^ / .f«« *iftii% i iimj /!«//<•«« 
/ tftxw »/*vf', /tisti ^'••^fi Tliclc* vcihii |NiitAkr ItiiiicwhAl ul 
the lUttUT ot' (1)0 ivAlllx'T vrih| iho\i|;h they havr (lill thr 
i^cAUci It^niticAtiun. The Auxili.ny <frf| ii>*i4| (lciinc» lUc 
iiii'iC «»l Ihr vnh. 

Thr two piiniM|Htl A\i\ihA»iri liAvr AlrcAily hrrn ilrilincil 
ihu>ti|{h aII thnr VAiiationik. Thci AUHiliAiy t$ l\ivr^ thtoviKli 
il^ Irvcul vAtialioni^i i« plAtril only hc(oi« thr pntcOl pAiti- 



«a m BII9USH CUUMHAJU 

dpie i i0 ii'n mVo pUced bdbre tLe prefent and pcrfed par 
ticipie. The other tiuiliviet are placed before the rerb^ o 
anoiber anxiliarj hi ita ongwal form. 

The natvre of the other auziliariea IbooU be jvft fnenCMHicd 
ih, p8ft titne M, e^reflea the aAioo, or the time of it, witJ 
yecofiar fefcc* It iamiiehiifedhiiiiterroptiTeandoeg^h?i 
fisteaoea. It aUb fapplies the place of a ferb, and render 
Ihe repetition of it unoeteflary : at, ^ fQ and Jf tfaoa like 
wife." I^cxpreflca permifion, but its chief iife is io fbrmifl| 
the imperaiiff mode* which it dotty 

ra fuperior, ^ ^petition* 
when to< an eqpal, r'7 1 P^^'^^^* 

Laa ioierior, J Lcommand* 

The f^fbility of peribrmtng an aftioo depends upon th 
power of the agent; and is exprefled. 

The Ithrif of performing an a^ioo depends upon a free 
dom from all hindraoces ; and is ezprefiedf 

When the agent ezprefles the refilutimi cfhis 0wm 'wiU^ U 
perform an aAion ; it is ezpreiled^ 

The necifiiy of performing an adion from fome §xterM 
Migmii$n^ whether it be umtursiox m^ral^ and what we cal 
ikiy ; is ezprtfled, 

« {S2SU } *^ ** ^^^ &. Z&& 

Some of the auxiliaries vary their import according to th 
perfon with which they are joined; thus nmili^ in the firf! per 
ion, both fingular and plural, promifes or threatens ; in th< 
ftcond and third perfons only foretels : /bsli^ on the contrary 
in the flrft only foretels ; in the fecond or third, promifes 
comroandsi or threatens. But this rule regards explicatiT 

■ • 

f fentcncc 



or KNOUIII OMMMAIi* t t 

ltHM«iw:«i wly I IW III muru)|;nuvi> tciucnsH*! i;chcun)' th« 

J^U y^nitfi^ ywxjh^ll m\W\ thrlr |>iiiiuiir. conuunnilt tir 
lhrtiit«n ) but, 1 JM wncr. we Ji^t wuiCi Uiry ^''tf wiiiPb 
y« 4wV/ wik«| ck|)i«U «vru( uiil>t Miul liu»|iiy l»trvi«l. The 
verb /• tiHM U ^uiu a vlitlVixut wtuxl litMU ihr nuKilUiy «««^» 
and it lurQHri u^uUily i ^%% 1 •o^^tf^ i)»(^u ^m/^i tw ^k^ 

Tha auiiilUrkii 4«*»/i/t ./k*»/iA ii»#ir/i/. «w.»y. m/^/*/. nrr utol 
in foimiut ihr UibjuiuMivv iuihIv. Thv aiwiilMiy v^^ bMM 

Whrn two i»r ninri? vri l>« lu <iuxilUi i«»| oi' butlt, irg ji>iiHi4 
tugcthrii ihf Mril (Mily ui iImiu u vttiMil Mvoulii^ l«» {wrtoiit 
Humbert timri and niuil«, 

VfRun wc |irecml ta inc^ulM' vciK it nwo' b« nm^cAki^ 
111 iiAY d tVw wm%U conccininKi wIimi Aiti c«il)vi)| b) uuiiuiii* 
rUhi» (HvntrMA«d vc)b«. 

Vri btt which «iul iii */i, »A /i a\ ik /^. b« loi iiilun ih<» |)<ift 
iim« m^tivci and th« |i(tiiu)plr pri trot 4m' |>tiilivr, ulivn chAtift 
lh« i/gr r</ (whivh mII kk^Iav vcitm rin) m» i>i iliotr lormi) 
iuuw ; tti*» /V/»6^7. 7^/J/i /ui*W, ^<. */i Z'.^a/*,*/, /»♦•/*# i 

Siiiu« vrilm ibcit «ntt in r^ IhtUJoa ilir i-oitcirtihon, ihAn|«« 

M(4t it»ntr4^tctl vrtttri luvo (hi* ^nliic* hi Will tX9 thr otm- 
(fdOtcvt ti^riUi Mint tlir rtiitir tt>iui N aUv^v^ Ii« b^ |MA*lmvd 
UuUr vt^iKM^Ioil I wbiib Uttn b only * <'i<ri\i|Mknit of dtr 
«9rb, ni\il <th riipr in ihr t\iUii o\ j^icunnui. tniuuhivnl iiU(% 
convrrfiitk^h for the (Av ^H a moir a^rccrilttr \o\\\u\, 'V\\\i ii 
thf rca(%m ot ihr i'(Min.u*tum ot tlic vc^rb I't ilu* iri^i^iul pcilun 
lin|*uUi\ which w»» Diif^utuUy written I*tvfM^^ tu>MrJt/^t 
Inic i» how i-omiVtcil uMo hi'^Jff^ iu^n^J/f, And (li.'> ih'U'ii 
|>«r(oi)« whuh W4II lonnrilv /^Hvr^, tutmHi'^ i> now in tnoft 
it>lM wnttvn /rfir^ #«rMf. 

Ik Mil- 



% 



n Of f,%mA%M OfiAHMAA* 



\%%%QMUh% Vk$m are n«iit to tie C4>iifidcicil. lnHlli«« 
fiil»r ¥€flH iN iddfAfiicc |>ift rlirm lAivc, luiil \\%t piitici))tf 
fmMti m |K«(nvr« wm form«4 lijr «<Mifig to rbc veib ///, oi 

V«Hh whi^ ¥#17 ffort) f hU rule «fe c«tli»4 irffK<rt4r vcrU. 

Tb« fiogli(h timgiiige bvtng eoinpoumM of fb« lAjiofi, 
•nI NomiMtf Fff mrhi ninft fu^4rAnly iwrrnke of tb« nature 
•f bmh^ W ttif form«ttoii of fill our verb* ii derived from 
ilm Sitfon* 

' AM our \ff9ffiUf verbi mv monofyllibl«f| <xre|jt tlie torn* 
pounded one* \ mA »r« gcnerelly tlie Uiiie verb* which /ire 
irrvgiiUf fn eht Sevon, 

There ere ihrve cUflIb of Irregtiliir verfN* The (Irfl cliff 
conAfti of thoie verbi whirh ere tiecome frregttler by ton- 
MAlofit end irither here the prefrnt v^nA peft rtme %f\\yt^ 
•lid fmnk\f^^ perfrAf or pf)(Bve« ell exe/tty elike ( or t\h 
very in ih«j ftn mHtion of the paft iim<?, end p^rtlrlpt^, Irg^n 
the prefiifif, by Afortt^nini; the dfphtlM/ng, or rtierigln{( the // kc 
ike end of the verb into /« The fccond ctifi of brr^nUr 
Wfbe Mt thofe th4t in ttie peft ttirie end p«ttirf|>le end hi j^ht^ 
end rbeitge the vowel or diphcboiij^ /)f th<: |»rricnt ti/nc Into 
su or #e# irrei^nlere ol th^' third rUfi form th<! f>aff thiie 
by chenging thr vowel m dipbihmig of tlw: prderit ) gnd 
furm tlic pertkiple, l^ edding tlie tcrrnnnetion #/r« with gtn<;* 
f^lly the chdHj^c of th<; vowel of diphtlionjK. 

Irregular yarlm of the Hrjl Clafi^ whhli have the 
Preji/nt, Pq/t Time^ and PartiftfjL aiih, 

.B^Mtf b«t*. lift*, reed, flied, fplle, 

tii^rH^ hit, light*, ii^ui^ ii\r€d^ (preed^ 

#et^ hiirr, pur, rid, flinr, thrutt, 

Ui\\, knit, <|aic% (eit ilit, w«t*. 

cui, kt, 

* The v$ih^i f*\4tVt<\ tnuo S tniAtifjiu/tif iM tiMM »UtrM44 mi» 
filiiie, hiiVf r)i« fC|t(iUi m writ 4« chf iMt-^uUi (uoh ii» ti(i(. 

'Ilw 



OF RNOLISII OIlAMMAir. S} 



The two lirfi have ui(o bedttn and hmrfitm in the participle; 
an<!l thus they fonietimet belong to the irrrguiari of the third 
daff . The verb li^bt is pronounced fliort in the paft time and 
paiticiple; at| I have lit the candle ; but the regular form ia 
prefcrable—iy^ifr/r^ The verb reaJ is alfo pronounced flioft 
in the pad tiroe and participle: at, I have rcd^ for rtati. 

The following vary in the form of the paft time and partK 
ciple from the prefent: lead, led ; fweat, fvrct*^; meet, met| 
bleed, Med; breed, bred; feed, fed ; fpeed, fped; bend, beot^f 
lend, lent; rend, rent; fend, fcnt ; fpend, fpcnt; build, buiic*| 
geld, gplt; g^d, gUt«; gird, girt ; lofe, loft. The following 
are formed by contraAion : have, had ; make, made ; Aee^ 
fled; flio^ fliod. And fome change the vowel alfo : ai, fell, 
fold ; tell^ told ; clothe, dad*; (land, ftood ; dare, durft. 

Irregular Verbs of the Second Clqfi* 

Bring, brought, 

buy, bought, 

catch, cnugnt. 

fight, fought, 

teach, tnught. 

think, thought, 

feck, fought , 

work, wrought. 

Irregular rcrh of the Third Claf. 

Prcrrnt Tim?. Pad Tiin". rjuticlpl^. 

^ changed intor. Fall, tell, l.il'in. 

is into 0. nwnkr, nwokc, (.iw.ikrj^, 

/forfakc, f(jribok, iorfiki.-iu 

a into 40. < (hake, ihook, ihakcn. 

Ctakc, took, Liken. 

^ci^ into rus draw, drew, ili:u\n. 

Ay into nc. flay. Hew,, ll.iiii. 

e into a or o. j»cr, j»at or Kof, j»ntfrn. 

iiclp, (helped), holpcfr. 

melt, (melted), nioltrrr. 

fwrll, (fwcllcd), Ivvollai. 

rear, ,Mte, cntrn. 

^a into a 01 o,< bear, bare or bore, ln)rne. 



Cbreuk, brukc or broke, broken. 



cleave, 



% 



^4 



Or ftVOLXSU OmAJtMAV. 



¥tticmt 1 ime. 

fpinV, 
firetrt 
tetr, 

(hear, 

(leal, 

tread. 



weive« 



inriDto#. 

#r iato aw» 

tlong into 
tfiiott« 



< ireeze, 
Licet he, 
fir, 

'bite. 



f lot)g ioto tf 



I long into u. 
i (hprt into n. 



I climb, 
f drive, 

ride, 

rife, 
J Ainc, 
• ^ (hrive, 

fmite, 

flride, 
• ilrivc, 

thrive, 
^ write, 

(Irike, 

bid, 



i ihort into »• 
if into tf^. 
9 into e. 
into I. 
§0 into tf. 



ibit, 

dig, 

lie, 

hold, 

do, 

choofe, 

{blow, 
crow, 
grow, 
know, 
throwi 
y into enju. fljr. 



P&ll Tunc. Ptrticiplc. 

clave or clove *^^ cloven or cMt 
Aiake or i^oke, fpoken* 
(Ware or f wore, (wonu 

tare or torci xmnu 
ware or wore^. worn, 

hove*, horea*. 

(liore, . Aerii* 

fiole, ftolen or nolo* 

trv6tf troddta* 

wove, wovea* 

crope*, crept*, 

firoze, hottn. 

(bd, hMau 

(aw, ieetii 

bit bilten. 

cbtd, chidden, 

hid, Mdden* 

(ltd, ilidden* 

ab«ck, mffrticitU, 

clomb, (ciimbea). 

drove, driren. 

rode, ridden, 

rofe, rifen. 

(hone*, ((hined)« 

(hrove, uriven. 

fniote, fmitten* 

llrode, ftridden. 

ft rove*, ilriven. 

throve, thriven* 

wrote, written, 

ft ruck, ftrucken or ftricken. 

bade, bidden, 

gave, grven. 

ht, fttten. 

fpat, fpitten. 

aog^, ^digged), 

lay, lien or lain, 

held, hoMen. 

did, done,/r#Mr <Ahr. 

chofe, choien. 

blew, blown, 

crew, (crowed), 

grew, grown, 

knew, * known, 

threw, thrown, 

ilewi flown. 

Tbe 



t 



or BKatim ohuiMAt. 



*$ 



The fellowiig vcrbt kwt the ptniciple wnm (oT\r\t\ with- 
out the termination m ; except two of thenii vit, drunitn 
And Uuwttfn; though thii was unduubtedly their original 
fonn. 



fliort into 

a or «• 



Piefrnt TSmt. 

ci»«» 
drinki 
5»ng, 

flirmki 

It 

fein, 
rpnng. 
fting, 
ftink* 
firings 
fwim, 
fwingi 
.wring, 



began, 

claog or cliMg^ 
drank, 
flung, 

rang or rang, 
flirank or (hrunk, 
lang or fung, 
)k 



fhrikiplc. 

begun, 
clung, 
drunk or drunkcA* 
flung, 
rung, 
flirunk* 
fun I 



fank or funk» 

Hang or flung, 

flunk, 

(pan or fpnn, 

iprang or fprung, 

Itung, 

flank or ftunk, 

ftrung, 

fwam or fwum, 

fwung^ 



funk. 



a uito »• 
## into #. 
f into*. 
into a, 
n into «• 
i into •• 



V.\vinil, 
hang, 
ftioot, 
flick, 
come, 
run, 
win. 



wrung, 

hoiina, 

found, 

ground, 

wound, 

hung*, 

fliot, 

flucic, 

came, 

ran, 

won. 



flung, 
flunk. 
" in. 

Eung. 
ng. 
flunk, 
flmng. 
fwum. 
fwung* 
wrung, 
bound or Doundcn. 
found. 
ground, 
wound, 
hnng*. 
flioC. 
flucic. 
conio. 
run. 
won. 



The following arc irregular in the participle otily ; and 

even then they do not change the vowel : 

IJide, (Indcd), 

rive, (rived), 

fluve, (fliuvcd), 

fliow, (fliowed), 

wreath, (wreathed), 

writhe, (writhed). 

The following alfo arc Irregular in the jmrticiple only, 
which they form in the fame manner : 
Vol. L P Bake, 



laden, 
riven, 
fliaven. 
fliown. 

wreathen. 
writhen. 



t6 OP XftOUIll ORAMMARt 

Bokfi httWi •w«i flic^i ftrew or ftrowi 

grave, itioW| fliipfi Aniw« wax. 

Thefo luive alfo th« regular m well as the irregular fomi \ 
and the regular form flinuld alway« be prafcrreil* 

Befidei the irreguUr verbii there are alfti others called dc- 
fefiive \*erbi { which are not only irregular in their forms, 
but al(b wanting in feme of their forms : fomc have no 
pad time, Ibrae no participle, and others neither* 

Moft oF the auxiliary verbs are of this clafs. 

Prtfent time. Paft Ttme. Purticlpte. 

Ami was, been, 

cani \ could, n^p^rtUpit, 

go, wenti gone, 

may, !nf^tgh^ Mt^rf/ifWr. 

QUoth, Quoth. n$fdrit\t^t. 

mall, inoula, n9p<trtutpk. 

weet, wti or wot, wot, «# /*ri7/. ///«•. 

will, WOtlld, •!# patiiapU, 

wis, wift| ir# p^riiaplu 

• The whole number of verbs in the Knglifli langtiage* 
regular and irregular, fimple and compounded, taiccn tngc* 
ther, amount to about 4300 j whereof 6ft)Mwo aiT irrex^ilars 
of the irilclari, eight irregulars of the fecond clafsi and 
107 irregulars of the third clafsi which, with the ten defec- 
tive vert)s, make 177: all the reft are regular verbs Mnd 
have the paft time a<^)ive, and participle perfect or ludTtve, 
formed alike, and ending in J or i^, as was l)elx>re oU- 
fcrved. Of the irregular verbs thei*e are not li> many as 
100, which have diilcrcnt forms for the paflb time ail^ive, atui 
the participle* This has given occalion to introduce a i^reat 
(Torrnption, by confounding the diftercnt forms of the pail 
ttme and participle with each other, in iritigular verbs • 
Thus, the participle is fometimes ufed for tlie pad time ; 
as, bt rwiTi for ^ mil ; be ^irf$nk^ for be dtytnkf bkii the \x\i\ 
lime is very frequently ufcd inllead of the participle; as, 

c I tvKf 



i(^ 



or ttVGitsfi GKAmfAm. dj 



I6cxvrii^, forliuftNrr^Unr; I litve ^, Ibr/rrnr ; I Itfvr 
^vf , for ^titiMm Tiiis error it frcqumriy fammitted bj our 
Udl WTicen^ and the Tiilgar traniatiea of the Old and New* 
Tcfaanent, which b the bet fandard of the Eng^ltrMMMr, 
isQoefirccfiromthisfiiall; Mliitliefvolteo ofediorMdBif 

ift/, fboKbiiKS for ^ijU^ t ndisc^ §m^Jdmi mikgm is 
t»ke nicd for Aigpims. Thit error it. bawcvcr, an cnomMNM 
iBkdfjs; and the m ipro |giety of it will appear bjcheabirfe 
of fooKTerbswhich have inc been fooorrBpced: a% Ihavt 
Jmt^ for I have ytffc ; IhaveiU^ for IhaveAar^ I hare 
v#«/« for I have ^mt; whkh arc ooi a whk nore woiffwak^ 
naocai Chan aof other verbs which have the pat tiihi^iBAnd 
of the participle, after the aiudfiary kmot. 

In the formatioo of the prcfoat partidpie, it is to be 
obCerved^ that if the verb end in a fngle coafeoatt, faUow^^ 
ing a fingle Towe!, and accented oo tho laft fyUafak^ if it 
confifis of more than one fvilable,- it doubles the Lift coiife- 
nant in forming the preient participle ; aUb in every odKT 
form of die fcrb in whidi a fjltable is adde41: as, rmt^tm/Hmgi 
rejret^ rtgrttthj^j regrtttetb^ re^retteJ. Veibs which etfi in e 
omit the r in the prefent participle: as, imcrtmfe^ rmcrem/mgi 
ail other verbs form the prefent participle by barely adcfing 
nrr to the verb in its original form : as, /srv, fmrmiag. 

The ADVERB, as its mme imports, is added to the verb^ 
and affo to the adjeflive, to cxprcfs fome mocfification, or 
other rircomftance of the adion expreflcd by die verb, or 
the cpulfty expreffKl by the adjedive : as, the time^ he reads 
fftfTAf; — diiiance, the countries lie wtJe i^^^rr;—' relation, 
they are ^if/ify united ;— quantity, an ejtcnJSmg h^ moun- 
sain ;-— quality, to live fi^hf ;— comparifoo, they are much 
^ki\ — doubt, f^ffibhj ferhmft\ — affirmation, jm, certmimfyi 
.— ocgarion, a» ;— dcmooiiration, nfiJimtfyi — interrogation, 
/^tfw, ve^Mi ; — maiucr, w.y//, /// ;^-order, rx^iW/f ;— place, 
iffre. A^-^r^;— motion, ,^!iw,^/W//. 

The adverb in Eogliib has no variation, except a few, 
which have xbe degrees of coroparitbo ; and in thefe the 

D a degrees 



t8 or iiwa tun <iiiAMlifAn> 

<lt|rtM of eompartfoti (houM tNi hmvti by thi wordi iMr# 
•ndffN^f as r(f^| mirtrii^i m^rigk\ aihI hoc by tbo 
ttrminAtloni «r aud o't Ul^<* idj«^iv«i i Mi fvjf^i rfjfhttr^ 
figiif^i though ihi btft writcn of tht ftv«ntc«nth ctntury 
hAw fn^ttcMly Jhlkn toto thii trrori 

Somi advcrbii whioh art derlv«(l tmnx irrtiuiir adjtdlvtit 
art ilib Irn^uinr in tbelr dogrM^ of com|Mrilbn i «• iho 
•dvtrb •iiW/ (which ii d<rlv«d from tho iiyt6livttfW;i aimI 
hn lff/#r and M io tho oom|MinitUo tmi foiierlAtivo dtgrtei* 

All ttdvorb ia fooietimf i Jolntd to snothor advarhi to «{y«» 
lUgr or ooferot in meanlof t M| #rr)r i((N«//| «^ir«'A m lirgo. 

niUOtlTIONS om pliMd bttwreti wt>rd«, to conntft 
thorn tOftthtTi and to Amw thoreUtitm h<?twctn th«m, 

Prapofitloni origiiiUy donoM tho itUtion of plocti but are 
BOW xiM to daoota o^r raiatiutui i us /«» w/#^ tkfugb^ 
J^9 ^fhrn^if^mn^ imitr^ /tfi «^ mw^ ^c. 0/ hai tha famo 
maaning wkh >Wm ip laarn ^f mc, that it, >Hw ma i >» 
igfiilat la tho placo or Aaad ol nnoUiar. All tho othera 
avidoiuly aonvay iha Uoa of placa^ according lo tha gtoeral 
ttwaobg of tha worda. 

Prapofitiont ara ibtiiattinpi ptacad bafora varbii and joined 
to Iham ib w to foim but ona v oitl i in which cnfe they 
4lwayi altar tho fanfa o( tha vet b t ai| f# /«a«^ lignltici a 
poftura-*la mtdtrJl^J^ intandi cowptrhanfion t alfo» ## jta» 
^ #M/^I la M^ i4 •virU^k* Somatiiiiai they foUow tha 
varbi and are not joiiiad to it ( wlian they no laiii alter tha 
meaning c»f the verb : ii> ngv^t^ f gtvt y i it <Vi ^ ^^ 

The (Mftpoiltlon a/i ii (bmetiiiiei converted into an ^ and 
that chiefly beft>ra tha preicnt pArtii^ipIo i ai| o nMUkii^^ m 
i^iH% Ikc* which ara evidently derived from the phrefes 
I wa« aa walking I wa« #e going i that iit employed ea that 
aftlon. AUoi twelve 4 ^locki ai it ii commonly pronounced^ 
but writteni twelve oVIocki wai otigiitallyi twelve a« tho 
ilocl. 

CON- 



OF BNOLISH OEAlllUR. ^9 

CONJUNCTIONS are ufed to conneft fcateoces toge- 
tbcr ; fb u from two or more fimple ientencet to fonn one, 
which is called a compouod feoteoce. 

What a fimple (cntence is has been ibewa in page la. A 
cooqwund feoceace is temed of two or more fuch fimple 
fenteaoes : as, ** John a$ul Tbomas love their book, but 
Edward it a dunce." This is a compound feotence, formed 
fay uoitiag the throe £oUowing fimple tetences together, by 
CheooDJuoAioostfWaiidfar; John loveshis book; Thomas 
loves his book ; Edward is a dunce. 

Copjuodioos are priocipalJy divided into copulative oon- 
juoAioBS^ and disjundive conjundioDS. They both ienre to 
conneA the fentence; but the disjundive coojuoAioa ex- 
pccflbs an oppofitioo in the fcn(iB» as h^ been ieen by the 
€oojuo£tion bitt* Alfo the coojunftions #r« tbatt^ exctfi^ 
wMlifs^ nUb^ugh (though), ^et^ nevertbiUfs^ &c. are disjunc- 
thrcs. 

INTERJECTIONS, though reckoned one of the parts of 
fpeech» are only a kind of natural ibunds, thrown into a 
fentence by the fpeaker, as the refult of his feeling and to 
exprcfs his ov^n affedions : as, O! nia-J &c« 

When the intcrjedion O is placed before a fubfbntive, it 
ihews that an addrefs is made to that particular perfon or 
thing of which the fiibftantivc is the name ; and the fubiha- 
tive is, in what in Latin is called, the vocative cafe. 



SECT. 






HvNTAx U th« light ordering iind fftmlnK of f^ordii in 
•rd«r m form fcntcncei widi gr«mmfttlcil propri«fyf A»»it 
ior cbtf pnriK^fet ^a/W/ #f # y^/y /# gtvirnf §r sgrtt ni4th esch 

When ft word govrrrtf ftooth^rf ff L'mife$ rhar pftrflmbr 
wordwbfrh Ugovmiff ro be In fmU k imnUiu^ui numUtrf 
getideri rafiff |»ci(<jni limt, or nunk, 

Wimn ft vi'oid ftgreei wifh anotiirM*, it l« in tliaf pnftkuhr 
ftoodrf nuinheo Cftfr^ fcCf whkli U uqniird Uy \Utt ivord that 
fOfcrnf if, Tbiiet ** Add (Ire ilmll iMinp; ioiih a Hon, and 
fboii fliftit iftit hi* n;ui)« Jdun ( lui h<; iUM iavt, lili penpf* 
Irom tb«ir flni/'-«M«u, i. ir. (n tliiN (eniciue //j^/ ti J 
pronoun of the rtdrd |>rrron, (ingubr, fc;M»iHiii<^ ^iMAfff ntnl 
Mgbt til ftgrM with iluf fubjcA fort|;oin|;, mnii^ly, (li£ Vh'mu 
t/lmy \--'JlmH Iffitfi^^ t lie fuiiir« tiioc of the a/Hvir vc/h //W//y 
(firftfrring (o ihtf liiDi; of (tic birth i/f tlic; child), rhcihiid 
fNTf fon, flnguUr numl>er, to ftgrfc* wirh the proit/;iin ^z/*, ;ind 
(mlkftCWft iiiodr* tt» It lim)ily di:':lartci ctir cvait ; fhih^ -4 

prc|N)r»tion added to tli« v<;it) hinp^^ and whiih iitfer^ lt» 
nmftidng ff oni /(r/^^, to krln^fnrlJi^ whit h fiz/Hfii'^ Xu l/t-4i oi 
piudMi'i; ; - /', thr indt'linite Mrlirlc ,— A^//, iiotiii hddlrfMiivr^ 
fin)^,ulftf' nuffilMr, niait nlinc gmdcr, nhfhxM*. caic (- •///r//, a 
rOffjiin^tiuM i'o|/ilUtlvry coiiiw-^,ting iIm; ^)llo^ingftfid hnr 
goifii'^ ii'iiU'iK'ftn i/y/'iher( — //>^iy, ihir pioMoun ol (li/- ImoimI 
|>frrl<in, (inguUr, iind Mgerttoi ihli {t,\\\t.\\i't, \^lhnli ,nII^ iIc 
|iHur« tiiitc id the unlive vrib /vi//| ^cuiful pciion, hn/^tilHt, 
l)chig govfiMrd Uy tliou^ indicMtlvft fiiof^e, b» it only h>M idci 
or dct'lMrcft ih<; naiiKj of ihft ihild, tnit %\t^% nor u;iiirii4iid m » 
--^/, ft iioilcrdivc |itoiioiin, rhird prtimi, ftngidur, inulMiltnr 
fpwdftf^ g'>Vi;rtMtft by the uoitu ^9H\'^Hamt% ft (uldl'infivi 

cunnuvft, 



cofamoD, aod tiic object of the leotcncc \~^JtJnH ^ fubftaotive 
proper, malitolnie gender, agrteirg wnb the noun &«, ani 
AooMUuiire caie; — /#r, a copulaiive conjun^ioo)— ^, a pro- 
no'JOy third per Con, fingular, ixioicuKne gender, noniinitivc 
caie, being a iubftitute kx the noun ^i/ri, and gDvemed \ff 
ir, and the agcnc of this ientence;'-:/M//Si9v, tbe future time 
4>f the adive verb (agreeing in time wiili tbe other verba in 
tbe ienience, «hkh are a^l fniure), tbird perfion, fingular, 
governed by tbe pcoooon ht^ indicative mode;— ifeu, a poie£- 
iive pronoan; — ftppU^ a piural noon, neuter gender, ok^ 
'}c£kvf€C9tci^~/r0Mt^ aprepofitioo, Ibewing tlierelatioo be- 
tween tbe nouns fe^ aod Ji^ 'i-^iheir, a poffci l Bv p fOiifr» 
^iaal Tfdjit&xwe^ and as fucb joined to tbe plur«il noon ^«i, 
objedive caie« 

Seht£vc£s are eitber finr.p!e or compounded* 
A fimple {ieatence hatb but one fabjed, or ageirt, and one 
vub in tbe indicative, icnperative, orfubjun^ive mode; and 
coniifis o( tbree parts, if the verb be adive; the agents tbe 
attribute, and tbe object ; as was ieen page la. 

A compound fcntencj confifh of two or more fimple fen- 
tcQces united together by the aid of conjtindioos, as hath 
been (hewn before ; or by relatives, as will he fern bereafier. 
As language and ilyle is only an aflem^hge of fentencet, 
too mucb jittc:.;ion can hardly be be (lowed upon their conftriK> 
tion. We will therefore take a view of the ru^es of £ngU(b 
Syntax, as tbey regaid the feveral pans of fpeech reipediveiy. 
The AaTicLE, as hath been ieen, if definite, 15 placed 
before both the lingular and pi urn 1 ooun c as, /^ man^ the 
mem : the indefinirc arri^Je a is placed before tbe Cingu'.ar 
noun orily : as, m manm 

The SucsTAMTivE governs both the pronoun and the 
verb : for i: rhc iv^c^v.t-riXwt, be plura), it requires both the 
pronoun a.iii vcr^ to Je plural alfo ; and if fingiiiar, they 
ji.uu alib lie r;ngk.:2r : r.s, '^ noch.ng has fo much expofed 
yntn of itarnin^ to f ">:rert:.~/ .ir.d ridicule, as iheir ignorance 
(A ihiiy; w!<.:h nre kiic^Wii to ail bxLl tbem/elvti*^ — ^Johnibns 

Ramb.er. 



\ 



$% or EMGU8H 09JiUUAM, * 

Rambler. Example of the iiugular : ** Semfa J^aks in tht 
natural and ^nuine language of a nan of hocxHirt wbai le 
Jeckrej, that were there no God to ice or puailb vice, 6e mmuld 
not oonunit it.*'— Guardian* 

There are fome nouns called nouns of nraJtitndc^ whkrh 
fignify many, and have the pronoun and verb agreeing with 
them, either in the Angular or plural number; but if they 
convey a plural idea,, the verb and pronoun fliould be plural 
Iikewife^ if they convey a fingular idea, the verb and prooono 
IKould be fingular i as, ** the ^Jptmkhf of the wicked hmvt en* 
doled ine."^»Pfalm xipi. i6. inftead of btuh encbfed mew 
«« My /«i^# it fooliib/'— Jer. iv. ta. inOcad ^mfi9mb. 

Two or more fingular nouns, joined by copulative con* 
jundions, have the verbs, nouns, and pronouns agreeing with 
them in the plural number i as, ** Shakefpeare and Milton 
%vtfrv the moft eminent /#f/i of the Englifh nadon/' 

Butfometims the verb follows in the fingular number, ind 
refers to each of the preceding nouns taken fepararely ; as, 
^^fmuiy and fmk^ and mafs tfim is eafier to bear than a 
man without underftanding.'* 

Nouns of number, weight, and meafure, are often ufed in 
the fingular fbim, when they are joined to ntfmeral adje^ives; 
though they denote plmality : as, ao hundred th^ufmnJI^ in* 
Aead of tbeu/ands ; an hundred fund weigl^t ; fix foot \ 
foriy/afbpm. 

Nouns, whether of the mafculine, femmine, or neuter 
gender, alwa3r8 govern the fame gender in the pronpun : as, 
«* I have a friend^ <uii^ becaufe bt knows his ow^ fidelity 
and pfefulnefs, is never willing to fink into a companion.*' 
«< I have a luz/i', whofe beauty firft feduced me, and wbofe 
wit confirmed htr conqueft." — ^Johnfon's R imbler. 

Every noun in the nominative cafe belongs to fome verb, 
either exprefled or underftootd, except tl^ cafe abfolute, as 
will be feen hereafter ; and M^htn an addreis is made to a 
perfon, called the vocative cafe. Tbus in the a^fwcr to diia 
queftion^ Who conquered tl^e Fcrfians \ — A^xMndtr: thi^^ 
is, Alexander conquered them, Everv 



Every AOini lb thi poitiA^e <iBXt has bfTHiftlAeTiiDii^'- he* 

Tbe Doun hae no ^i^isretit fomt ih &f»glift for tlrie" A* 
jcAm cale, 4lR>iigti cbis cafb be founded in nature and griih'- 
mar : at, *^ ic^ks tan ni^^er teach the ufe of hookt.** 

The FaoNOUK, being a fubftitutc for the noun, mtlll: 
C(Afeq(ientl]r have the fame nature, with regtfrd to tbc go- 
vernment a^d agreemeut "of houns and verbs. 

When two dr niokv fM'ononns of tfhe fingnlar mfhiber ffie 
joined no^htTj to make the pluralj^hmoun agree with them 
in peribo, the fecond perTon is pfeferitd bdkftt the third, tStki, 
the firft peribn before both : as, be and y^u did as you Mrere 
cottintaftded ; /, tbou^ and he loft i>ier chara^ers by it. 

The neuter pronoun it is ettipk>yed in a threefold Cenik : 
— firft, it e9q>re4fiss the ruhje6t of any difoourfe : as, // 4o 
happened ; who i» «# f — fecoodly, the ftate of any perfon or 
thing : ^s, how is // with you ?— thirdly, the thing that is the 
caufe of any ev^nt.: at, // was I that did it ; rr is thefe that 
corrupt the mind. 

Pa OKOMINAL Adjectives have feme fHb(lanti\rk; belong- 
ing to tliem, either expreiTeJ or uuderftood. 

The definitives this^ that, in the plural thefe^ thoft^ mud 
always agree with their iubflantive in number : thus, ^* ^s 
thit meant thou fhalt have no portion on this fide the river." 
Ezra, ir, i6. ** i have not wept this fony years.' It iliould 
be tif^t means ; tife/^ forty years. Again, •' Th/y arc theft 
kMof gods which Horacij mentions in his allegorical vd*- 
fel." — Addiibn's Dialogues, ii. on Medals. Here it Iboiild 
be thefi kintity or this kind. 

The relatives ««^, nMchy that^ have no variation of gen- 
der, and therefore muil agree ^ith their antecedent in this 
refpeiL^. For every relative muft have a noun or pronoun, to 
which it refers,, either expre^ed or undci^ood $ which is 
therefore called its antecedent: as, *' Who deals my purft, 
fteals trafli ."••^SbldLefpte^e. That js, th» man nvho Iksola t»y 
p!irfc, Heals trafti. 

Vol. I. E /^^ 



<; 



34 OF Birniill OSAMMiMI* 

MTtf it applied to perfoot only* and n ciclicr maiSnilifM or 
fcminioe ; nvJUJ!/ it now applied to chiogt only, and irrational 
itiiinali ; ibat it ufed both for perfont and tlung^ but it 
iM>uld be roofiocd to the latter, particularly in the fioiemn 
flyie ; 'w^Mi flandi for both the relative and the antecedent : 
ai, thii ii tAf/jai was fpokeii of before ; that is, the ihiitg nttbUL 
wai fpoken of before. 

The relative ii tlie nominative cafe of the verb, when so 
other nominative comes between it and the verb) but if 
wiother nominative comet between ic and the verb, the rela- 
tive it governed according to (he icnie lA the icntetice : fls* 
* '* the God ivU sMcle me, *wh§/e I amy and wb§m I ought to 
iiervu*' in the different mcmbcrt of this fentcnce, the rela- 
tive is ufed in a different fenfe ; in the fiift member it fiaads 
for the nominative cafe of the verb, having do other nomi- 
native cafe between it and the verb \ in the fecond menbcr 
it flandt for the pofTcffive cafe i in the third member it repre* 
fents the object. 

Every relative is of the fime perfon with the antecedent to 
which it refers, and the verb miifl therefore agree with it: as, 
'^ I thai (who) ipeak unto ttice am htm' John, iv.ae. " Vhou 
that (whrO (Iwellcft tietwecn the Clici iihims." Ffalm Ixxx. i. 

The relative is of>cn omitted, and nnderftood, without 
bring cxpreflcd : at, ** the God I ferve ; ' that ii, the God 
Ti'^w 1 ierve. The relative ftionld fcldom be omitted even in 
the fsmiliar ilylr, and never in tlic ferioiis and folcmn Aylei. 

The proper ufe of the relative confiftt in the property of 
pr^'fenting the antecedent to the mind of the hearer or reader, 
: without any amtiiguity. 

The diftribiitivc pronominal adje^ivet «/-?•, tvtry^ either^ 

alwnyt agree with the nouns, pronounsi and verbs in the fin- 

. ^iar number oulv : at, *' The Ung of I frael, and Jehof^phat 

'.rSe king of Jndah, yir/ iach <king) on hit throne, having 

« ;boih) put on ;hcir r>bes/"— i Kingt* xxii. lo. " Evtry we 

tmgk to chcrifh and encourage in himfilf thi» modcfly and 

aiTtttaace Uavc Jiere niefltldncdtf'^^Speadtor, ' Each figni- 

' ! tie* 



OF ENMilSii QKAHMJ^*"* SS 



fin iptih ttken diftiadi/ m'^tfrnrntHy, ti^ktr 
psf , or tin nhrr^ Uken di^Oidncly. 

Tl« Ao jccTi rE« bariog no vviaiion of oaoibcr or geo* 
icr, mnfi ap«e with iti fubjhnpyt* 

Tbc adjcAire it alwairs pbecd munrdiafieW before the 
zwuD : aiy a ;##^ mmt, eaucpC io the foUoviog iaftaorcs : 
iirft, when idmetfavig depends upon the adje^ve : at| **feed 
:jit « itb f9§J cmrnvftuami Ui me.*' Here the relative and the 
Tcrb are uoderSood : 'c\, foud thmt is conrciiient.— Secoadij*, 
when the akdje^tive k crmphatical: as* Gcorige \ht Third % 
'?t. j^tai the D/«rar.— -ThifdSr, when the Tcib f# fr, or any 
kuxilian' beluigiug to it, ii pJaced between the adMtire and 
the x^oun : as, *' How btawtiful mrt the tabemaLles of the 
Lctfd of Hofts V* h^fy fiai: he be^— Foonhif, when two or 
mgre adicSlTcs belung to the lame noon : at, *^ a general 

The arude Ii placed nxiiUj hefacc the adje&ive, except 
the adjedit'Cf ^ jmth^ aandmtmp: as, mil t^ji vaeai fmcl* a 
iTOD ; mmn^ a man. Or when an adjeSire is joined to the 
adverbs /r, as, U^v .- as, not /& ^rgt a conccrL' ; aj -ccJ a 
zsiftL i cVii fiMf M fight IS ttiis. 

ETC17 adjfiitivc has iuoie 62fa2antiv«; belonging to it, eithti 
expre€«d or nudeiflood : as, " the /«ur/w,' for the twdre 

^ometimei the adje&ive is ufcd as a fubAaniiTe, and has 
Ui ad^^ettve jutned to il : as, sU irtMjrfi nilf the dufg^^d. 
A: other times the fubflantire becomes an a^K^Jvc, and has 
• (diftantiTe added \q u, and linked to il bjr a mark of coo- 
j un&oo ; as, mMimal'f9md. mlk'di^tm 

TikC Veii, or attribu'.c of a Icnteticc, aluap agr>ces with 
tji^ sgtnt or Dooiinativt ca^c- 

For e^'trjr vrrb, ez'^pt tht paractplc or t::e in£:jiliTt n)od(^, 
hath a noajixi;;!iTe tait b^!on^r;g u» it, tiiiitr ixprtfTtcl or 
crder&ur^ : s!, •• a-v.^if. a-/ r, or ^< fyr rrcr frtiifn ; ' tbit 
il , arj^air ^ r, an/e j *•, 4c : . A 'i'.' w hr": U.'. "k • ; h ■* v '.'. i v•^ , ; ; 
hktL, ruorcovtr, ?:* ^l;cc';v' \J^ -. ^.j. •■ r;'.r; rtbci' rr.cn," 



^6 n^ v<v(^f«(if rtiii«i»rv\i». 

I . J — ■— i^— 



wlirn tlir .i,;rMr i-f nhjct'^ i« Pttpr^^il I'v :i |irr>noun, in which 
f.ifr fhrv Jif ofr#n rrvfrfrtf In f 1ii!lri»rHrr : M, •* ff^hm vc 

iffiir.i.if.ilv •;••/»• '''■.■^, '■•'/; ,fffi,nrr I iwtfi Vf»n, ■ - Sf rftfiHW, when 
tltf rrili 15 nnifi, tlir inMrtiliMlivr p.ilr tvfnrnrtimrf ]il:icrcl 
a»ifr ir ? a*, •• pri*i»«ffily fntf rrl rhr tt-vrfx" — Thinlly, when 
ilif Jiilvff^ r'.-'r i: roTitif^tur! wiih thr TiriUrf vrrli : ni, 
* /Afr \tj* .1 *• f»; ifi f!ir IhntI nf T -x.*' Jnli, i. i. 1\iunh1)% 
v,!uMi rhf ri-liMrr* :irr tifrd, thniifh ij flic objcfti\c rifr, 
tNrv :iir nT'.v.iVi. pbrnl Ufntr thf verb, M lire alf'V thrir 
iciO\oMnH», ri'^ri^vr, *i«/.ifAM'^r, RfC. n«, •• •rrV'"/d/':vr Volt 
./.M', ;•• •« ill" ?•. li'- 'f«-'vw •■•Ml /'vt.' -fjftMjr, when n irii- 
rriifr ii intriirt;;MMvi', or whi n ,i f|iirfti'in li alked, the nomi* 
iiMiKr Mlfhvv \}\r pi1iirlj)M vrrb, nr the tfiixiliary : ns, /^tv^ 
f^rf frifi ? Ill /Vi/f ^/'"M !ovr mv } Sixthly, ivhcii x\\^ irti|»tirt- 
rivc iiKuIr ih iinp!«>yf«l, (»r win ii any thing itrrnnniiimk'ctor 
:rcjnrftfi> r.» iir rfrtiir, fll^ nniiiinnrhe r.ifo fdhws the veiU 
I'f .iiixUl.^ry . jv, ro'fir //•/?/ Iirrr, ni «/» tl'^m cninf hric ; or 
ih'» :in>ili iry /i/ uiiji tlift C5ilirr0livr(!ifr r. oM: a»i /rf w j»"; 
'. • ;. I !»•• j-niM*. "xTiuhlv, w hm thc ronjiin<*!ioiiii »»' or 
"/•','/' .IK niiiiiri-.l, (III- iiiiriiiirilivr » :tfr fiMurtinrft fnllmvi 
•lit- :i If V iM.lt V iM' flif vrrh, Mful fhr Vfiii i« Jii fhf itlhjun^livr. 
.....'If- ;r/ •♦ Z-.;./ /■(. f!f,nc !!)!■ h" Im'I brrfi ii>thi:*' "A^.r 

The* iiiifLf ^'••^H v^pirflin;* n»> a«Minii, but only i ft.'ifr m 
^rM:.!n.ii;i ("if Urinr; u iVynfVfjiirntly «Ait h.ivf nn ohjrftnc v\\n 
r I'utiitU' f^i' nhi«*«'l nfrtn i«*>l«»M. Whrnorr .t nnnn ff»no\v«i 
. iir itri ^•.•il\ It t'ltliri rxfiirflr!. thr l.iinr iilrn wifh the vcil>, 
M J.»nu » iirniiiH iriif nl thc vib ; » pifpfifition lirini^ nn- 
^'-illnO'! : n', fi' /.' /-f a ifhct \ tp r/tfr it mik\ th.it if, fhr \\rA\ r 
• t .1 inilf . 

WInsi thr •>;Niioiin fciMow. tl»c nnitrr verb to hr^ if IhnuM 
.jlu'.iyr. W in Uic rMiiunnllvr i-.ifr ; \\^^ if tim' ^; it '.ivrr /-r. 
I'Ar'jit i!ir vcth In- in thc tnlinitivr mode: ;is it wai tli'»nj;ht 
'r. .V Ai-;. ThtJ'-, ** //V-rw fny yr tiial I nw.**- Miitt. xiv. Is 
.iMpioprr ; ir onijlit to hr, iri'/w fiy yC| fcc. 
Whrn a vfih itiiintcjiarrly f(»l|n-.v8 jiiiothri vcih, t'^r l.»ll 

vc»l' 






▼cvbil]oal4beiadie infakireiiiode: as» boyt Ivvrct ^l«|p .* 

but the following verbs admit of other verbs fbllowing tbem 
UEJiiiatIt bciipg in die iiiCnithe mode : M^ Jmn^ mee^ witJte, 
fti^Mmy fitly and all the aaxilianes, except ht and kmve^ 
whkh have dready been fpoken of. 

The iofiaitive mode bat the nature of a fubftantive, ex- 
prcCng the a^ion itfelf in tiie abfiraA, withont regard to 
svj^. pafpn at an agent. Thus the infinitive is employed as a 
fubftan^ve in the nominative cafe ; as, to uacb is a mailer's 
duty ; and in the objedivc cafe : as, mankind love /» lemm* 

The prepo&tion fir^ placed before the infinitive mode, is 
DOW becomci obfolete. 

The prttdple has the natmv of an adjedive, as the infi- 
pitrve- mode has that of a iiibfiantive; and the participle ts 
fometimes joined to a fubftantive, like an adjedive, merely 
t^ d4|K}te iti quality ; and admits of the degrees of compa- 
rifon: as, aitantdmrnif' m m^riUarutdmam^ a nufihMmd 
wiau : and the prefcnt participle is varied in the faice man* 
per : as, a loving fyther^ a more loving father y a mofi Jfiving 
father. 

When the participle has an article before it, and the prc- 
pofitioB ef after it, it then hat the nature of a lubftantive, 
fcxpreffing tl^ a6Uoo itielf which the verb (ignifies : as, *' by 
tbefreacbing #^n^cntancc,* and not by preiching of repent- 
ance, as is ermoeonfly written in the Colled for St. John the 
Baptifl. For when the participle has the article before it^ 
the prepodtion ihould always follow it ; and when the pre- 
pofition follows it, the article (hould precede it. But the 
participle may have a prepofition before it : which anfwers to 
what is in Latin called the gerund : as, *•*• Juflice confids in 
fmnlfbing the guilty ; and in protcSling the innocent.'* 

The cafe abfolute is, when a fentcnce is formed without n 
finite verb, by the aid of the participle, or infinitive mode. 
This cafe is in Englilli always the nomina*^ive ; and the 
adverbs of time, 'wben^ 'lubile, after^ &r. which Ili^uld other- 
wife be inferted, are omitted : as, ♦* the doors being fhut, 

Jcfus 



3^ or hUGhinH oaammar. 

JdiM itood in the midft ;** inftewi of, <4iAm the doort \»tn 

The iafinithre mod« ii often made abfohtCey when tc (np^ 
pKet iLe place of the conjunAion Mtff with the fubjtNittve 
mode : 33, ** /« %/>f with the ftrik;" ** toc§n£ltuti:**(tiax\%^tb^ 
J mmy kfgim with the firft ; thst I mtty contluAr, 

The {Mttjciple r. ntfo made fli>Mute in the fame manaer 
M Che itifiimWe mode : as, ** thii, ftrW.t!)r /ptmking^ tt fbe 
icnie:" that i«, thii, iflmnifffeak ftri^tyi it the fenfe* 

AoiTEtat have no goirernmeni. Thejr ihould always be 
placed aa nrarai pofitbic xn the word which tbry modify* 

Their place ii ^lerally before adjedtivei, after aAive and 
AcMer rcrhi, and fometknet betwoen ibe amutiarf ami the 
verb; at^ *^ He was a ^try wife piince ; he governed mildfy ; 
and wai mmtntrmUy beloved by bk fubjeftf •'* • ' 

Wken two negativea occur to ont fentencCf tbey deflroj 
one MNitheft aiul are eqvat to an affinsntive : ai, 

iVw <1M they mt prfccfifr (hr cril p1tc:ht 

In which ch<:y wcrt, or ibc (hurp pft^f iwf fcef, 

MitToWjP. L. i. 3^r. 

There is no adverb fo ll;iUe Xf^ be m»fplaced as tbe adverb 
#/riy ,- moA of oivr claflit al writers have erred in placing tbia 
adverb at t'M) f^rctit di (lance froni rlie word which it modifies: 
tljtv.,. it is coiiiiiioiily faid, ** tbey mif fpught smp# k§wri* 
ivh<;Kas it ihouli) be, they fought ^mly oiic iKiur, 

F>'£V(>';rriu*<s linrc a governiiicot of cafe, and in Englifli 
tliey alW'-yi rrcy.iiic \\\t: oojcAivc cafe after cliem; as» 'mib 
h$r^from mcf to Lim^ hy ut^ Uc, 

V/brii the prepcifitioii goverov » relative, it fbonld be 
pUrrrj before the relative; as, '* this \^ lie tf mi}h§m it ia 
'<rrittcn;'* the ngli fome writers have placet the prepoiitioa 
St the rod of the frnfeoce, and feparate from the relative^ 
which is a!way:» ungraceful, and can hardly be reconciled to 
the rnles of grammar : at, ^' Horace is an author ovAmi I am 
r.ut;li ^.IcIiglitc'J w;/^*' 

M^ny 



OPEliOU«H a&AMMAB. 39 

■1— g^WWeesggggggB-s :: 



Maoy of our bc^ Hriten have oomautted erran in tije ufie 
of the prcpofition, {oaae omittsog it entirely «rhea it OmuJA 
be ufedi other* ofing one prepoiition for another: ^mim 
for ifl| 49, or muu ; far for §f% §fiox M| hx^ at may be &efi 
by an atteotive peniial of the ciaf&cal wricera iu the EficliA 
tongue. 

The noun moilly requires after k the iame prcpofi^oo as 
the verb from which it is fornied would do ; as, '* the wileft 
princes need not think it any diminutioo t4 (of) their gixat- 
nets, or derogatioo u (from) their fufficiency, to rely upoa 
coun&L''— -BacoRi Eflay ao. Here the nouns Jimimaim and 
JtrtgatlpMy being formed ftom the verbs dimiuifi and Jer^^u^ 
require the prepofitions ofzvAfrom. 

The prepofitions i# and far are often nnderfiood, without 
being exprefled^ before the objedive cafe of the pronoun : 
ast get JM a pbce; pay blm the money you omt thim ; that 
is, get far me a phce ; pay /# him the money you owe /# 
them." This is a xelic of the Saxon : iu wliich language, 
thofe pronouns which are in the objet^ive cafe in Engli(b, 
are in the dative cafe ; and coufequently have tlie prtpofttioo« 
/0 and far uuderfiood. Im or pn is aifo often oniitred btfor^ 
nouns expreiling time : as, lafi week ; next year ; to-iuorpjw : 
that is, tM laft week ; m next year ; en to-niurrow. 

The prepofition fubjoined to the adverbs ^^, t/jerr, 
when f as, lerewiA or btrtof^ therefan^ theren/jith^ mjtjtrtvyitb^ 
*wberiupon^ Uc. have the conflrudlion or nature of a pron(;uu ; 
but they are now almoll obiblete, except in the very foicnu: 
llyle only. 

Conjunctions have only a gwcmnwnt of mode. Some 
itquire the indicative, others the fubjwnftive niode. 

The following govern the fubjunAive : firft, hypotLetiui' 
conj\inAions : a% *' ^thou be the Son of QiA.'* Matt« ivr. 3. 
—Secondly, conditional conjun6tiofi«;: as, *' thou^b h^Jlajxu*:^ 
yet will 1 put my truft in him." Job, xiii. — ^Thirdly, r^iftribu- 
tivc conjunctions \ " 'ujhethcr It wen J, dr (whether it were, 
they, fc wc preach." xCor. xv. xi. — Fourthly, conccflivc 

cor.jUH'ftionst 



40 OP KMOUSH OKAMMAR. 

conjunAioni ; ^ UmU/i he mmjt his flefti.'* Le? . xfi* 6.— 
FiMily, excepchre conjiinftiont t '* no power excfpt it nvere 
gpnn from above/* — Sixthly, the conjun^ioni t(^ ind f^/, 
fblkming a verb in the imperative mode : as, *' kt htm that 
fiaodeth taiic heed iffi he /#//." i Cor. x. 1 1. •* Take heed 
/Art/ thow/j^ak not to Jncob." Gen. xxxi. 24. 

Here it muft be noted, that all the foregoing eoninnAiona 
tnajT be ufcd, and often arc, with the indicative mode ; vrhen 
the circumftancc cxprefTed it of a more abfolute and certain 
nature. It is the cHTumftance being of a doubtful nature^ 
or exprefled under a condition, orfuppofition, or in the fr>rni 
of a wifliy that determines the verb to be iu the fubjuo^live 
mode. 

Other conjunctions of 1 more politive nature govern the 
indicative mode. 

There nre fome con jnnAions which have other conjunc- 
tions bclonguig to them, and nnfwering to them : as, mUh^^^j 
(though), jirr, ntvcrihtlffs \ Vihtbtr — w ; neither Or nor — ndr\ 
eltfjtr — or ; at— as ; as--fo\ fo-^as. -/^j— rtj 'exprefi a com- 
panion of equality ; ai good .t; anotlirr, that is, equal iti 
fornc or every quality; as— Jo cxprcfa a romparifon foinctimcs 
of equality ; •* as he is,yt> fliull we be ;" fomctimcs a conipa- 
rifon of quality ; •* as the onedicth,yi dicth the other /'that 
is, in like manner; Jo — as cxprcfs both quality and quantity: 
as, *• Pope was not Jo fublimc a poet as Milton, nor ^ great 
a man as Johnl'on ;'* neither^ nor^ and nct^ nor^ exprefs a 
double negative, as in the foregoing example ; either-^or^ a 
double diilributivc, as, either choolc yc tinsc;;* that. 

In comparative fohtcnces, or when ditferent qualities are 
compared, the talc of the latter noun or pronoun is governed 
by the veib or prepolltion, which arc iomotimes not ex- 
preffcd : as, thou art a greater man than he \ that ia, than he 
u ; you flicvv him more favour than me ; that ia, than (you 
jhtKK*) m^." Thus, by fupplying that part of the Icntencc 
that is unc!cr{t6od| the cafe of the latter noun or pronoun will 
fcc under ftood. ^ 

•* ' LVTER- 



OV BKOLISn ORAMMAH. 4C 



IvTft&jKCTiovt in Engliihhivc no goverDment. nor any 
putic\Uar pltcc in i feotenoe ; they ire ufied only to exprtft 
the fpoaker^i aft&ioo} but when they tre nM too frequently, 
thc)rrtthprex|ioff hit •i&Aation. 

Thefe are the rulei of Englifii fyntax, in the cooftniftion 
ot* fentences. But there are alfo phrafcs. conlifting of two or 
moi-e words, employed in the foriimtion of fentencei ; of 
which the following art the mnft common : 

ift Phrafe : when a fubftantive ur pronoun is placed before 
averbadtive, paflive, or neuter: as, / love ;.ife it loved; 
tlcm art. 

sd Phrafe : when the fubftantive follows a verb neuter, ur 
pafHve ; or when the (ubAantive following the verb intends 
the faine thing as the fubftantive before the verb: as, I am 
lei Milton is efteemed i sisfic. 

3d Phrtfe : when the adje6Hve follows a verb neuter, or 
pafflvtt i»| llfeisjSWls txmsiit h ffinmtd moUkfbme. 

4th Phrafe I when the fubtantlve follows a verb aAive : 
as, to build m hcuft. 

jth Phrafe : when a verb follows attpthcr verb : as, tlty 
defire /# di€% 

6th Phrafe : when one thing is faid to belong to another : 
as, Milton's poems ; or the poems of Milton. 

7thPhnfe: when a fubftantive is added to another, to ex- 
plain It more folly: as, St. John the Baptift; King Cscorge ; 
Robert Brown, &c. Here the latter noun is faid to be in 
appofition to the former. 

Sth Phrafe ) when the adjef^ive or participle is pUccd be- 
fore the noun i aa, a ftut day ; a /pvmf friend. 

9th Phrafe t when the adjoAive is placed before a verb in 
the infinitive mode t at, iMtrtfy to live. 

toth Phrafe : when an adverb ii ufed whh an adjeAive, or 
a verb: as, he writes quick ; he is vtryjufi. 

X ith Phrafe : when a fubftnntive whh a prcpofition before 
it, is added to a verb or an ad}eAive : as, he ads wtb fru- 
^fnce ; good for nothing. 



41 OF SHQLISH aRAMMAl. 

wmmmfm^mmmmmmmmmBmmmmmammmmmmmmmm 
lath VhmUi when the qtftlity of a fubje^t ii com|Mre<l 
with tb«t of miotber fubjeft; the pofirive Adjeftive haviiig 
iiftfr it th6 conjunAioR 4/t the eorofNimive the coojuuc* 
tton t^au i the fuperUtive the prepofition #/; m, n% tall 4f 
yon ) tftller i/>«« he i tailed 0/ all. 



SECT. V. 



OF rnifOTI74TIOW. 



PvMCTVATiow ii the art of maUng the fevaral pointii 
Mrcd in feistetieeii to expvaft the da grtet of eotinexion be- 
tweeu ieotanoea and their partft and to expraiii the floni 
or pauiet, ai they are aspreftd in a juft and aoeurate pro- 
nuneiation. 

Notwithftanding the diCerent paufti in fentmeei, and de- 
gree* of connexion between them, admit of great variety, 
3ret we have but (bur pointa by which to exprefi them. 

Thu» we are often obJiged to eapreiii pautci of the famr 
quantity, on difterant oeeafionii l>y diflbrent pointp) but 
•more frequently to egpraii paiifei of dilTerent quaotitiea by 
f ne fame poiotit 

The dodrine of punAuation mud ibarafora be very im? 
perfeft I tw rulei ean be givep thac will bqld good in alt 
eafei ; but mueb mnft be left to the judgment of the wriiiFf 

Orammariam have followed the divilioa of the Bb^iori* 
cianf , who divide all the p^ulei in wrifiog or difcourie Intf 
the fiour following 1 

The PerkA umM thui • ( . ) 

The Coleot marked ibua • ( i ) 

The Semicolont markid tliuf . • ( 1 ) 
The Commai marked tbua * ( 1 ) 



0# iMttiili ttnAiiiiAil: 43 



The Pteriod nuurki t whole fentence, tidier Ample or con- 
Ifoundi' making t fiill an4 perreQ fenfei tad ndc cowiefted 
in conftruAion wiih tnoiher fentence. 

The Culoii marki^the gmiett divifion Of a ftnt«iioe» and 
it a member theroof 1 containing a perfeft fenfe» but not a 
perfeift lentence. 

The Semicolon it a left confiruAive part of a fentenco 
than the colon, and doel not form a perfeA fenfe, but holdt 
a middle place between the colon and the comma, being a 
greater jMufe thM the httefi and kA than the former. 

The Comma markt the lead oonftruftivt parts of a ftn* 
wott; or it markt a fimplOiiientence. 

The precife quantity of time required At each of thefe 
paaftfs or points is uncertain 1 at the time compofitiolk may 
be rehearfed in a longer or Ihorter time t but the propor^ 
quantity of time of the points is as follows i the pe- 
ls a paufe of double the quantity of time of the ooloni 
the colon h double of the frmicolon ; the ftcniooloo it 
double of the c6romt% 

In orJer to difcover the proper ufe of thefe pointSi we 
muft confider the nature of a fentenccy n» Jiviiled into ir« 
conftruAive parts, and the degrees of connexion between 
thefe parts I at alio the nature of an imperfeA phrafe* 

An imperfeA phrafe contains no airertion» or does nor • 
amount to a propofition or (enteucci at wai fccn in p^ij^t 41. 

A fimple fenteooei as was before hintetli confiftt of an 
sgeot» or fiibjeA, an attribute, and (if the verb be ai^ive or 
paffive) an objeft : or it confiftt of one agent or liibjrA, and 
ene finite verb; that is, a verb in the indicative, impemtlvei 
cefubjunAive mode; at, ** Ood nuide man ;'* here Oni is the 
sgent or fubjcA, as he performs the a6bion, viz. msdtAim: 
the verb mtJe it the attribute which always exprclTct the ac« 
tion ; and «r«a it the objcA upon which the a^ion is exer- 
cifed ; that it, the aOion of creation. 

But the fubje^, or agent, and the attribute, and the ob- 
. tft, nroy each of them be accompanied with fcveral cifcum- 

F * itaficft 



44 ^V BI^GUifi 0&i^MM4A. 

wBmmBSBtammtBBBSSSBam 



Aances or cbarj^riftict, adlod thertfbre ibeir adjuiifU; «b 
tlM motivet piacCf time, mtoiitri caufef and tb« like ; wid 
thefe may be conne£led cither hmnedialelyi or mediatdy* to 
the pafU of the ftntcnce co which thty btloog. 

J^ the fevera) adjttn^s are related to the parti of a (eat«nce 
in a different manner, they are tlien only fo many imperfbft 
pbraici, and tlie fentence ii finople* 

But if the feveral adjimAt beloog to the partt of a ftnieact 
io the fame manner, they then become ib many fimfilc hB^ 
tencei } and the fentcoce it theo compound. 

For a compound fentence confiftt of two or more (impie 
fcntcnccs conne^ed together ; or it hatb more than one fiib* 
jedy and one finite verb* 

Thus, if feveral fubjcAi beloog io the iam manotr to one 
verb, or feveral verbs belong in the fame oianner to one fub* 
je&, the fubjeds and verbi are to be accounted c<iual in mmb* 
ber I for every fubjed, except the cafe aUbhite, a&d the vo» 
cative cafe, mull have its verb ; and every finite verb its fub« 
je£t ; and generally has its pcunt of diftioAiotu 

LsVaitiples of the life of ihe Comma. 

*^ This fingie confidciation wiD- be fufficient to exCio* 
j^uifl) all envy in inferior natures/' In this fentence c9i^ 
Jtrmtlon U the fubjc^ or agent, extingui/h the attribute or 
vcrl), imvy the objc^ ; each of which is connoted tvith its 
adjiinds. The fubjed does not ineau any confideraiion iade* 
finitely, but a particular confideratioiii treated of in the ftb#* 
mcr part of the kflay (namely, tlie conlidcration of tlmppo* 
grcfn of a in I man ioul cowaids peilVdtioii in knowledge), and 
here (Icfnicd by the ;iJjun^^ thnfinglt ^i on ft deration }• The 
attriMkrc or verb is alio connected wiih its adjuuAs \ immc* 
<iiatcly with envy^ as thr objefl \A the action; and mediately 
by the intervention of the word tnvy with in/tiltr HtUnrts^ tbc 
lutijc(*t in which envy it extiiaguidicd ; the adverb yiit^iViil 
ii the a(lj;mi5t of the vcib, denoting i^s power* It it to be 
<)bfcrvcd, that saah of thefe adj,iknfts belong to the verb in a 
1 difcreiit 



or nOLIttI ORAMMlAII. 4S 

■■ ■ ,1 J s^ 

ditfilcftDtiDaniicr; 0wwy hticnp to \l mm Xht tik^t^ ^ mfiritr mm 
imm n the fsbjeft in which the objeft m extlnptUbtd, and 
JkJkiiHi aiCht power of the verb to prodaoe the efsA. The 
adjtfndi ere, therefere, only fo nmny ImperfcA phnfei ; and 
the fentence n fifti^, end admltf of no peinti to diAin|iiifl» 
it into partf • 

«' Methinks, thn fingle oonfiderationi of the progreA of • 
finite f|nrit to perft Alon, will be fufllciem to exthlpiifti all 
tntf in inferior natures, and all contempt In fiiperier.** 
Here two new fentcncet are introduced ; the one inferied in 
the n\idd\e of the fomncr fentence, and the other added to the 
end of it. The former of thenOf •fthipr9it$fi$fmfitiiHf^U 
iopirfiffhn^ ii conneded with the attribute in the fame manner 
ai the agenl| or thitfingU fnfiJkrtitiw^ for they both cxprefi 
«the liime idea ; and the verb may be joined .with either of 
•cbem, and the fentence have the lame fenfe t as, ** the pro- 
^rdaof a finite fpirit to perfr Aion, will be fuAcient to citin* 
guifli all envy in inferior natures.*' The latter fentence, 
ondM c0Hiimpi in fuperior^ is conneAed exactly in the fame 
manner with the attribute as the objefk in the iSrll fentence 
iS| though it does not convey the fame idea \ and may be made 
the obje^ of the fentence '\\\ the fame luanncr as the former 
fentence was made the agent ; as, *' Methinks this fingle con- 
fideration will be fuillcicnt to cxtinguifli all contempt in fu- 
pcrior. (beings) The fiiA of thefc newly inferted fentencea 
may therefore be confidercd as only another agent : and the 
latter as another objett to the verb, in tlie firft- mentioned 
fentence. They arc therefore fo many (imple fcntenccs, and 
ftiuuld each be diftinguiflied by a comma ^ and the whole is a 
compounded fentence. 

And again, ** A wife man will dcfire no more than what he 
may get juflly, ufe foberly, diflribute chceflfully, and live 
upon contentedly.*' In this fentence, the phrafes,^r//«//K, 
^fi/Qhtrl)'^ d\ftrihuU ihrer/uUy^ mnd live nfivfi ctntenttMy^ are 
each conneAcd with the fubjeO, he, in the fame manner^ 
and in cfleA^ form fo 4nany diftinft kntencci ; aS| ** a 

wife 



or KNUMlff ORAMMAfti 



.A., ^ma-aa^t,^^. a» 



wite mtn will defire no more than what Ae may gn ju/llff 
t wife nuin will drfire no more than what bi mny ^{ffjifhryi 
a wife man will dcfirc no more than what he mmy diJlrihuH 
tkur/nliy i a wife man will dcfirc no more than what be may 
tev mf^m C0menitjfy. They muft each of them, lberefore# 
be diftinguifhed by a comma. They are fo many fimplc 
fentemNMp and the whole ii a compound fentence* 

At feoCencei themfelvci are divided into fimpie and com* 
poindi 4b tbe members of fentcncei may be divided into 
fimpie and compound members t for whole fentcnces* 
whether fimpie or compound, may become members of 
•iber fentences^ by meuns of a connesuon* 

The following arc marked ly a Comma : 
F'irft, fimpie mciubci's of fentenceSi clofely conne^d toge- 
ther in one compound member or fentence : as in the fefe* 
going example : excepti flrA, when the members are fliort in 
compaittflvG fcntcncci : ai, in the former part of the laft ex* 
ample, *^ a wife mni\ will defire no more than what he may get 
jufily.'* Tlicfc arc, in fu£(, two fimpie fcntences fmpartd by 
the conjuiidtiun than \ bet| being fliort, they are not feparated 
by a comma. Secondly, when two fimpie members or fcn- 
tences nrc clufely conncAcd by a relative, and the fubjcA of 
the aotecrdctit is confined to a particular fenfe : as, '* the man 
who is poiTeiTed of this excellent frame of mind, is not only 
eafjr in hin thoughts, hut a peifcA mafier of til the povhers 
and faculties ot his foul.**— $|K:Antor. In this fentence, ibe 
man^ is coniiedtcd to the following fcntences by the relative 
nuh^i which retrains the idea gf the antecedent to ttiefenfc 
here mentioned. 

Sfcoudlyi the calc abfolutc : an, ** the doors being fliur, 
JeCiis IkxKl in the midll.'* 

Thirdly, nuttni In appofitionv when confiding of many 
^ms: as, '* Alexander, the great, cruel, and unjuft/* 

Fourthly, the vocative cafe, or when an addrefs is made to 
a pcrfon s as, *' Thi:. i^id, be foimed thee, Adams thee, O 
tt|tfi.**«4Ailtocif 

Fifthly, 



or fiKOUSH ORAWAR, ^J 

Fifthly^ when there are more tlun two nouoii or ^j«divcH 0\ 
conne&ed by copulatives or diijuoAives ; or when there art ^ 
only two, if the oonjunAioa be uodcrftood : as» *^ lUpcuiei« 
traoiportf, and ecftafiet are the rcwanU which they coo&r,s 
fight and tear^ prayen and broken hearts, are the offerioi^ 
which are paid to them/'-— Spectator. 

Siitblyi a circumftance of importance, though ooly an 
impcr&ft phrafe : as, ** the principle may be defcQive or 
fiMiky ; but the coofeqiiences it produces are fo good, tim^ 
for the benefit of mankind, it ought not to be extinguUbed.** 
^peAator, 

JLaftly, the participle with fomething depending on It: at, 

** Now monit htr rofy Hi pi In th' rsftrrn cUin« 
Ahmticit^t fow'd the fltrth with otient pctrl. mi trow. 

The SiMicoLov is uied whea a fentence, or member of 
1^ fentenpe, requires a greater paufe than a comma, yet neither 
forms a perfeA feofe, nor a perfect fentence ; but is followed 
by (pme other member, or fentence, with which it is clofelj 
.coonefied; as, 

*^ To look upon the foul as going from ftrength to ftrength, 
to confulcr that flie is to (hine for ever with new accclFions of 
glor/t and brighten to all eternity; that Ihe will be iUlt add- 
ing virtue to Virtue, and knowledge to knowledge ; carries 
In it fomething wonderfully agreeable to that ambition which 
is natural to the ipind of man.'*— Spet^ator. 

This compound fentence is divided into three principal 
parts by the fcmicolon; each part requires a greater pauie 
than a comma ; bat neither of thcin cxprciTes perfc<A fenA^ 
or forms a perfect fentence, being clolcly conncitted in fenfe 
with each other. 

The Colon is ufcd when a fentence, whether (imple or 
compouud, requires a greater paufc than a fcmicolon : it al- 
ways forms a perfect icnfc, and would by itfclf form a com* 
pkte fentence, but is followed by another member, or fens 
fence, making the fcnfe more full and complete : as, 

*«Wew 



l4 at 8M0if»N OUAIilMAl. 

** Wtf« ill beoki r«4(S«id (o thtir quintiifdncff mtfiy # 
tefky itithor wmttd mtlM kii ipfMiranf • in i penny pupir * 
ttMftf weuld ki feffrei my fvf b thing in iMtui e ti a feflo i rb^ 
worlri nf in ige wmild bi enntnitied on i few flieWii i nni i9 
mcntimi fflilll^fli of vnlumii^ tb«r wcmld bt utretly annihl- 
JiiUd.'*»«8p«/tif^9 N')* fi4f 

Tbii Ariir#ne« It dlvi<M inii) ttmr fnttn by fbo relon i tha 
<lr(l And lift ptrtf irt f4)mpdiift4 memb^rii dif i4«(i by (hr 
commit tbd firfund ind third Are fimpie memberi. 

Iieb 9l the fe pum ^ntAin« perff ft fenf«i And wcmid Alfo 
tttrm A cmnpUie font«n<;ir, if tb« atber pAri<» bid niM been 

J9in«dtAil« 

The €^1^0 li AJfo itfid wtiin a kmmlntt gtm befurr, tit\i\ 
A ffAMt pAiife ii req^iled > though tbt Antenui be not c^/m- 
jplAti I Alio wh«n A {p9$eh 0f An i«Ampl# in (ntrodtieAd. 

Tbf Fak inn if yftd when a finten^^ l« fo fir flniitied At 
f»nt tn bi r^nniAfd in eonftrnAinn with the fnllmvlng (iin- 
Itnee \ And mif ki bnth perfrA finfe^ And pirtd\ f«niAnet9 Atfy 

M MiDf r^nfiderrd in bit pr^unt flAte, ftttni <»nly t$nt into 
thi wnrUl tr* propAgflt^ hi§ liind. lie |/rn¥lde« bittiftlf with a 
AMe«4bri And bntnediAtely quiti bii poft to mAkt rnom foi 
Mm/'— 'SpeAAfnT* 

Thffii Afe two perfeA fenrfneeif divided ftwm eei'b otbei 
by the perindi And fMbdlrided into dmpli ftntene«i by the 
eomniAi The flift of tiiere two fenteneei repreftnti the ^^/eh. 
ffMi end of mAn*§ ntifflon into thli prefeni world ) nemety^ to 
pmpAgnte bit kind i the liMond fliewi the rtnl it0nfifii§nt0 ol 
bl# reddenee here \ begetting a AtseeHbr, end mAking room 
4bf him* They Are entirely diftinft ftntenr ei \ uneonnefted 
In eonftrn^ion with eeeh other, nnd wentlng nothing to mrtki) 
eeeh f%fh^ both in fenie end tentenee. 

ieilde the four foregoing pohttif yftd to expreft ttte peutre 
In dhl^oitrfei there ere three oiherif whWh eUb Aibft the mo- 
dvlAtion of the volee i nemelyi 
The Note of Int^rrogAt ioH| merked fhui - ( f ) 

The Note of AdmirAtloni or EnelAmAtioni nMrhed tb«ft ( t ) 
Thr PArenthcflK, merked thui - - ( ) 

I Tha 



01* I^MQUSII OKAMMAft. 49 

The NoTi or iNriRROGArtoN is nfcd when i qiieftioii 
is ulked ; nil ** Would tn infinitely wife Being make fuch glo- 
rious (TtfAmres for (o mean a pari>ofe f Can he deliglit in the 
produAion of fuch Abortive iiitclligences, fuch fliort-Uved 
rcnfonablc beings f Would lie give us talents that are not tu 
\yf exerted f Capacities that are never to be gratified f ** Spe£t, 
Thefc are all intemigattvc i'cntenceSi and as fuchi arc marked 
by the interrogation point. 

The Nora or AoMta ation» or Exclam/itioni is ufed 
to mark the fpcaker's admiratt()n» and any fudden paf- 
fion : asi 

«<Andlfet 
*T ii come» the glorious mem ! th« rccuod birth 
Or HcAvcn and earth !" thomion'i wiNrkM 

Borti thefe points mark an elevation of the voice. The 
length of time required by them as paufcs is uncertatUi and 
rmy be equal to that of a femieolon, coloni or a period. 

The Pa«knthisis is uftpd to enclofe a word or fentencc» 
inferted in attother lentence ( which b not neceflary to the 
fenfc, nor does it at all affcft the conftrudion : m», " Pompcy 
xn\ the other fide (ttiat hardly ever fpake in public without a 
bludi) had a wonderful fwcctnefs of nature." This point 
marks a moderate deprcffion uf the voiccy with a ]>aurc fonte 
what grtfatcr than a crmimn^ 

There arc alfo othrr marks uftti in writing, which, though 
tiicy do not affe^!^ the voice as pnufcs, yet arc ot'tcri neceffiiry 
to the fcnfe 5 the principal of which marks wc fliall juft men- 
tion. 

The ArosTKoruK, marked thus ( ' )« is only a coamu 
placed at the head of a letter, and fignrfies cither that fome 
\cttcr or letters arc left out for a quicker pronunciation ; as, 
/•//, for / toiH J be itont^ for he dots not : or clfc it marks the 
poilc(fivc cafe { as, John*s book. 

The Acc&NT ( ' ) is placed over a vowel to denote that 
the word is accented on that fy liable ; as, Com^prt-hin-Jioii. 
• Vol. I. CJ The 



50 OF ENOLtSn GRAMMAS. 

agaa— — 1^— — Liw ft ■■iiwww^ 



The BftLVE ( " ), placed over a vowel to iignify it (boold 
be founded ihort : at ^ Fii't^. 

The CiRcuMFLix ( ), placed over fome vowel to tbew 
that it 28 to be pronounced long : as, difpHte. 

The Carit, of the fame form with the circumflex, tnit 
pUiced beneath the line, to fliew that fomething is omitted 
which is iitferted over the line : ns, thi% '/ he. 

The Di AL YII8 (••)»<>'■ ^wo points placed over two vowds 
in a word, to (hew the)' are to be parted, ix>t being a diph- 
thong : as, Du'il. 

The Hyphen, or note of conjunction ( - ), being a ftraight 
line, ufed to connect compound wurds together s as. Heart* 
hreakhg ; Book-keeper, And wlien inferted at the end of a line, 
it (hews the word is divided according to its fyllaUcs: v^difiiM' 
guijh. 

The Ihdex (JgT)y or hand, pointing to fomethmg re* 

markable. 

The AsTExisM (*), or Star, directing to (ome note io 
the margin, or at the bottom of the page. Several of them 
together denote ibmething defective, or improper to be re- 
peated. 

The Okelisx (i ), is u&d to refer to a note like the fore- 
going. And in fome dictionaries it denotes the word to be 
pbfolete. 

The Paxacraph (5F) marks a divifion of fentences un- 
der one bead. It is ufed chiefly in the vulgar tranflatioo of 
the Bible. 

The Section ($) (hews a greater dividon than the pa- 
ragraph. 

The Ckocthets ([]) include a word or feotence explo- 
ratory of what was jxientioned before. 

The Quotation ('^—'O >• a double comma (the firft 
reverfed), and placed at the beginning and end of afentenc^ 
or fentenccs, taken from another author* 1r 



A PRAXIS I 



OP BNGUSII OMiMMAR. ^l 

A IMlAXISj 

Or ExampliHi of Grammaikal Rifolution, 

JoilN^ IV. 

X When therefojc the Lord knew how the riiarifcci had 
heard thttt J/ffui made and baptized luorc dilciplci than 
John i 

% (TlK)Ug.h Jcfus hijiiftlf baptized Dut| but hit difciplci ;) 

J He left JudxAi and departed ugaiu into Galilee. 

4 Ajid he oiuR oeeds j;o tliron^li Samaria. 

c Then conieth he to a city of Samaria, which ii cdled 
S)'char> near to x\\c paiccl of ground tluit Jacob gave to bil 
fon Jofeph. 

6 Now Jacob's well was there. Jcfui tlvc^eforp being wea» 
ricd with hit journe;^', fat thus on the well : and it was about 
the £xth hour. 

J There cometh a woman of Samaria to draw water : Jcfu» 
faith unto her. Give me to drink. 

X Wben is an adverb (»f time; thoffore^ an advcib with a 
prepf^fition added to it; th, the definite anicie; y,tf'-«/, common 
novin, fiugular number, mafculinc gender, nominative calef 
being the agent of the fentrnrc ; knc^^ the vei b neuter, third 
perfon, fmgvilar, governed by the noun L^ni^ and agrcring 
with ir, pad tin^e, indicative mode, and the attribute of the 
fentence; /^:t;, an adverb of mamur ; //r, di- finite ait iclr ; 
yharifen^ noun common, plural number, nominative calr ; 
bail heani^ yah neuter with the auxiliary l>a,/^ pluial, third 
perfon, pad lime, indicative m(ulc,govf rncd by yVz/ry^r/ j r/**?/, 
a copulative con jun<5tion; yi-yi/i, h proper name, mafcnline, 
nominative cafe, and the aijtnt of the fcucnce ; ma/fc^ unJ 
hjftiaietiy two verba a^ive, third perfnn, fmi^ulnr, |%all time, 
indicative mode, conn? ftcd with cai bother hv the copulative 
conjun^ion atj^ and are the attribute of the fcnteucr ; ///4>r<*, 
an adverb of comparifon; MflipUs^ noun pluial, objcrtivc 
cafci and the objcft of the frnteHice ; ^/'tf«, comparative con- 

(i a juueUun, 



cumj^aring tlui numl>er inciuionpi) ii) the turrgoin^ fcniencg 
with that uf the ft'llmvlng; w% hptinni ttrnt ti{jMplo^ tk^4u 
y^lm (lii(i) I y#/»*, i« proper name. 

• T^^ji^ A (tlijuiiAivtf conjqndioii { 7(/iii« i proper nanta 
At before i Ni^/tt/i tha ubjci^livo pronoun of the tiurd perlou 
fuiguliu, nink'oliue geniteri joined to the fin|;tilar fubOantivc 
J*\f% to r^tprefa »(^ exrlofivt einphiifm \ ktfii%tJ% verb fx(\\\^:% 
third jifilbn, Angular, pad thiie, and indicaiive mode, though 
it b« governed by the cai>juu£tion ihn^l>% for it it not of a 
doubtful, but al^folote nature, declaring that Jtjus M n^ 
hfti%t HM^f \ It fornu the 4tiribiUe of the icntcnce to the agent 
y^/ia ##/, a negative adverb, added to the verb, and alter- 
ing it& fenfei the |)otle(Iive pronoun ««> being underftcunl i 
^iv/, a dujuuAivc t\>njiinAion, correfpcmdlng to the former 
conjunction //h»m^<s and I'l^prelUngan opj^ofitionin ineaulng i 
lt\ th« pofllfiive pronoun, third perfon, Hngular, ipafculino 
gender ) iHfiifhi^ the plural fubftantiye, nominattv« cafe, the 
iiuxiliary (did) heii\g undei flood \ at, hh ^i/afhs tliJ, The 
whole verfo i» included in a parcnthefiii at)d it not connro>ed 
in fenfe, or conftru^ion, with the reft of the chapter, 

3 7/f, a pronoun of the third |M:rfon fingulur, niufi \dine 
gender, nominative cuir i ofed ai a fubftitute for the noun 
"Jt/uu ttiul governed by it i /{/>, a verb aAivei third peifon^ 
dnguUr, governed by t))e pronoun lff% pail time, indicative 
iDode i 7«^<r«f, a prop(!r name of a city, objeAive cale, a» i( 
forma the otyeA to the fentence i nnj^ a copulative conjunc* 
lion ) i/tfartifJ^ a verb ncutt|-| third perfon, fingtdar, gf^verncd 
alfo by the pronoun h^ jff^X time, indicative mode \ ^mih, au 
adverb \ Vw/d, a prepolicion j QMi*f% a proper noun, objcw** 
tive.cafr« governed by the pvepotition /«/#. 

4 JnJ^ a copulative eonjuuChon, oipirtrtng an adilition i 
/v, a pronoun a« before, agreiping with iti antecedeiu noun 
^(/«M i m*\ft\ an auxiliary, deuoting necrdity, and having no 
variation i i^ftM^ an adverb) ^^ a neutvrveibi /^«»«^^sa 
prrpofuioni Samaris^ a proper name for a country, objck'iiv« 
cafe, being |overn«d by the prcpoUiion tkr0%t* 



or VNUI.UII OKAMMAR. 5J 



f; ?%#«^ Au Mlvtrb vf ttiiur i %^mfi\ a titfuttr verbi |ovaiii«d 
by th« (MXHiMun it in |H*iion Ami luimbrri and pUctni btfurt kt 
IM i« liMiifCiitMM (he €iil« when thcNfccnt it i praiuniBi IndicA* 
ciw iiMHlf, mhI prciciu tiote (Improptrtyi fcr U lliould bi ui 
ih« pnft tlim I ««» thvn tttM^ Itfi) ; ^ri • pmnoiin \ i#i « 
})r«|M>li(K>n i #1 the indrfiaitv ArtWlei Wf^i NcotiHncm t/»m^ 
linguliri ntutrr grujcri vl>jvi^(iv« ctttt, iitiug gtivtrnml bf 
th« |>r«|H)titmn /# i «/| « |HV|»AA(ion i •V>4MiVtf| i profMir 
nttmci Itngylnrt ohj«AI\ii r^ff i ^*M^ t rrUtlvr, iKrvting 
with \\% «ul«iv\WiU ifVvt III tho m\mx verb !• if| pidiim 
tinie, fiii)tul(tri thiitl perfou, indicative modt; r«/M, Hwperw 
IW^ parciriplf ot th« neuter vrrb /# »'4//» Utnn placed aftti 
ihc aoiiliary h\ 4W'Aifr» a pmf^tr name i)f a cit^i itoiniiiRllv« 
\^aU% being pla^tnl ^htt th« iMutcr vrib, «WWi ntmt^ ati ad* 
vcrbolfdiiUttct) ##i a|)iepuittio«)t '^ ^Im dclitiirci artictt^ 
p^r\ti^ a con^mon iiouni linfuUri ot)j«Al¥« carci ipivtrtMKl by 
tlK prt|»o(iti<m /#! i^; a pit|MH)ti(Mi) |rNfW| fubAaniivteom* 
m^U ohjtiiflivt cat«i gfivetucd Uy th« {irfpoliiiun «/i ii«tf% a 
itlative^ a||r«ttin| with its aitiovtd«nt| iAr^«W#/x»#««)/| 
ydf^f^i a pivprr nunm ofthr |NitiUiTh| itmrmlinri nomiuaiivc 
CAfci X^t*i\ Avrih M^bvc, (hud |)ei(oni linKnUr, |Mlt imiri 
iuiUvtulWc nnulr, };ov<rinril bv y.«i«*/s the Umc an yMp^j^vf 
fihii \ Hf>^ a )>ir|H^liilith \ />/f. a |H)llr(Kvr pronoun, a^'irclnj^ in 
l»rrlt)n» iuu\)lH?r« anil gcnOrr. wuh (hr noun yi«»«A, mJi go» 
teinril by i?| anti in the |M>tlHlivf cafe to Hiew thn it laiion \J 
IKittcithm t^otwron ,%««#/• An«l /t*« ) ./#« ua ionunon tiuuu. (in- 
guJar, nwdVulinr gcnJcri objciMlvr cai'ci |{fivvmcii by ihcpic- 
jvuiUion /«: 7#y^/A a piitpcr iminci put in apportion iojiim\ 
ihM \$^ m {\\< luuic laft?! anil governed by (he (MWf pii:|>o(i« 
tion /*•• 

6 AW« an AilvcrlM y«#f i*^^, a fiihrtAtxivf prtJ|)cri poflTctliva 
caIV t HvWA a connutM) niMuu liuguKu • nominative rale, th« 
Uinca^H //v ns'// »»/\'/i#*i».^i ms#«, ihr nriitrr verb f* h^ thiid 
IK'ihHi lia);ulAi| (mU (imr, huli^ Aiivc nuuio \ //tf^yi an t^Jvrib 
ot pl4vT{ ,y^*'j»f, a pumper n4mr ; /A*»^I«»ti anailvcrb wi^h a 
p(tiK>u(ivH). the lan\« ai fkn «nU /<»/'» it kai the conUnu^Unn 

of 



i 






... ^x 



df ft pm^i\ i hJffgf tbn ptetient fmnkipk fit rfm utxn^r verb 

44^/^f;^f biirvg pt«£iid tfttr (b« pftrtictpU of fbe m^^itbry 10 h^ 
whkhf «# h4f biwn flfrwn^ tn ^11 if« U^x^^ re^H^r «« the pfe- 
i!rm i7f p«f/#/l p^irf kiplif dfMf ir s wlt/^ » fifcpofff i^n j hu, n 
poArfBvc prmimin, tMr^t p«ffo» fiflftilftff m/iArttlm« gcndrr^ 
4l/iiidiiif for tbir prHTfflive ^sf« ^f the fm\n JftHis j^arnpf^ « 
Aftiftnotin finKtiliifi <ibj«Aif eftfiTf govirntrd Hj' fbe pr«p<^(l- 
t^ iW/'^ } fai^ ft n<;tffir vrfb« ibtrd p^t^^ ^fs%\s\^x^ pftft 
f imty ffl^ftiiy« m^i^,, gw«m<rd liy ^i/iyi j thuh m tdtf 1 H 
^ fnftfm«ff Wnpf^perlx ^^f<«rf ^a tliif pl^f^^ «« h rrfm to 
f h« mftnueri^/ flftif% or tb« p^ftuf^ ^ wb<fr»» no p'^rtimltir 
poflitr« Of fffftOAcfof ftffing }« mcfllioocd, dtber htffore or 
ft/fer ib)i feof0hc«) #«, » pripoiicbo) ih^ fbc rt«flfiife ftrti' 
rkj w///f ft toomiow omio, fiogutftff ohjcftlve^ifr, gf/vcrfi«<1 
by ibc priPfMiiifion ^//^ ly/r/Z^ 11 (^ojonAt^ loptitftiive < //^ (b« 
ii«m«r pronoufii ftombmtivt; cafifi ftftortiof; for tbe limo of tbn 
dftyi Htm^ the lUfttf^r v«fb /^ ^/Cf third pcfrfoii, fiiYgulftr« paft 
f im«, bidi(?ftfWft mcK(«9 gov«rti«d by tb« fi«m§r pr^ /tN;(m // > 

i^^/VTf ft €{)\fmm ftibftftAtiv« (io/$ubr 

7 yJi//*/, fliiftdvftriM <^/ifl^///'f fhe fiffulrr vrrtt, ffiirtl pcrftm, 
Kngtilftr^ indi^fttWft mod«| dmi prcf'^fit fht^^ f boM^h if flt/mld 
^9 ib« pftft timftf fti& tb« «vrtft here mrtiHooed wtt« cvide/itly 
paft, ftnd in kSmi frvrfUe^nrb ^Mfkff( thhi\nnitet fhc wrmm 
of Hftmfirift in fpokrn (ft In fb« {^it (irtK^i »<», '* fhft w<miiin 
ff'f/wiffJt^tiA (mii^* {t/m(k(^tiHe nrimUi wi^w/y^f ft ftibftftHfiv* 
AOffio»oO| fll^gfikr, tantWma fiGmkr, mmimtUa trnf^^ hdtif; 
fbft ftg«of of tbft r«offme« rtHtdgh plM«4 tifut the vrrb ; ^^ ft 
prepofitiofM Siiffhirifit n nibitinl ivcr tornftfon, fiti^Mhir, ^^bj^f* 
^ i)ve ^ftfir, g^^v^rocd by tbr prrpoflr ion ^/j tn ^m-w^ Jbr b»flf»i* 
live fiw>dff of fb« V0»b //r^'U/j -Mz/f/rf, (t tffmnuifi iu\fHtiut)yr^ 
AoguLif) ^</*#f rt proper iwfiitf «* before j /////A, « fMriitcr verb, 
third peffoii 6ti^u\Mf, f^nve.fueA by J^/yt/, «rid prefertf fime, 
iioproperty foi* ibi p^fti m* fbi# (hou)d ftifo br «» it AaihU bt 
iUe tetllb verfe (^ tM« ehftpter 1 ^ JftAii a^/wtrtti mA J^ld 

ifnt9 



OF RKOLl^K GRA^fMAn• 5$ 



unto herV* ««/«! t prepoCiion; ^^, % pronoun^ Aird perfoa 
(ingiilar, feminine gender, obje<^live cafci ftandmg for iti 
^*0waM of Samaria \ givt^ n verb aAivc, fecond perfon fingular, 
imperative mode ( me^ a pronoun, iirft perfon fiagulari ob- 
jcdtive cafe, (landing for Jtfus^ and governed by the verb in 
the imperative mode, the word o^'tf/rr being nnderftood; /# 
drink^ the infinitive mode of the ai^tivc verb ; it it here made 
abfohite, &pplyi^g the place of tlie eoijim^ion tbmt with the 
iubjunAive mode : »•» give to me /^>4/ 1 may irink. 



SECT. VI. 
OP KLocrrio:^. 

EtocVTiON is the art of rending or fpeaking with pro* 
priery and elegance; or delivering our wordi in a juft and 
graceful mannrr. untainted with pedantry or afFcftation, and 
uncorrupted with any provincial found. 

Few people need be told ibc ncccflity of a graceful clocu* 
tion. All will allow, that what a man has occafion daily to do, 
(hould be done well; yet fo little attention hai fomctimcs 
been paid to this accontplil^mcnt, even by thofe from who.n 
(from their profcfTion as public fpeakcrs) we have been led to 
cxpedl a ()etfe<fl mudt.l of the art, as hath tended greatly to 
edipfe all their other merits, however great ; while others, of 
inferior attainmenta, by the help of a tolerably good llyle, 
and a jufl elocution, have rifen to u confiderabie eminence. 

A graceful elocution is to a good flyle, what a good ftyle il 
to the fubjeA matter of a difcourfe, an elTential ornament. 
For if the lubje«5l of a difcourfe be ever fo intcrcfting, and the 
fpeakcr's knowledge ever fo profound, without a corrc^ flyiet 
Che difcourfe mud fuffer greatly in its reputation ; and though 
the fpeaker's abilities be great, and the {lytegood, with a bad 

eIocutk)n, 



OF EMOtISM GtlAMMJlJI. 

elocution, It will fare licilc better. So great an e ffcA bav« 
thcfe etterior accompliihmentu upr;n public taf!c. 

The fird rule in Elocution, as in Rhetoric, is i§ f§Uo^ mm* 
turt. All other rulei, without a ftrict rc^rird to this, will oftly 
produce the aficAcd declaimcr, an<l not the gr;H:cful fpcaker* 
Theexcellrncy of this rule, and the nfilrtationof fome modern 
examples of eloc]ucnce, have induced fome to difregard il) 
other rules as fuperfluous; and to imagine that thb^le alone^ 
in a perfun of gr>od fenfc, and ctihivated taf!e» is fufficicnl ro 
form a public fpeaker. This, however, \% an error. But ic 
is necelFary to obierre the eHe/ts of nature, in order to diftin* 
gttifli between them, nml thofe of arbitrary cullom, or falfe 
tafte ; and to obfcrve the various wHys by which nature ex* 
preflcs the feveral pallioiis, emotions, aiul perceptions of the 
human mind : in order to which, much afliHance may cer- 
tainly be derived from the following particular rules : 

x» A difiind and delibtrate artUulailon is the firft particular 
rule* This confifls in giving a clear and full utterance to aJl 
the foundSf both fimplc and cumpicx. Fur this purpofe^ the 
nature of thofe founds flionid be well nndeinood, and much 
pains taken to corrc^ any faults in ih'j pronunciation. Sontc- 
t'tmes a fault in articulation is afcribcl to a natural defe£^ in 
fomc of the organs of fpecch, when it ib the ctfccl of bad ex- 
ample, or inattention ouly. Many of thcfe faults cnncem 
the founding o^ the conibnant*. *Sorr.e cannot pronounce the 
letter/, oihcfs the fimplc founds r, j, th^Jh\ others omit 
the afpirate /». Thefc may be corrected by reading fen- 
tenccs cbofen for that purpofe, wherein thcfe founds fre* 
quently occur ; and by conilantly guarding againil them in 
convcffation. 

. The other fault in articulation confifly in the confufionand 
cluttering of words together. Moil p<.'ople, who have not 
learned the art of fpeaking, have a habit of uttering their 
words fo rnpidiy and iiuliAindly, that it is in)poirible for them 
to give any.emphafu to their words, or natural tone to their 
icmences ; though they may pronounce every word plainly* 

'5 The 



OF SKQUaH ORAMUAl. J) 



Tht tnoft effiftdoil meant to conquer thii hftbit Mti to itad 
iiiloud paflkgts chofen fbr timt pnqHifci which abound with 
langtttd unuliMd worda i and to read much (lower than the 
fenfe and juA fpcakiug would m^utrc. Ami at nothing 
h^her till you can read dittiii^ly and drlibciatrly. 

t» Lti ewT} wtrJ it ^M»Mtr</ ^fh pi-^fritty. Thii ii a 
VM& necefTary rulei a» cuxm • in pronum iation are more fre- 
quently eomiaitted^ and tcfi* guai ded agaiull than any otherk 
Ktulta in p^nunciAtion t\x innumcrM)lc. Soinc of them are 
the following: omiiting the nipiratc /• whctc it fliouUl be 
ttfedi as d«r fbr^iarr; and uling it whcii: lUctc (lioutd bo 
none : a«, Ai^ for ^ ; oinfbundlng and intcnhan^ing the 
er and w \ |)roaouucing the di|'luhong «»« like aw^ or ## { and 
Ihe vowel < tike #i« or # ) and cluttering Tcvcral contbnanti 
together^ without neganting the vowcli. Thefc cmMs, and 
many otheri too nutneroui to mention here* m\ill all Ik care- 
fully guarded againfti hy every (Ktlbn who would be thought 
a Gorreft (peaker. 

It ii ditteult to point out any ftandard by which the pro- 
{M-ictj of pranundatkm ia to be determined. Prafound Icho* 
Un generally make the etymology of the word the r\i1e of 
pronunciation, and thui bring U|x>n thcmlelvci the cliargc 
of pedantry and affitdation, by a delivery ahogrthcr novel to 
the red of mankind. While, on tlic other hand| the mere 
man of the world, notwithtlanding »1l hik other accomplitlt* 
ment<» often retains (6 much of his provincial diMc^, ai 
juilly to exclude him fmni tlic honour ot being tlie pattern 
of a juft pronunciation. Thii excellency in perhaps to be 
found in thofe only who unite (hole two i hara£\crs and who, 
to the correiShiefa of true learningi add the elegance and ealc 
of genieel life. An atttiitifn tfi/mih m^M^ ah inttntrnvft *wiih 
the f&liit mmid^ atul m tf^rJ f4 th rtym^Ujgy ef tin WH-^i 
them/ihii^ are the heft rules that can U: f>i\eT), to nirrei*'! jtny 
errors in pronunciation, and to ^^u^rd .i^;ainlt Any ixsuliaii- 
tiea of plt)vincial found : which every p* i ton (liouM emlcA- 
vour to avoids wko is fuppofed to have (ccn too nuu h of ihc 
Vot. I. H world. 



woild^ ui Hx9\n the (^eculUiitits of ih^ (hftiiA in whkh ht 
waK lM)rn« 

With ^/j/ri/t'r Ai'CbNT, Many wriiert bav^r )«kl ii down un 
a fuuiijmcata) nile, that the aacnl of «Mit*s in Uw bn|>r)iU 
hnjtu«[j;e fl)Ou)d be thrown aa far Ixav^k ai |>oA)ble iron> ihc 
•nd of the word* A very enai\cons r\ile! and one which 
hat no foundation in \\\c Knghfli bn^ua|« ; tor many wokU 
in the BngUfli have the accent on the laft fyHahle, and iha 
||«nerai)ty of thew have it on the frciw* or thinl fyiiable ti oni 
the ends but a very few on the founh fv))ahk fr^un the enJ 
of the woid, T\\c bcrt rule ihal ran be given for i!\is |n^ 
cept. ta the finv|»oing ; nanwlvi a ftriA attention lu liie ht rt 
fxampleii always ohftrving that the accent h not h» he d«» 
tcindneil by any rules of quantity » but by the number ami 
oature of the Ample fuunds, 

4* y*V ^rM«4h/<ji!>4» jh^kU ^ MJ ami /^rv:^if^ Mciny 
public fpeakerft deliver their ditWuufe with inch a fairt an4 
fbeble utterancci and feem fo wholly unconcerned with ihiiv^ 
fUbjeA, thnt their wonh way hr Aid rather to diMp* frt^tii 
their li)tt than to tnn dellwred by thent, Thii fcKiom fuilc^ 
of proilucing the fame unconcern and Indilleience antong^ 
their auditory, Jnanlm.uhm h a principal fault : a ) pea Iter 
whhoui energy i« Imie better than a litfiefn Oatue. 

To remcvlv this evil, inure >ourlelf, when readini,', H^ take 
In as much l\reaih an you can with eafc ctiniaiui and u^ ex|H*l 
it \x ith vehen)en«T| in uttering ihofe fout\ds whi^^h leipnie ia\ 
emphatical pronuiKiatitu) \ ie4d aUuid in the o|Hn air, with M 
the energy ytm can cummand ; preterve your Uuly in an ere A 
attitude i let all the ituuuU| both vowels anii ronfonant<« ha\^ 
a free, full, and btdd utterance, rradite ihrl'e ruKi with |kei. 
teverance, till you are nuib-r of a bold and maniy delivery, 

Uut in av(|uiring an enrr^^y of fperch, the followinn cauiioi\ 

ii nccetlarv, nanwl) » that the t)Kaker avoid the (tpiktfnv ek* 

trtn^r, ot tunning intoa palliona.e and dillracling vtwil'e ration* 

This exitU amoujj thofe tpeaker«| who v^lne nothing abovo 

4 Uva 



lh« mlmir«tkm of the vulgar. TlielW am Stiakci'iKiiir Imi 
jviftly obferveUi ^^Olfoiiil ihe jviillciuui bvAitrio the foul» 
i)y tvurlng « jMflion to ragHi to vciy tuiteik, to fyWx the cur* 
"of the |;imuuHin^«%" CMccio t*uiii|)iiie« luvh l'|)eAkert to 
vHppltMii who get 00 hoi'lcbaik Itrcttol'r ihcy cannot walk 1— 
tkwy brilow, U«cjiu(tf ihi;y caunoi i\\cA\* 

f#4«^ #/ /A# 4*^/4#. It ii owing to tlie ncglr^\ of thii rutci 
ihnt^cHiiily In^ar fmh tuni^nul Anil un«itlr^inK Uilconrfc*. 
Speakerfit wIki dcliwr thoir Icntintcntiii ur rend their coinpo- 
fuiontt in a tlulK ttud iniipitl nmnner, wh^icvvr uthcr merit! 
4\\ey mtty potV«(i« (clUoot tunviiice ov ttttr^'l their auilitori* 
This Iknic unnuiiiiung ouhIc uf deli very, t'u univerAiUy'pre* 
Viiirnt, ii cnllcii ««#«#fMVi aoU civnlilU in one unvurird tone 
"of delivery* Molt people^ in fctniihar convcilAtion, can de« 
4hrer their thtt\iKhta wirh lome variety, both iu the tone and 
the he')|{ht of their voice, which they generally modify at* 
curding to the nature ot their dilcourfe 1 yet the fame |)erfuiui, 
when requhed to read any con^iMificioni innuediately airmne 
« drys uniform manner of delivery i at though reading and 
converfailon were to he |>erformed in (|uite a diiferent man* 
ner from f.u'h other : whrie4«i the fcuuc fr lUcmctii whether 
delivered ijtontancinilly l»y the l)»C(tkri, 01 u*iul hy the Itc* 
Uucft ihould always he drlivried with thr fame toufi and ua 
the fame key. notwiihllaiuling <tll that lui hron fuid by fu|H;r« 
iit'ml criticn lu ihc rontuiy. 

A pcrfou ot a moiUiittc i\tiMcity willi thcictuir, he Mc to 
alter the tunc* uv well a> \\w hci|;la uf tiin vitii r,a« it i\\a\ be 
necetrdry, Uittvicnt Ipeciei uf fpetikiii)^. requiie diilcient 
nuHlitii-aciun* wt tUe mucc, DiAeicnt i huxtilciii in ditleicut 
lituationii l))eak in vciy ditlcreiit kryn. TUo vagrant when 
lie bega, the loltlicr when he glve« the wgrd of commatHl, 
the watchman when \\c aiuuuuK-e« thr houi- uf the night, the 
fenator when \\c )iai4Ugue«, the luvei when he whilpcii hit 
tender tale, ditirr uu wuwU in thr key an in the tune in which 
ihcy fpeak. Thi* f^tnit* [k\\o\\ aho, in the fHino iituation, 

1 1 z may 



6o OP BNOLIfllf GRAMMAat 



mty have occafion for all the variety of rone and divcrAcy of 
voice: as, bi the fiipport of an argumcnfi the relatinnof A 
ftory, the command gi vrn to a fervant| a lamentatioiii ao 
cxclamorion of anger, and many other cafei, require not 
only ditfercnt tonei, but difcrent elevations of the voice. 
Reading, tliercforc, in uhich all the varieties of exprefkm 
in real life are copiedi mud have continual variations in the 
height of the v(^ce. 

To acquire the power of diangifig the key on which you 
fpeakf accuftom yourfclt to pitch your voice in dit'ercnc 
keyf| from the lowclt to the hi)»heil notes you can comnrumd; 
rea^ingv as excrcifci on this rule, fuch compofitiona it 
at)ound with a variety uf Ijieakrrs, obierving the height and 
tone of the\oice nertlfary to each fentence, and changing 
them as tlu: nature of the (uhjeA requires. This will give 
you ^urh a command ot voice, as is not to be acquired by 
any other method. 

6. DiJIiMj^ui/fj iljt mtrt fignificmni vj^rdi in §viry ftn^iua hf 
$htirfr§ptr emfhasks. The emphafis fervet to point out the 
precife meaning of a (ientence, ftiewii how otic tdet Is cou^ 
ne^ed with another, gives to every part of a fentence ila 
proper iound, and conveys the fenfe ol the whole to the mind 
of the hearer. It alio ex[ii etfcb the oppofition between tlie 
parts of a (entence, wheie ihe fenl'e is pointed. Sontetimee 
the emphafis is doubl<*, and iomeiimes treble in a fenteooe, 
Emphafib ferves likewise to ex|ire(6 fome particular meaning 
which ^Qt% not ariie fiom the words thcmfelvos ; as in this 
Hioit fentence : '* Did Alexander coii<iuer the IVriians V^ Thia 
fimple queAion may have three different meanings, accord* 
ing to the intention of the f()eaker \ and the emphafis bas^ 
confequently, three different places : as, when the fpeaker 
knew that the Perfians were conqneird, but did not knouT 
by whom, then the emph:tfi^ is plarnl on the word JhxMm/hp: 
as, "did Jlhxander LonqiKT the Perfians?" ^Tien ft if 
known that Alexander atteiDpted the conquef^, but the ifRit 
is i\o\ known, tlic cniplMfi:: is tluii placed on the ^qx^ $•%* 



or ftSOUSH QSAIIMAt. 6f 



f Mr ; M^ '» did Alexander ^m^mt tke Perfiiu ?** Wheo ic 
w known that he conquered the adjacent conntneii but it if 
not ceitaioiy knonrn that be conquered tbe Perfiaas ibe coi- 
pliafii u placed on tbe word Fer/ams: «i% ** did Alnandrr 
conquer the FtrJUns /'* 

There are four waji by which the emphafia of a 
generally deliroyed, or naifapplied. Fii^ by pbcrng ib 
an cmphafit on any one word, aa to fTrLarir si: rbe 
words in the fentence finom bemg in acr d e gre e ^ii^ii ..a j. 
which they often require ; for, aa was befoc ci:J=r 
cmphafit is fometin^es doubie, and 
cence. There are aiib, of niijrfMfrt ic 
foxm which require a more iiaidfatf 
is an error which nsanj 

Secondly, by pbciag too grea: 
particles^ and tbofe words cf 
ihottgb fometimet proper, ya i: is 

Another way h^ which 
in one unifonn muficai 
calkd reading wteUimfly. Ac i 
of the voice, as far as is 
attention ; but to fubtia:;j 

exclufion to aU the ^-ar: ex yr i gi g. . . i.. 
can be tbe effc^ aoly v£ il-sl- csbccz::.^ r . -r^r*. 

Laftly» the empbau u zr. 
Sentence. This is ;De 
fo be conamitteci. 



^*»M\. 



knowledge of the ies^ sc tie v-se- . ^ 

reader be not peri=s:^acs3i.i:3:. *z:. ;«-rs 
and fnllmeMuaiaf e«s7.a£:aac£*^:.. ««. 
poffible be flxxkc fiir* 
▼oioe which 

difficulty oc npr^ aacTie 
tmphafis 
which is tbe 
To ipeik w.:r a .;;r t- ----.rf=. .^*^ -^:^ ^^ 




6a err RffnuiiH ouaumaH. 



n neecifary than prcvtoiifly to enter mto the meaning ffnd fpi^ 
fit of every fcntcnce ; and to txprcU it as ncarJy a$ pofibitf 
to the manner in which we exprcff otirfeWcf in conrerfatWin f 
for, in faiiiitiar difroikfc'i we generally exprefs onridvtt em* 
phntically, and place the cmphafn properly* Ai to artificial 
help f ftich as d i ft ingm filing word) by panicubr chxradcrs^ 
fhey generally miflead rather than affid th: reader, by coo* 
fining him to a particular Word or fentence, which he gene- 
rally overQraiM. 

7. I. earn to a*, quire n luji vorltty of falife and eaJence, Tbfc 
paufes crmfifl of thofe certain ilopSt whidi are ufed both fft 
reading and converfatioti, and which are alirayt neceffary tib 
the fcnfe. The cadence is that fall of tbe ▼oicc which li 
generally dire6>ed to be made before every foil ftop. 

There arc principally two faults committed wich rtpiA tc^ 
paufes. The firft, and one of the word faults a fpeaker caft 
have, n to mnke no other paufes than what are necefEuy for 
breathing. Such fpcakcrs or readers make no di(tin£lion be« 
twecn a goo<i fpeaker and a quick one ; and feem Ui confider 
reading (juick the fame thing at reading well« Biit| withovt 
pnufcs, the Ante m»ift al*.vays appear cohfufed and obfcure, 
the nic.ining ot'ren he mifuriHcrftooil, and confeqnently the 
energy of the pitcc vs holly loft. 

The next fmlt confifts in n too m'tihanical attention to the 
flops or panfcs iifcd in prinrinj;. Thcfc, though very proper 
in wiiting, nrc ofrcn unnatiirni in f|Knking ; for, as wan ob- 
fervcd in ViMK^hiatJon, the dor^rine of points is ytry imper* 
ii:f\ ; the varirty of pnufcs requirrd in difcourfc is fo great. 
A flri<ft regard, therefore, to tlicfc points has l>ecii one chief 
caufe of monot^'Py, by ufing the reader to an uniform found 
at every imperfc<^t break, and an uniform cadence at every 
period. The ufe of points is to ailifV the reader in difcemivg 
the grammatical conf!ru6tion ; not todircA his pronuncbrtioi* 
In reading, it i^ often neccirtry to make a paufe where tbe 
grammatical conflru^ion rcquirei none, for the fake of poiot- 
ing out the knic more firr^ngly, preparing the audienee for 

whU 



64 ^f tS(l\A$U ONAMMAK. 

by the lUiniii'i in wlnrli \\v ultii luii wouUi titc loiin ot iht 
rouiitcfiancr, unit tiilur wc'.i. known li^.m. AihI c\rtk when 
u'c deliver oil 1 ihiiii|;lici on jiiy icU inlciaUing liibjcdt, and 
when llic nioiv: uiilciit rnmlituit .iir not rxiilcili li»ilic kind 
of l'erlin|{ uuuh)panic\ uiii v\tiiil», which ihuulii alwuya 
have it*> pioprr rxtcnmi rK)iiilii >n. Thrlr t-ktctiui cX(McU 
lioiib iiie the died u( iMhiir jKuiCi 4ntl c\ery juihtioiia 
iinttaiioii of it in u iprukci u-ill iilwj)it u|||icji KiAtrfu) ami 
|))caliP|{i iKJiic ftiu ilclcive iltr npiiclUiHHi ol a gracclul 
f|)cakcr. till» to «i ihllincl auii nljtion, a |Krlc^K cuntinaiid «! 
voicci and a Hue cinphafiD, hr lan add t)ir variotii eaprcUiima 
of the pafliiNii and cnioiiuiu ol the ntindt 

It U iiniMitlllilc to Uy down any ht ol nilci by which Kte 
fprakti inay (uiiii ilirlc oum»iid c»)»iQlhi>ns. at ihoy mutt bo 
ai variuiirt ublhc tMllit>ni llicy induair ; thn loHowing (iiMral 
riirc6iiiin it llic oidy one thiit ejii Ix; drjKiidrd n|ioiii— • 

In ai (|uiritiK thin arcnmiihlhtiicni, at uU othrra in chli artg 
tlic fundjinrnijl iitic i»« to /ii/Zruf mmiurt. OUarvf in what 
minnci' tlie Icveial rinmiout, or |Mflionii| aie rxprcilM in 
reai HtC| or by tliofo whu have with Kteat laliour and taflo 
acquired tlic happy |»owrr r»l iniiiatiiiK niittti'r i and nilhar 
follow the ^>rrat oM};in:d hnirll, <ii ihr brl) (opir» to l)c nitt 
ivitlif alw.iyaobli ivini; thr iiiiMimi |;ivrn b) iihiikcliwuic ; «• 
•* (yerfiff Hit /'■<• iftin/ffiv 0f Miittttf/* 

Alorc ii Ui ht- Ir.nnecl by a Uiht .iitrntinti to Hoo«! rxatn- 
fdea titan ij }rih:ipn inu^.tncil. I'MmpIc h.ik .isntuththa 
advunta^,'* ol prrrfpt, a» piiu'liir li.tu ol (hroty; unit niuny, 
wlui huvr :u rived to f^irui priU-ihoti in ihrijii, have can- 
didly ncknowlrdiTi) it to hr iiioir ilir ribrt of imiMiiuni ihaii 
.my throirticd i uli *.. 

In oiilrr to apply (hr Uuv.yuwv^ inh-i to piu^lur, it ii iib< 
fiilntrly m ilhtiyUi ytt ihioiipjt a ir;;ii).it louilr of rxrii'ifet; 
br^'.innin^; i*. irh itu h .n jm moll r.il\ , .mil pim rrihiif^ by (low 
mlv.nu.rl to thod: th.it uir niorr ilnhi iih. ^o| it the iradcl 
CiniiOt dciivri uit'i pioptif ty Ihr pUiili Irntlinriilii of luupti) 

naiuii*.c, aiid duUiu pinr-:, hovvi4u il be r»|H-Cicd br niouhl 

dj 



* J**;^i=: ~ --^ 



r 



■^■P""*— 



^» 



■ ^ ■■'jFy 



*^^ ' 






it s =e I1.V 



191 M 






Udcn 



-m. mt. 



it:on W..J. .t:u^ . 
area v-..^-^ 1 ^. 

/hen :-c - :- -. 

verec, iiii i:r:_>: 

ZC^ vi .>}•.. ^o .&.. . . 

.ens, ic, rr.^r>iz..- 

lucentior.. ..? 

as GKca ia --r. ■=;- 
IS pcr.bn. He -l: - 
:\ mesne r*. .^ t— 
nory, -na :7tr. .=r.: 
iing it. 1: ira^icc 
ir.iagar.ri.'^i;.: - ■ 



— -«A 



■ » •- ■• 



66 Of BlCOLTtn OKAMMAir. 

the ideas which he if to exprefi. It givei him a prraooa 
knowledfe of the fcveral inirxions^ cmphafet, and tOMi^ 
which the wordi requite And by not having hit eye conflned 
to the hooli, it relicvci him from the fchool-bojr habit of 
holding down hk head, and|C(infc(|iient1y« reading in a differ* 
cm Itey and tone from that of convcrfation i and leaves bim 
at full liberty lo eaprefi his own ftelingSr by aU tiM raricties 
^countcnanct and gcftvrc. 

It generally requires fome timei and many ami liequeul 
cxersiieii before the ftudent can be brought to ooaCder read- 
ing in the fame light as converfation ; and be perfhaded tkrt 
h AouM be condiiAed in the fame manner. Tberalst mam 
or Icfs, in all people (except in a very lisir accompMhedl 
fpeakcrs), an artiflcia! uniformity, wKich always diMnguifees 
reading from coiiverfation : the ffxcd pofture, tUc bending of 
the head» and the attentive look at the book^ whiclr are re« 
quifite, are al> dcfiruftive of that eafc» freedom, and variety 
•f both expreiion and a£Kon, Acceiiiry to a }uft eloentkm. 

It would fuperfede the neceCty of moft of the fc re g oi Bg 
rules, if public leakers would deliver their difeourfes fhmi 
immediate eonception, or from memory. But if thii be too- 
much to be expcAect, ef^eially from preachers of divinity, 
who have fo much to compofe, and are fo frequently called 
ujK)ii to Jj)p;ik in public ; it ii, however, very neccffary, that 
they flioiiici make themfelves fo well acquainted with their 
clikonrfe, that they may he able to take in a confiderablff 
portion with a fingic gtanoe of the eye. 

After the ftuilcnt has acquired a juft and Aatnra) elocntlont 
It is, perhaps, not the lend difllcult part of this art to apply 
this accompUftunent to the purpofci of real Wk-. Many can 
deliver their diicourreB in a gra( eful manner in private, or 
before a few fcleA friendi, who, when required to fyeak in a 
public capacity, at the bar, from the pulpit, or in the fenate^ 
generally betray either a timid baflifulnefs, or an impertinent 
affurance. The former is apt to lead the fpeaker into an 
awkward uniformityi the latter into a difguSing affe£latieii| 

tho 




tfae fanner uife» from aa hunUe HMhIrnff of tkt ^Kikcr*! 
own f irHrs Md idpeS 6r tke uodcriudaaMi of hk 
facauen; the falter it tkecfbftof cooceiw and ooHteBft 
fir Ac QpaioMof Us wmStani fbe fonser «ugr iboa fae 
cw ma o aac bf a faoncfcftil stteation to dw tottgoimi nda; 
iIk famr GU.AUoai be iiibdflod» til^ bf fcpotod diii^ 
pobtmeottp the nlh adveoturer is comooB^ tbiC be audo 
a blft cJiaiitr of bii own valac 

We ftull dofe tiiit feftioo wkb Ifankt's inftmAioM to 
tbe pfafcrit ukam firon S^atefpear ; u'htch bu aiwaji beso 
co pfidcud fli 0— laiiiiiif aa ioyoitaac icAba oadocotiQi^ 
md mmf 1 1 wiplii| oagj of ihc fortjfmt naiei. 

'^ SfcA tbe ifeecby I piaf foo, ai I praooaooad k to foo^ 
cripping^ oo xfae roogue. But if vpq momii it, at wuof of 
onr pla]fen do. I bad ai iieve die tova crier bad fpofce nqr 
I'lnek And do not law tbe air too miicb vitb jroar baiid^ 
tbas ; bat ole aJI ^jbdhIj ; for io tbe very loncaty loapeA^ 
aody as I aoajr Uy^ whirlwtfid of your p^Soa, yoa moft 
acquire aod befet a temperaaoe tbat may give it ^miwfr- 
odu O! it oCealiBe to tbe fimlt to bear a roboftioiia 
perivig-pated feflov tear a pafion to tatten^ to very ragi^ 
to fplit the ean of tbe grotiadiii^t wbo (for die xxiofl patt) 
are cap^k of Docbiiig b« innrplicahk daab iboin, and 
noife ; I ooold bave fncb a ftUam vbtpp*d for o*cidoiDg ter* 
ma^^t ; It ont-faerodf Herod. Pray you^ avoid it. 

'* Be oot too ume oeitber; bat let your ova diicretioa 
be roar tutor. Suit tbe adion to tbe word, tbe word to tbe 
adioD, witb this fpecial obfervanoe, tbat yoo o'erii^ not 
tbe modefiy of oatare; for aoy tbing fe overdooe u fioia 
tbepoipofirof pbyiog; mbofe eod^botbat tbefirft and now, 
was, aod i^ to bold, as 't were, tbe mirror up to nature ; to 
ihew virtue ber owa feature, (com ber owd image, aod the 
very age and bodj of tbe time, liifi form aod prdfore. Now, 
this overdone, or come tardy o€^ tbongh it make tbe uo* 
4iifal laaj^b, caooot bat make tbe judicioui grie\'c : tbe 
LtuiLTt cf one of wbicb mufi, in youi ai o.vaLce^ oVrweigb 

la a whole 



^^ 



s 



^: 



^ 



O 










•V VBimAmHtv. t% 




CHAP, II. 

m 

Of penmanship, 




SECT, I. 



|iptE;( YOB THE ATTAINMENT OV THE AST 4(9 

WRITING. ijP^ I 



7H£RSk aofart of literature acquired with lei^ Mbltj 
tino the art of writing. Few people, be their capacities 
CTCrfeioean, are incapable of learning this. Henoewefes 
io RMuij, who, though ignorant of the more early parts of 
icKoce, fuch as Engiiih granfrar, and even fpelliag good 
Eogiiih, jet can write a tolerably good hand. This is a 
glariog faolt ; for the more corrcd the peomanihip, tke more 
does it diffhy the ortbc^rapbical and grammatical crnrs. I 
tbereldfie adviie all thoie who may have occafioa tQ write 
mtfcby a» sake themiclves perfe&Iy acquainted wlfh .wrfaat 
ias been delivered in the former chapter conceniif|( Englifli 
paar.3iar. I truft it need not be mentioned, that tbqrihouU 
leoder themiiEivcs perfed in fpelling : every oof luiows the 
occe^&ry of this, and the ridicule and contempt which only 
one or two wordi wrongly fpelJed bring upon the writer* 

J (hail proceed to give a few diredioni, by the help of 
whxh JO ioexpericsced perfoo may qualify bimielf m tip 

ait; 



7# or FKNMAlffllllF. 

an i ami wichoiit which, though iicihaps dccinrd fuper- 
fliHiiia l)y lijine, a woiL of ihia kind might poAibly appcsir 
deficient. 

It il aeccflary that ttic learner be proviilc<l ivith the implc* 
menu rcqiiifite for willing t • %tnfd \ku^ and f^ood tret iok^ 
without which it ii iiniNiffilik to wnir « fair ropy ; a romid 
or lilt ruirr (the found rjiic it ufcd for diljialrhi and the flat 
one for fuirnefi), a lc:idrn |jlinnnicr» or l)Iark Irad |icncil, to 
rnlt tho lines, wiliioiit whii h ihc learner will never wrkf 
iraighc I and lonie |>oiinrr, or fiuni-fandrack priwdcr, to rub 
the Mper with, il it Ur too thin to Ixar the ink| and when 
tioWwuli are to he wiiitrn, ai Urge tcit, ficrman icxfp or 
the like i ith when a woid or Icntrm t in frratrhed out villi 
llie jienknife, in whi( h eafr, ihr place inufl /irft lie rubbed 
finoolh with the hafr of the knite, or a piece of c:lcan paper, 
aiiJ iImo rubbed with the pouniOi tu rnMlile it to bar the 
ink* ' AQUarui lired copyUiok is the mofV pro|)er» ai each 
pagf will contain a copy uf tni or a iloirn Unoi which will 
tm ioflcicnC to wiitr al nui*. iiiiic. 

Bihg provided with thrfe inipfrnirnti, the leamcr WMy 
proceed lo praAice, The liiirs Oiould \tc ruird flraigbt and 
even, and at the (ainc dilianrc- fiom cm i\ othrr, at the dotted 
linei, nnrktd N<i. r, in the plate. The dillance between 
every two iincbot writing ftiould Ih: about twice or three 
liriM:^ ihediiiancr which there it lictwcen ihc two |)rncil linck 
thai belong to the lanoe line of writing ; though fhta it ofieu 
nunie or Icfb, act ording to ihc caprice ol ihr wiitcr. 

The pen mull l>e held in the right h;<iid, lictwccn tlie 
thuutli and tlie lore and niiddie tingeii. The middle finger 
mnft br placed on ihe hack of the pen, ojipolite to the upper 
pait of die cur i^r cradle of the |ieii, and the lore- finger cio& 
ti> i(, And both held Kraighr. Tlie thumb mull be placed 
iguinfl itu: oppofile tide of the pen, ralkd iht: Ijclly of the 
quill| and mull In: hcnt a IkiIl* in the joint. Tlic tup ol ilic 
pen ibould point towardv the riglit flKiiilder. I'he cIImim 
Aould be druwn iik cowardu the body, but not tuocluic. Tin 

aim 



0€ P£KMA«SHIP. 7 1 

•ffli mty ftfc liglitly oa tiic tdgt of the <ielk, or uble, be- 
twccA toe cibow aad the wrifi; but the ionuich fiiauid not 
pre& a^nfl the 4e§i. The pea muft be held very ligbciy ; 
for tf'ic be griped har<l,tke iearoer will never acquire weak 
ezpeditioD io writing. 

The learocr, hftTing aoquirod a juft hsdiit of holdiag the 
majr copy the fimll letters /, e, e; haviog ^ ^u^t ruled 
■ccordiog to the dotted iiocs in the p!ate. He may next copy 
the other fifnal! letters ; ukrog ctre to be perfe£k in eichp 
before be proceeds to the ntxu Then the capital letters ; 
ruling hii copy in fquares, according vj the pattern io the 
pljie : and aJfi^ join-ha/id copies, as foon as he can aribc 
Ibe capiulf. When the learner can write an indiflenent goo4 
roMid hinft tt^t^ he oiaj proceed tp the fm^U fouod htn<^ 
and running hand ; in wridog which hSif the pen ihould 
■Cfvr be taken off the paper tiil ttie word is fiaiXUed* 

The learner ihould imitate the bed copies. Copper^fibte 
copies are to be preferred to thofe written by die fi% as 
besog mort correft. Thoie liBall letters which have cope or 
Aems, •^K^f/f^fk^if/f muft all be of the £uLe heig^ 
And thoSt with tails, as /^ g,J^ p^ i%f%y% *^*^^ ^ ^^ ^^ ^ 
bnac length. A due diflance nr.uft be o'jfci ved ixrtween the 
vords, and betv.-een the letters of lae LiiiC wjrc. The 
^^pitals lEuft be ail cf iivi frLrr.e f.ze. Ti*t xn^il^Lt ilrokes, 
or rho£e thit ire fornr^d l-/ iL'^ -prig^- f:r'.V:e of the pea, 
■Bufi he fi--.e or hi:i: f^roLes ; ar.d :Le c;-wi:::^".: ^.roVes mjft 
be fuller an J fi.'ackcr; b::t 2 CG:2f*ir*: attc:.:'/;!i to the copy 
wo^id ill a great ir.ti-'urc f^p^ntdt t!.c ncce.^:/ of rnoft of 
t!iC foregobg rj:«. The lesicer fiic.-id r.ot fit long at 
ociC time, lefi he grow tired cf lezi:iAr*g, in which cafe he 
m Jl not ixr^prove ; n sr be arr. L i lio'J $ of w ri t i r. ? ^: f . , f >r ^ vc 
or iixiines, wtli wrirtcr:, will i.T.prov<r th. J'--*.rfi'^ -i,^c tr.i:-. 
tfty lines, wr/'cn :r* the f^:;.. .mc, without atter.tioD \'^ 
tLtJ corrtirr.cfi. 

Wr.en tLc learner has ar:iv«d to for:.e profl'.ier. y . 
wr.ii- g, it is Tt'^\i^*x tfcit he krcv hew v; .T.ii:c a^.d r*t.-.': 



^i «iP I'leNMANtfllff*. 

Lif yirn. 'I hi* it (tmner to be Mnjuircd by in ifffcncifi 
9^}(r.t¥.ittrti ffi ilif^fr whfi f.aii niAkf. ■ jh*!! wfU than ^ly uif 
%crt>Ml (!ir<*^fi'irii ; Oir friiU,i«m]^ ril!r<!, hnwcvfr, iniy ba nf 
Hvii^. Ill* I II f; |irir/iil'fl M.r)i 4 f^o/iH goofe #|iiill (ihoU mlM 

If Lohiift iilr t)ii: 111 ft;, If I j|«f. llir, fi ti|f honi It, M^llll iht liACk 

ol ilir |KrikiiifC| iLifejiiiifp. ihi: l''J(k ol rhr f|iiill mftt^ llut 

flic fiif mj/ ff. (*lcir, III' It MM ilirf|uill h4ll tbroiiKti, iicif 

tfu: cfict, «iil lltfr l^rk piiM ; uinl rut clic Arlifi fi4c of iIm 
<|iit)1 «|iiiir i)i(oij|'^h, ne.ir hii'l un if\'U Unm ihr emi. Thi 
<|iil]| will now ji)>tirji ffiik'tl I iirii I 'It JMfjy j very fltcirt M 
III ttirlMfk i.'ifiti, wliPir rhe Oir ««f ihr ptriii to l)« | and 
Jllltfin£ Hh: pc «* iif llif jirnkiff )i.ifl, *ti i\^c tlU\ ijf iiilOfhtf 

qnlll, iiiNlei t)i.« flif , ittid li/iMiiij^ t\*t n.til «)f tli« kft ibufrfl 
l^rrff) h.ii(f on iKr limik of thr f|iiill, it hi^lt a<ii ii iiit^ffiAul 
the flit fliill p/», i^ifh n fjiifk lii«1'l^it f'^if i: irrii! ii|) eh« flitf 
At ihuil Ik vtry iwUWn uu'\ rpii« k, ili.ir ilir flir iniiy km rlrtf 
aiid cMt ; f"i if tbc flif li** « \idt awS 1 loff, ritU Ir rtiiimit itt 
Irrn fhrmivfi, ir it f!oi,r writ, 'flini, tiy IrMtrA nrreihry 
niffe, rtir r|iiiil i» to I'lT l;i(#ii{2lif info iln- innu of g pfn ( anfl 
tufbiit l)roii|{lir it to a fjur point i,utr.ii U UtU uf tlir flir, it il 

to lit illMinl III lli.i iiiaiiltir : p!.t'^ ll.f thUi\r itf tht I lit I //ft 
flic U'ft tlllllli^ r. Illy lirnillii^ tl.i' prri \,iiArrn ihnUilr Hfj#| 
li.i<f(lir fiMjMjs fit III! li |< ):i!.f!, diift fiiffi ihf knilr fli lli^ 
CxtM-iJiiry of itif i,.\i, -.(id 1 iji ii iliiinyfi 4 lifllc (loping f 
tticfi, y. iffi .:ii .liifi'iO «l'#'^i.ii!dif I III itl rli# kiiiftfy Mit off th^S 
Ijili. I:ifll/, f'yoil.'i piopri Mll^, ilif |,fii u fo I ir |)i ought 
ififii .ih liJii<!/'iiji( ffffiii. f'.iii i},f '. i« j» ji'it ufrri v>,.itf!t t»i bt 

Hi' ri'li.'l fiy ;ii,y I |lfif;'i,| fM.i|.|i;^, i'rt iImI f iljfi 9 j rOO;/f(. 
II/-!-.. ^iii'l .'.'A*/. I'*'/ fj.'ii; .1*. ti rl.* f.i'., ff»'r* /nir, hr nln iH, 
•*i iiM-i,'!' •!> / ill '!.»• / lilt', jf'' J »• I ; f..Mi' #1, if iiniA II'. J.i'.*/««l 
j^jiji, j\ I,' loM '111* Mill. Ai.'l '.sf'ivi, ilijif iltf tfif.iiMi of 
fIm- mIi dnif' 1,1 '.|u ! 'o'l.^ '. '. 'ffi! ot »I,r .Jowuii;dii<ti0lc4i 

of ii •• ;■ ' •#. 



/.v//i 



OP mVMAIfSfllt^. 



73 



Copies fw Round Hand Text. 



Av(^k1 Kid company. 
Cnrc lied I oy 9 the body. 
£xpf c^ to rc(*eive as you give. 
God is (HTfcA in h'\i worki. 
Innocriicy ncct! not fear. 
Keep t'aiih with all men. 
Money corrupti many* 
Opportunitiei arc flighted. 
Qtiier men have q^ritt minds. 
Sin pmduccs (hame. 
Value a good confcience. 
Wifdom is valuaUc. 
Yield patiently to fate* 



Be wife betimes. 
Do the things that ire jufi. 
Frequent good company. 
Hours fly fwift away. 
Join experience to theory. 
Le;irn in the time of youth. 
No ca(k is too hard lo Icaru. 
Provide againft poverty. 
Remember your dut]f» 
Time and tide ftay for none* 
Underftand your trade. 
Xerxes wept at mortality. 
Zeal is fometimet proper* 



Cities for Rmnd Hand. 

All letters even at head and tail muft (land ; 
Bear light your pen, and keep a ileady hand. 
Carefully ftrivc in each line to excel ; 
Do every thingi tliat is to be dt)nr, well. 
F.aocel in each new line, in every p.^rt : 
Faults for the future (Imn, by rules of art. 
Gripe not your pen, but hold it very flight. 
Hold in your elbow, have a left h^nd light. 
In all your writing at the copy look; 
Join all your letters by a tine hau-Ihoke : 
Keep free from faults, and blots, your copy-book. 
Learn the command of hand by frequent \ife. 
Much pra«fticc will good pcniuandiip produce. 
Never Urivc to write too lull at firil; 
Of all a Ic.unciVs faults, this in the worft. 
Pra^icc alone can produce expedition ; 
Quick writing is uioft learners* vain ambition. 
Vol. I. K . 



Rule 



94^ At fMMANSUir. 



»^ ' *" 



KuW YOU) )iuc« i^raight » and iitiikethcm very fiuci 
Set t\rm« of Ifitcn fiiir Abovt iht \\\\e% 
TlW io|>s <^bovc ihc flcn)^ tli« uib t^elow. 
lUe poxinct to ppefi if ihe ink |o througfi. 
Vir\r well jrour eopy^ fee how much you mend ; 
Wij>e cJean your ptui your tnik beinf at an end. 
Your fpdUni; mind, write each word tnie and well; 
Zealoufly Arive good writ^rt to excel* 

J Hectifilfor making hhch Ink^ 

To 0P9 quart of fell water« put four ouAces of frefli blue 
lalti of Aleppo, Im uiled pretty fnuill i two ounces of cop« 
perat \ and two o^mcet of f um«Ar4bic% Bottle It up, ami 
(bake it once a day^ and in three or four weeki it will be fit 
for ultf* 

The green peelingt of walnuts^ foakrd in the water before 
the ink it mado (if they bo in ftafon)) will render it the 
Aron]{er| and more beautifuK 

Simn^er three pinH of Hale beer^ or vinegar* wiih four 
ountea of ground Bratil wotx)| for an hour; then drain it 
through a flanneU «nd bottle it up for ufe* 

Or a liitW gunuwaier and venuilion will m^e a curiout 
red ink fv^r preleot purpofe* 



SECT. II. 

OF SlJtCAST WIIITINO. 

SfcaKr writing may be perfom>ed fe\*erAl ways. Former 
am well) very feitilein invenuon» of this kind ; an%U by 
ihcfe n)eanSft inteDigeiiee has been obtained by countries, from 
••* ■• others. 



OF PBNNfANSHXP. 75 



othert« with whom they were in a il.ire of holtilit)* ; nnd 
that not unfreqtientiv in mcxlem times. It may alio fervo 
individual purpofei, where fccrecyis required. 

There are principally three ways of writing, fo a« not to 
be read by any, but thofe who can difcnver the manner in 
which it i« written. Firft, writing in cipher, which requires 
great ingenuity, and of which, my limiti will not permit me 
to fpeak. Secondly, fubftiturlng other arbit rni)' nurkb or 
characters, for words or letters, than the words or letters 
themfelvcs. And, thirdly, writing with fome ink or liquid 
which trill not appear legible, till rendered fo by fome me* 
chnnical operation. 

The fecond method, of fubflituting one chai-at^Ter for ano- 
ther, is eafily performed ; as any perfon might make an 
alphabet of his own, confiding of twenty-fix rhara^^eiSi 
each of which might (land for fome one letter of the Engliih 
alphabet ; and thus the writing would be unintelligible to 
any but thofe who have the key or index. Or, the nume- 
rical figures may be ufed to the fame ptirpufc : as for cxamplcy 
tf may be reprefcnted by i ; hy by a ; r, by 3 ; &c. a« follows : 

1 a 3 4 5 ft 78 9 10 11 11 n 14 15 16 17 r8 fo io'ii IS i) ?4 2 ; 26 

a,b,c,d,c,f,g,h, i, j, k, I, m, n,o, p, q, r, f, t, v, u, w, x,y, /.. 
According to this index, the following fcntcncc, riihn gain 
fricnA^y will be written thus : 18, 9, 3, 8, 5, 19. 7, i, 9t »4- 
6, 18, 9> St 14, 4, 19. Or the figures, to corrcipond to 
the letters, may be placed in any othtT order. Or the letters 
in the alphalKt may l)c tranipofcd. Certain conl'onants 
may l>c fuhllituted ioftjcnd of the vowels, and the vowels 
^illcad of the confonnnts : as, inftend of the vowels, /r, /•, /, 
#, MyXy life /, w, «f, ^, q^ r. nnd i/.Vr Tvr/ii, rcfpe«5livcly ; then, 
iho foregoing fcnteiKC will Hand thus : ynifms j^ini /yfimuii. 
And an infinite number of o:hcr uays \W\ghi be invented, 
by this mode of fublliintional wriiinj;, which the in^'vnious 
reader will difcover; fuch as, dividin»>; the alphabet into two 

part3> and tranfpofirg the letters whkh (land in the fnfl or 

Jv a fecond 



I 



z 



6 Off nnuAm§mVi 



Ucrmd pU^c, ia oa# p»it, wifh tiutfn ia Ui« ftrft <»r kUihd 
pUicr, in tb« otter pdrt f or^ 4ivMliD|j{ U iam ihrna ciAumuM^ 
and applying iUi$ f iiW alternately ( firft, lo (be fit tt £/jMmn« 
>o4 tbeis lf» ttie ftcofui ; «md a number of <4b«rr wayo ih«r« 
»r«$t too fiiim«rmi« to meoiioo* 

The third way of writing (krrtly, i<f ^ifft» by wruing 
witk tiiejuii^ofa UfDOfii the JMice of an onion^ uiuu:, or 
tbt ifhritft of vitrbly which will not ap^r UgibU uU it bf 
boUieo u> the fit e, 

6econdl) t by treeing the letterc on the beck ^( the p^peff 
efter it ii writti;f}« with a pen dipped in milk » th«(e lirtterc^ 
fo trm^df will not appear legible^ till che paper be holikn to 
the Are » then they will appear of a bluiOi coUmr. But, m 
lbi« nuinner of writingt the paper AotiM be vtry thin* 

The U9 metbwt I fliaU meotioot i«» by ufing fympathetie 
inkff aa they are g/fwnily called { there are various prepare' 
tkioe under thi« n^rnc* I fliall mention only Hko, and 
which may fafely be ilepende4 upon* 

f « If a little green vitriol be diffoUed in water* h ifU h little 
nirrPii^ acid^ thecberai^rf written with it will be iuuUiMf 
till fhey are wetied with the following mhmfci — 

Put two onneiES of 6nall Aleppo galU in h«df a |iini of 
water s witen it haa taod three or four day«| pour it olf . A 
pefieili dipp<c4 in tbia mitturei and drawn over the leti^rip 
written wii i) tlie (ormef ink, wilt render tbeoi of n Uauhful 
Mack* 

Ort tetterc written with the latter ink, will be invir»tit<r, uU 
they ara wirtted with a Muuon of Pruflian blue iii waier $ 
and lettcrc written with thia fotution* will atfo be invi(ibt«, 
till wetied with tlie above ink of galU, and water. 

a. fncorp^irate one ounce of litharge of lead with iwo 
ouneec of diftilled vinegar $ let it (land rwetiiyrfour lioure, 
then drain it off, and let It fettle. 

Put one nunce of wrpiment^ m powder, and two ouncet 
of qui'.k lime, in a quart bottle, with WJiter fullcicf.t ro 

tovcr 



or fKMUAIUIHI? 




cover th«m ttout nu inch abovt the ingi'Mlicnts IHacc tb« 
bottltin a modermt haati fur twenty -fuur bauni then pour 
ieolt; iiid cork it cloftf . 

The lettci*« written with the form«r of thoftf inki» willnal 
appear tillthtytM cxpoltd to the vapourt of tlili latter iok| 
when they wUl appear perfe^^y plain. 



nMHOMI 



SECT. in. 



^r BFiaTOLARY WMiTiNa, ANP aupitaaciiirriuai 

OV LttTTKIia. 

Op every i^iei of compofition, there i< none thnt* In 
iff natnrri appmachci nearer to familiar converUtioo 
(except plain dialogue) thnn epiftolaiy writing. A letter 
ia a dircA addrefa fruin one perfon to another, niul fliould, 
therefore, eontttln all the c;\re, clcj;.u\ic, au»l l.imili.miy of 
converlfition ; paying; ihc ianic ic^mk\ tn ilu- naiuir ot ihr li|!*> 
je^\, ami the prrfon aiUlirlUil, im it\ a priiiMiaLippliiatiott. 
Tha principal tluiaitciiirunof a kuw air, lutuic, (impli* 
t'ity, fprijjhllincU, ami wit. The HylcDf .i Unci rt»*>\iKI l>c 
natorat) anil appear to cx|Mrl'a ihc f'cnviinr lri*lin^;H ol ihr 
mint!. It flu)ulil not ituliiMtr th^- ti.ill n^aik ot ihul). Tlirie 
flioviUl Ih: nt) t'otmal (livilii)u o( tlir paitn, ui) lahoincil iiitro* 
dut^\ion, nor pailucic coiuUiiioui hm all (hnuM aj>|)r.u' tht; 
f|H)ntaneo\i« product ot' th(* wiKri':. own nuutioiu. h IhooM 
likewiie be wholly tlovtiwl oj" any nMuplcxuy ov aoibiiMilty 
of expiclllon I lot' thin pinpoii*, ihr rruirmrH lluuiM hr tUtm, 
and ihc flylr prrlpiruoiis, li !lu)iilil rtuU.iin all thr viv.uify 
ofconvrrlahon. And, il t\\c wiitri hr lo.ilirr t)( anv svk, a 
kitcr (it ihr luhicCl pcrnul) alliUiU a» pi»»prr a pl.i»'r Uu ihr 

tliljtUv 



78 OF rexwAVsHir. 



difplay of if, ni any compofition whatever. A gentle fatire, 
a repartee, or a burlefque« may fooietimcf be introduced with 
fuccefi ; nay, it if often expf ^cd, in Icltcri on domedic fub- 
je^i, between familiar friendi. 

It is needleff to give copiea of letters on different occafiontt 
in fuch a number as is ufualty done ; the fubje^s of letr 
ters being as various as ihofc of converfation : any at- 
tempt, therefore, to give fpccirncns of letters, to fervc for 
every purpofc for which the writer may have occafion, muft 
be abfurd. A learner who copies his letter from any prece* 
dent, will not be able to exprefs his own thoughts with eafe 
and freedom. By being confined to a copy, from which he 
will find it difficult to depart, his letters will carry an awk* 
ward iliffhefs and formality $ and he will be a long tiirx be* 
fore he acquires that freedom^ and unadorned elegance, always 
cxpe^ed in extemporary writing. 

To form an epidolary wrirer no more is requifite than an 
intimate acquaintance with Englifli grammar ; whereby he 
will be able to deliver his fentiments with propriety in con- 
verfatiou. If he pofTefs this qnnlification, it will fuperfccfe 
the ncceflity of any artificial helps ; but if this be wanting, 
other afliftnnccs will be of little life, except to fcrve lo pub- 
lifli his deficiency to his foncrponcj'cntjj. 

Ncvcrthclers, in conformity to general cuftom, I have 
added a few examples. It need hardly be mentioned, that 
the name, by which the pcrfon is addicfTcd, be placed on 
the left hnnd fide of the page, at the top of the letter; and 
the letter begun jiift under it ; llu nanie of the writer at the 
Ix>ttoni of the letter, on the right hand ; the date of the 
letter, either on the right hnnd, at the top of the letter, or 
on the Ui't^ and at the bottom: and the letter flunild con- 
clude with the nan:c by which the receiver of it is adclnlfed 
ht the beginning. 



Fro?H 



OP ruNMAifiHtr. 79 



fVoM tf Mq/hr io kh Scholar, during tk9 HQlUofs. 

De«r Georgf , 

I take the firfl opportunity th^t bat offiii'eii 
to inquire after your health, and that of your friendit And 
I expci^i that you will regularly anfwer each of my lettcrti 
that, during thia time of Irifurci I may have an opp«irtunuy 
of ohfciving, whether you rrmcmber, or have forgotten^ (lit 
rulc« I formerly gave you, concerning wi iting Irtrcri. 1 noW| 
therefore, call upon you to put thof'e rulei iitto pradicc* 
i}ur, willing to grant you every imi\)lgence at thii time of 
f^flivityi and left your recolle^ion (liould ikK be to citart 
a< when in conftantexeiTifc, I fliall briefly re(ieat thoi'a rulti^ 
to which, I hope, ytm will [My a (ki\t\ attention* 

You rememberi no doubt, my full direi'Uon wai, to be very 
rorreA and circumfpeA in pur fpelling : thii ii the fltO, and 
ntoft eirential i^equifite in all kindi of writing i and make ufe 
of no woiti^ of which you do not perfeAly underDand tht 
ff nfc. The vulgar p;trt of the world, in general, are very 
much nddit^\ed to (hit al)l\irdity« You will, now, oCtrn hear 
profile ("ondemn a work, an ut)gramntanr:U. and dcticiciit in 
the ornawcntu of ftylo, (hough thnnlclvrn l>r unacfpinintcd 
with ihc ftrll tx>rm of gi honour, and know not the meaning 
vi a fluvcr in rhcioiic. — Avoid rc|H:tition8 : ihcy alwayn of- 
fciul the judicious car, ;«iul .ire fcldoiu pn)|>cr, cxrrpl when 
they enforce M\y particular mcainnp,. or explain It more fully, 
rarcnlhcrci arc alwayn inelegant, ami (hould never ht ute\l 
(/'*/ ^i»/v« ^h/olkuty HetxffUry)^ an thcv render the lenience loo 
complex. Never uie the lon^y in a woivl, cxerjit when two 
meet, in which cafe it is ncceflary for dilliurtion. A letter 
interlined ha« a very tinj;iacclul appeal aiur ; it is alio an af* 
lV*^nt : K)r it indiv ates cither la/inriii or inililVeirncc, or hoth. 
I Mo noc;)pital letters, but at the br^inninj; of a Icntenco* to 
pn^l^er name^, and to the fud wotd of every line in |>octry» 
Wl^cn you wifli to l.'v a ilronp en^phalis on any woid, or in* 

tend 



td or VBVM Aifsnip. 

tend that it (hould be paiticularly noticed^ it is common ta 
draw a ilrokc under it with the peoi tHiu ; fucb wordi^ when 
printed^ are put into Italics : bur, when thefc cmphatical words 
are employed too frequently^ they lofc their efeft, and when 
vfed imprdperly, they piutle the reader. Beware of ufing 
many monofyllablci, they are infignificant words i nor life 
many too long words, left yon exceed comprehenfion* Sbua 
particles, as much at poAiblo : be tcry fparing of jonr 4Kmdt^ 
firSf and buts* He not fond of inventing new words ; thcro 
9xt enoagby alrcadyi to exprcfs ail our ideas : and raorCf I 
fear, than you will ever fully comprehend. Be atltmivc X6 
the rules of grammar, and do not jumble the prdeot^ pBft» 
and fucnre times of the verb together ; as many inconrcA 
writers do : neither confound the genders of the pronoon i 
nor ufe the Angular, for the plural verb; which is frequently 
done s as, ^mt lutfi, for yau vttrt. If the ientenoe be coftdi* 
tiooaU ufe the conditional mode. Let your flyle be fimple 
and perfpicnous, and yoor femcnces fliort : let it be as coocife 
as pofliblf ; for a prolix writer tires the patience of his reader. 
Obferve that your points be all placed juftly, which wiH add 
grace and perfpicuity to your writing. Thcfe hints I hope 
will be attended to : let me fee the cffcAs of them in your next 
letter ; while I remain, with compliments to your father and 
mother. 

Dear George, 

Ser^/hire^ Your finccrc friend, &c. Jcc, 

Jam. a, 1803, 



The Scholar's Anfwer. 

Honoured Sir, 

I return you my finccre thanks {<yt the kind 

attention you (hew mc. J t fhall always be my ftudy and am- 

bstioo toiblJow your inflrudions, 1 never write a letter to 

3 any 



or rSHMANSHlP. St 

any of my fr'tcDdt, but 1 pay « paakuUr ngud Co ail (be Ui« 
re&ioni you have given mci on the fiimcft of lctur«wj itiiin, 
I exeiriie niyfelf dailyi in grjunauir, arithmetic^ or (oa^ 
other part of. litemtnre; my tutbcr infiiii upon my fettiqg 
apart two hotiri every niorning for that ptrpofe. >ly t4^. u: 
and mother defire their bed rcl'pcAs to you, aiid return yu^ 
their kind thanks for the trouble you hu«c taken in your l^tq 
letter. I renaaio, with the greatcft refpeAy 

Honoured Sir, 

Your very much obliged 
Ltfeibnf And huntblc Scrvapt* 

^0/1. i0| x8o3* GaoAGi «**. 

.itfi . 

A Letter from a Dather to kli SoUy ai St hoot. : 

My dear Boy« 

I am cxcetdingly happy to hear of tbc greaf 
progrefi you have piadc in your learning. I hope you will 
continue to pay the fame attention to all your mallcr% ii^ 
ftruCtions as you have done hitherto. 1 have herewith (^ 
you a prcfent of a goUl watch ; which 1 dclii^i), in the lii ft 
pl\ce| aa an encouragement tor you to piocced ; and, in the 
fccond place, ai a monitor, to remind you of the fwittiufs 
and importance of time. This little machine travcU with 
the hours, yet keeps pace with months ; ii keeps time with 
minutes, yet does not outrun yeais. Whenever you look 
upon this little prompter, let it remind you of your time* 
Every complete revolution oi tlic minute hand filently in- 
forms you, that there has elapled, what a whole world can* 
not redeem — nn lour of your precious time. And, though you 
niay perform in the following hour, or half hour, the bulincls 
that (hould have been done, in the torc^oiii^ houri yet you 
mud remcnibcr, thai one hour is tor ever ir^ (^ ovevxihly lo/i. 
The whole life of man, at the longell, is but fliort ; there is 
no time to lofe« Though you make the bell ufc oi your 

Vol. I. L time 



time potRbkt while youngi you will lietcafYcr (if yoti hftve 
Any ferioui reflcAion) chide youtfetf, thflt yon improved 
y6tir time no bertef. 8uffer no portion of your time, thnui(h 
•ver to fmnllt to pafi unemployed i btit let me give you the 
•dvioe which Lord Chefterfldid gWe$ hit foti, on thii fub* 
Je^i ** TakO un of the mlnuten, for the Tiouri will take 
care of themfefvci.*' I hflve read of an Augdftliie monk, who 
kept a daily diary of hii timey for upwfirdi Of rhirry yenr^t 
that he might know how many houn, out of each twenty* 
four^ ho had employed in literary and religioiin rxercifen, 
how many In fleep, how many in the neceffary avncationi of 
the dajTf and how many he had fliamefully l6{f In floth, or 
unpiidCabie cooverfatton. And Cato^ having fpent a day in 
which ha bad done nothings thotight it a matter of furh con- 
(aqueftcc, aa !• ba Umanted during the raft of hii life. 

I do fiot mean by what I have faid, that 1 would have you 
always at your book, and allow you no time for recreation, 
tn the houn appointed for play. If you And yourfclf fo dif- 
pofad, Join in the diverfloni of your coihpanloni ; but If, at 
my of thcfa tlmei, you prefer your bookt either to anticipate 
*yitlr future tafli»i or to refer to any of thofe yott have gfrnc 
through, it will letter anfwrr the purpoib of your rrfidrnce 
at fchool, which it to improve your mind in iifefui know- 
ledget and not In childifli ('imrtsi It will redound more to 
your prefent crediti and conti'lbute infinitely more to your 
future advantage. 

All that i mean by what I have advanced, Ifi, that T would 
never have ynu perfrt'lly idlr. When you arc not at yoiu 
piny, be Ht your work i aiul whrn you are not engaged at 
your work, you may Join in play at the appoititrd times but 
nootberi. Ilcwarc of an InanimHte indolcnrr • foinc l)oyi arc 
too great cowards to play, and too great dunrrq tolcain. 
Hence tlicy fland idle fpefthtors of alt that jids, and grnc- 
rally, in thr iiUir, prove idle mi»n, who arc the inofl nnpro 
fitable animalN in the creation. The Arabiaiis Imvc a prove tb» 
Mint *' an WIc perfon Is a' playfellow for tlic devil." And it 



OV PSNMAMSHIF. 83 

is A maxim of the Chincic law, thnt, " for one idle perfon. 
the whole Kate luffcra." Whkh ii •• tnie «• it may appear 
novel to til I for he eati the produce of others* iabour» with- 
out making an adequate return. 

In order to guard again ft idlcnefs, never give way to pro* 
araftinationi or defer that till to-mormw which may he at 
well done to-day. Many people poftpone their hufincfs till 
a future dayi merely l)ccaufe it is future 1 but you muft re* 
mcinlKri that two days agoi yefteriiay was a t(>-morn>w ; and 
two days hcncci to-morruw will be yefterday. Ncvefi tlicre- 
fnre, defer that to a future time which may be done at the 
j>rcrcnt« without a very fubftantial reafon. 

Laltlyi attend to the manner in whirh every thing is per- 
fbrmedi even the moft trivial matters. It is not (MRcient 
that a chapter Im read| or a copy written, without a fiiultt 
but they IhouUi be done welli with all the Ikill you are mailer 
ofi if you mean to excel. Whenever you fpeak* though it 
be to your own a>mpanioaS| be furc to exprefs yourfclf in 
the moft proper and expreflive words, paying a ftriA atten- 
tion to their grammatical conftruQion. Whenever you read« 
though It be but a fign-poft in the iircct, icad it with pro* 
priety and cmphafli. And, whenever you have orcnfion to 
Nvntc« thouf;h it be only your name, let it be done as coircA 
as poiTihle. Thcfe dirc^liun^. (xmllantly oblcrvcdi will render 
you an accompiiflird cluiraiMcri in wlutever department ot 
life you may Ik engaged. 1 ho|)c the fote|rning hints will l>c 
furticicnt. l.ct them be well attended to, at\d 1 (lialli no 
doubty fee the effet'l of them in your future acquifiiions. 
Your mother and fiHer join with me in their love to you. 

I ami 

Dear Boy* 
Lcnti0itt Yottr loving Father, 

iifttrrAaoi tBoj. Thomas »•», 



L ^ Ttf 



(14. ^^ W^fMAMrnNII'. 



<■■ I I 



Irrcelved your Ictitr, with yortr MnJ prefuu 
,of the watvh ; for which I return yon many thcinVi. I hope 
it will ^\\\^)'% have the tf^A you flc(irC| of retniuding me of 
the (liortncr» and importance of tintc. I nc%*er look at it, 
t)vtt I recollcift your alarming letter. I fhall alw.iy» fet a juft 
sA\\\t hw lime — it in impoffihle to over-value it. I (hall be 
|Mti!cuUily attentive to all the commands in your letter. 1 
nUcn decline the dWernohi of my Ichoolfetlowii and appty 
to hiy btKiki conformably to your de(ire« Yeftenlay t entered 
luto DccimaJ )'>ai!lipii« | which having gone through, my 
m^ftcr infoimi me, t mall begin Algebra. When I have the 
plcjiiurc of .coming homei ockt Chridmai hoYidayii t have 
no doul)t| but you will be well (atiified 4hat I have m:ide a 

'• I 

);;oo<l ule of my time. Pray give my duty to my mothrri and 
piy kin() love \o tity (ifter. 1 ami 

' , Honoured Patheri ' 

Yoiur moft obeArent and duitfnl Son» 



:l 



fVom a ffoutig Shopivrpfir to a tf%otrfale Drain . 

' Sir, 

By the rtGommemlation of Mr. Clwtpmnni wlti> 

U n)y neighbour, I think |)rci|)er to apply to you for the fol- 

lowitij^ attijci :<— Two doxcn picrc» of yard-wide ca-ico, trti 

piece* of the bcft jacmiet Amflin, thirty piccei of cll-wittc 

town ptintsd cottmi^ 4c. &c. I hope yr»n will let thcni Ik* 

of the hdk i|uilil^v of tlirir Itxt, and at :i rcHionable pi kc; an 

I intend all oni clmlingi fliall Ix; fur icady money. 

//''//« 1 anil Sir, 

March aO| 1803. Ynuri| 3(c. 

• fir 



r. 



Sir, Lmuitm^ Msrcl 04, 1^3. 

I Imvc, in onfwer to ymir fiTour of the 
Aaot, fent you cbc articlet you oniered. Should you thhih 
-vpcr ro favour me with your orden, 1 have 00 lioidit hot 
0ulII giire you ample iatishifticm. 1 imi 

Sir, 

Your obliged Senrant, 



Prom Whuhfah Deebn it n JtgHM mm. 

A« you have lately been very backward in your 
:tiuttanccff wc arc uoder the oeoeffity of iu&rming yout 
uc, uolcf« you icod ui ao hnmcdiate draft, or order, &r 
cX fibirh hai (b long been due, wc muft uie fucb nyaoi 
i »i!i prove \tTy difjgrecable both to you and ourtelviei. 

Wc remtin, 
Liverpcal^ Sir, 



7 /ue Afijwtf. 



Gtntlc:n;cn, 



Se^rril fe^ere and uocxpeAcd lotfb lure Iwen 
lir 6>lc auic of m^ Ure rtmiSotU, I am very feofible of 
i^ Jcoity you bkvc atiw2/« flicwn me. I ooly rofueft youf 
ccepcance cf i»y Uil, payabx in two flno9tb«; nviory bciof 
; xtU iifTA: scty k^rcc^ ^ui my dr^tors vcfy hacknar^d io 
brii {.4) «)ciit(«-*Sb<;uid tbii be igrcCibie LQ yxM^ I Iball 
,%'. *;► t ^/e very puL^uii ioi tlic (uliifc. I am, 
JJ/riJh.r/, CitnCitrtnttlf 

'l^rJy 30, i^G; . Y^-t:f n.'jch cbiigcd Servant^ ft(c« 

7^/ 



OP nnntimsHiF* 



Sir, L iv er f m l ^ ^/rf/3, itej. 

As wc (houM be iorrj to diilrds you^ we irt 

willmg to accede to your propo&I ; and hope, that, hj the 

time joo mentioD, you wUI be able to make good yoor pfO> 

mile. We remain. 

Sir, 

Your honUe Senrantt, te. 



JFVofli a Tradefimtm to kis Fricmd. 

Sir, 

Relying iipoo the flnoerity of your friefMlihip^ 

] have taken the liberty to Ibltcit your afEflaoce at this cri* 

tical juo£Kire. My affairs are greatly erobarraflcd ; and^ 

nnleit I can procure the fum of soo^ I fhall inevitably be 

ruined. If, thereferr, you can oblige me w:th the abate 

film, to be paid by inflalmentt, at three, fix, nine, and twelve 

months, at jo/, each payment, you will fave noe from im> 

pending bankruptcy, and infinitely oblige. 

Sir, 

Mttrcb a?, i8ot. Your diflrcflcd Friend, && 

I 

F. S. You know the Talue of my ftock, and alfo my ex* 
pcdations. 

The Anjwer* 

My dear Friend; 

I am very forry to hear of your preicnt £S» 
cultiet* I defire you will call upon me to-morrow, when t 
kope I Aall be able to accomnnodate you with the fum yo« 
want; or, if I cannot fumifh you with the whole, I can let 
you haie the greater pact, and the remainder in a few d|yt. 

lam, 
Wyiwumjier^ My dear Friend, 

30, 1803* Youn fincerely, &c. 

It 



4P**PBNMAlfSHlP, 87 

■ i^^M^^B— — ■ ■ m n I 

. It IS as necciniiy to know how to direft, or fvblcnbe, at 
to write a letter. PerioM in high rank| and peculiar ftatkni 
in life, are to be addrefled in a peculiar maniier. 

For ihe DireSHons or Superfcriptions of Letters. 

Te the King^To the King's Moft Excellent Majefty. 
Te-ibi ^mtim^To the Queen^s Moft Exoelleot Majefij. 
7# d)€ Prmci #/ M^«/b— To Hit Royal Highoeft, George 

Prince of Wales, 
7# tbi Princefs^To Her Royal Highners, &c« 

To the NfJMity. 

7e a Dhke^To [HlsGracc] the Duke of, 2rc.« 
fea Marquis'^To [the Mod Noble] the Marquis of^ ttc. 
Te an Eari-— To [the Right Honourable] the Earl of, &c. 
f # m FifceuMi^To [the Right Hon.] Lord Vifcount, &c. 
Te • Lmrd^To [the Right Honourable] Lord, &c. 

The fons of dukes, RMrquilTes, and the eldeft fons of earlt, 
bavc the title of Lord, and Right Honourable ; and the title 
of Lady belongs to their daughters, with the addition of their 
Chriflian and furnames : as. Lady Caroline Ru (Tel, &c. 

The eldeft fons of dukes, marquKTc?, and earls, enjoy the 
fecond title of their father, by the courtefy of England. 

The children of vifcounts and barons are alfo (lyled 
Honourable. 

7# a Baromt — To [the Honourable] Sir J. H. Bart. &c. 
lo a Kui^bt— To [the Right WorOiipful] Sir J. H. Knt. 
7§ a Privy CounJtUcr — To [the Right Honourable] J. H. one 

of His Majefty*s Moft Honourable Privy Council. 
70 an AmhaJJador — To His Excellency, &c. 

Alfo plenipotentiaries, foreign governors the lord Hdli- 
tenant of Ireland, and lords jnftices of Ireland, and the 
captain general of His Majcfty's forces, have all the title of 
Excellency added to their other titles, 

* The words included in crotchety are fomctimes omitted. 

The 



or fKITMAIIffifr. 



TK« im1# of Rigla H«*fi<««ir»bl« it jfivcfi i«i fu* t^iiunttm^r^ 

of Uindnii, Yorkf nod Dublini m^ itM iitni^prt^vtA if 
iuliiiburghi diii iiig ttiKir pffu:« cHily* 

T# «v ^MUhthmTTn fb« Mutt lUvmnH Faih«r in Cj«4 
te* I Of, Ta Hif tifiiM thn UmI ArchMAiAp ol Yurt 

or PiiMUrbiiryr 
r# n nubu^-^-TQ tivi RiglH iUy«mid K«tli«r in Ud(1, Ikes 
or, To this UifA lliAui|i of, kc, 

U^* I or, To ctitf R<rv, h, Uf Aah(i04C<>fi of« Ike, 
T# //># /«/rr/#r Chrg^^TQ tlie IUv« Mr* A# la:, i or. To ihf 
R«f » Dr. kc. 

To thfi MUliarjf and Katfy, 

All coloiieU «r# ftylfd Hoi lOiifiibU { aud all irtfci ior oArtra 
(bimld biv# ibtt niiiut of tbi^ir r«Mk fet fiift j Mi To M»jtf 
O.C{ To Cjipuiii I. II. fcc« 

All ftdnurgU in ib# mivy iira ftykd Hono(ir»bU { dm uJ^f 
rior oMcrrf jtrc ftyUd by itusir ui»k| •« io ib« aroiy. 

70 tb0 L0rJ High Cbanitibr of Urtni JinniU -To ihe Kight 
Hoonurable J. U^rd U,, Lord U\p,h LMuiueWmof Givtc 
hrUain — l^rd Prrfi«lant of ib« Coiiiicil—l^iiiJ Privy ^tl 
MivOne of HIa Maj«Ay'f \^rm ipat hcrret^rif * of ^tau, Ikf » 

7Vf /^ MU^0i^ 0/ $bt Moih—To the Kigtit litmiturMc bir 
W.(i, Knt. Matter of ibaRotli. 

7$ s ]fit/^ji0^TB cbe Kighf linMrnrMt li. I^hiI H. L/ird 
Chief JuAica of tb« Kiiig'i BcikIi, or of ihc (.'ommoii 

T0 iht piL^r Judj^tt-'To rbtf Kigbi \htumiH\,\v, A. B, %{i\. 
oua of tlva JuAicai of| Ul, \ or. To JimI^i A« 

7# 






I 



r# ibi Oif^Jlmm^To che Hon. Sir A. M. l^rd Chief Bmua. 
7# Jfis l^fidhft AiHwutyx S^dttr^ mr AioHoH Qtmfrml-- 
To Sir A. B. Hit M^fty'i Attorneyi Solicitor, or Ail- 
vocate GfaenJ* 

Every judge hai the title of Right Hoooorablc, if a Privy 
CounTf Uor 1 etherwife ouly HoAourable. All otberi in the 
law are ftyled according to tlie otiice tliey bear % and ail bar- 
r'tflers iuve tlie title of Efqiiire. 

To t\e iMulenanaj and Maghtrttcy. 
7i a Shtrif^To A. B. Efq. High Sheriff of the County (ol 

York.) 
7# a Rec0rJfr^To the Right Worfhipful A. B. Recorder of 

the City of, &c. 
To mm AUtrmoM^To the Right \Vorfliipf\il A. B.. Ffq. 
Alderman of Tower Wai*d. 

The aJdermen^and recorder of I/)ndon aie ftyled Right 
Worfliipful, and Efquirr ; as are alfo all flierifiii and mayors 
of corporations, during their office. 

Ever)' gentleman in the commiflion of the peace Imb the 
title of Efquirr, and Woi Hiipful. 

To th^ Governors i>/* the Crown, 
To t^ Lord LiftittnMHi of hflami'^'To his txccllency A. 

Lord B. Lord Lieutenant of Ireland. 
Ts iU G9verMwf I^wtr Ciifiif^To the Right Honourable 
A. Earl of D. Governor of Dover Caftle, ^cc. 
The fecond governors of foreign fittiemcnts, np|H>inteil 
by the King, arc called I.ieutenaiU CSovcrnois. Thole iip- 
pointcd by the pro|U'ictors of the fcttlen^cnt, as the ILail India 
Company, &:c. arc called Deputy Governors. 

To fiihtr Hoftjl of VarUamenty to Comjf!fffiont'r<^ 

Bodit's Corporate^ &c. 
7§ iht H^uft 0/ Lord^ — To the Right Honourable the I.oul. 

Spiritual and Temporal, iu Parliament nflcmblcd. 
7# thf Hom/t 0f C^mmcMS^To the Honourable the Knights 
Citizens, and BurgelTcs, in Parliament a(Vcn)blcd. 
Vol. I. M Iv 



fj0, fij rffi\f^*'>'.iitr- 



mmf^mi^mm^mmmr 



r/* r|»/, P,.i;f /• :.' :, 

/♦ //*# /•*! •/ ^.i>Hfl 'iff tUr If/.j.Mit iMr WV*/ /if fh« 

'the jc^'/fft.f'f*, f:iif»rt«, '''. '#^ h/ff|#.rHl., foil^xf-if Ut, 
jfr ffylf! UV,:f'.ij.f.jl /»r I' jjKf W/,r flu; fill, '*f If/iWrtiMNV /.f 
Pi;|rhf Mon'Mif,!',!'-, if itiy ^f 'Sirm j^,ff f; 4f./ <.f fh'»if: fifln. 

/Vy/ //i/ f',t;nrinin;.' *.f lt*l»f< 

!,tf. K'"' .1.' . ',r V* i/ .• f,i' if' yoi. M.J/J?/. 
/.w/i- '■'//..« Ml/' .»,, /.: Miy if-.lrif/- ^',iir M; .'■fty. 

i -I it /'rifi f/i M I'l if/i, '.f */ 1/ I? J#.r ,k /'p'if i''i/ 1 1 Miifjhiii • .. 

'//»/! /;■/'/• •?•/ fy. ! Jrjrf', '.. ?!•/ .f jf'r.if^ y ,iir r#rw. 

/•/ / •,'/////., /':.'/-/, /'//#////. *^ //, /:.tff*tt' M/ I/.i^!, ^f Mj/ 

. J». :'■ , '. |- f '.. ;fl». y 
/ .* // /.If j'l// . I , '.: \i .y I? J»' I' ^0:ii M'»ri/iir« 

'/» /I h •! J'l i.r, M M</ 1' j/i" ii'r /'#'ii V/itffjj If, 

i It lift ( i>nl„tl, *' :'!.!;,,, '.f Ml/ iT j,'"./' /M.f f.;k/|^rii Jl 

7/# ///I 'U' il'ijhnj. ^^ \ J r J,i' i'' y^fipr ill \19-. 

7'/ « //'/A/»yi M/ l^'I'l, '/f M.iy It |il' 4ff /'illf l/ff'lfllip. 



Of ffsrieiafc^nr. 



ssnoig fan*' ccaer sf liicr Iiif wn'S iroirid he«c beeii toaiiztol 



SECT. r\". 

rjor* ti :.»!::-: ii»:^i :r*3T«r: tr.i.i i^ lie turiTiji unfit, v-«- 



;-»: i -■>-:' :f KTrnJ iCTi.-r-rL;*:i »:.i:± Bi crier u*.**r a 
_ : ''tC. Ht i.:.i M«t 1 ^^r'; c: 'itrniiE i^ s.pixjtr. oz :,i 

: 'riTTiT :.■: i^t tr^.'tr v, :rc- t^f: utt ?iT<t : <: .'arfr-v.-r 
r* 2.r'2 "-I* ic.Ti^ :-":-!'^--.T*r 12 :'*'rT» yx rr& c " :,5: j:—.f:- : 

'^ " •■ ■- '-■••,T»'ii-.7-'*-' -' --,^ -Ti*- ^'r»*" '*•* 'lT'"j*''' - " J ^^ryrc*'^^^^ 

t . ".t i:s * vM*:fi:t*^: k I'f «-.': las r a:ji '.titi .', t3br r nri 

■ • • • * 



94 ^^ MMMANMIir. 

The fliort-hniui uTitcr, bc:i(Je» thcfc advantj^cit roinct'nnes 
niakci life of fingle cluro^tcri to rxprefi whulc wordi, and 
eveii whole fentcncci : bat of ihit hercafier. 

Tlkc inik and pi iiicipal rule in fliort hand, ii, /^ mah nfi 
9j n0 mere Ulicn ibam are mtt^iarj 99 ^iifc /^r tci^tr an idia §/ 
the jQuml fif the "MerJ. For if the wriCrriife all the letters 
lh:it arc ncccHary to expreli x\\c/t>unJ itj'flj\ he will gain but 
little advantjge by it ; at be will be obiif^cil to ufc too many 
letters to l)c very cxpcduiout. 

But it muft i)c here obfervcd, that this rule rmid not be fol- 
lowed too ftrii'tly at fuft, and during the Icarnei'i excrtifcs; 
left it render hii writing loo imperfc^, and unintelligible to 
Iiinifclf. He fliould, therefore, at fii ft, Cf>nttnt liiinrelf with 
ufing every character for every confonant, till he be per- 
fectly arqtiainrcd with then) all, and ran very readily form 
then)} mat king the points for the vowcli, ai u hereafter 
direAed. 

Of the Short 'hand Alphabet. 

The fliort-hand alphalnrt ronfiiU of the following con- 
Ibuants : i, </, fox v^ ^ or /, k or hard <., /, m, xr,^, ^, r» i or 
loft I, and &, /, ':v, x: c.i'.h of which hai iti proper cliarac- 
(ci, as fecn in the plate. The ( liara^crA li uuling ffif thefc 
letters arc to lie neatly joined together, to form U'ord%; and 
ivrittcn in the mofl ex|>rrlitionii manner pollihlc, without 
takiii;; the pen of! the )j;tprr till the word hr finiflitd; and 
the voweU are to l>c noted atteiw^ndfi (if necefliny] by (lointi. 

I'hongh the oniifTion of tttc vowcU may at iirll fomcwliai 
pu/zic tiic reader, to read even his own writing; yet a little 
pi Malice will render it perfr/tly faiiiiliar to him ; as the chief 
difficulty, both in wiiting and reading fliort hand, aiirri> from 
the novelty of the <:hara^eii, and from tlic w.int ol .1 familiar 
aopiaiiitancc with them. 

, In order to perfc^ the learner in the am fl ruction of all 
the (:h:ira£!er4 in the ihort-hand alplut;ct| it is ahfblutely 
ixxeflary thnt he fre<picntly co|9y them* Jk fliould| (bily, 

write 



cr Ve^makseii^. ^^ 



•arrt i c:»Z'j o: 'hs iharr-hand alpfaab?: : nilxng fai? ime 
i^ici/rf iTg :o zht dxr.sd iincE h dit firf: line rf" the firt isfTos 
;i lilt ^''.jcs ; aiji v.rrtbg tht f.gT;rfiza:i3r or eaci: crar a ficr 
2: rljt £::*i zjc caih lint. End trit isncr it rrprcfenti. a: -the 
bir^'-^ '-£ of tilt Ilrsr : i:f-::|: thrcs ar four lines of ? nnarto 

li "iiit *- z/i'^itsi r'vci, I douiit not bir. fhf cliaraft^rr wHl 
'ii* :':"-- hi CLzn'ir. \i^i fi*: p-ai:i=t ar arvrrtsnt. Z have 
t-itLiccrtf :: zi.:?L.t * iiD^iEfc o: ^it tnuft impk. and, m. 
ti*t i«.rit r.Tt. tjt nnjz c:f::uc: thanif-.LTL. Z fi;^". on**}- 
cco'fTte rht: :t 1:*^ iit.p itz ri.i: uipiiitiitn, ani ::it uiiDrt- 
Vtr^T-i -tf t^iTT : 1^ Jc«ir. 7 ii?vt becii abk tc fulicm ihe mofi hipia 

Tiii i/ptasbr^ diotir-- ::o-£f:ir-p of tht diarafters for & 

bcrr fix»fei br cnncr i or x. arccrdinf » r k Tro'ponuccr 
Lsri tr i'jr. Tnt r zirr i^trj -wcL' Dt omittcc ir Ch-jr: iiancL 
2X ".'^ '^'y^ *.:. i.':jnr::v.ir yf tbt b'satr ■ and ttit fuiino of tiK 

:'ir- v;.i:*r t;iii *iii iuzit jcmiiri /^ ir a'lL vjppittd br ^» 
'r ':■':: g :»i > t r.-.zHft:: :/j..!»i "::«it riR:: icr-er. 7' it rrursieuttC. 
:: licrEijy, "T" tie v-jwi^ :. r.i'\-.r:e^j:a.c:'vxxK ianit i-JiinC ; 
-.r - = :7 i, f • ^*~ V t.ii^i r d:fi*n ii, i-jun:. n;r. * In.iL. ocinr 

U:;=,tl ; i.1 "W .« Cii .it:*:L iiKTCSfAS^'- 

1 . r:c .. -i>. ^ -ac^ n^^zn i.. ^ ^ c^^amcu'^. c*Tt li iiux'Ukb. 

l_^ .• '.1 .X,- i; Itf C»l. TK Ut 1. • &.-'. ..<: ^.. M* ..••II. *» t^ L 

' ■ ^ r ' ' 

" - *~- - •i'v'' - 1. ■ ■- • 4>-» ..■^.tv'i. j^.,« ^ , : , jr. , L. • .'^ -C^- >.■ ..«M — 

•■|* i'*"'!"" - t r • 1*1' • '"•i* -r •(*•• - ■ » • f 

.. . . f» • • t . I 1. I... w.ftt- n^ M I* 

- ■ ■ : •- -.1.' - .-c. i« -...1. t^^.-t, 1 -. 'i ■ ■-'- '-* '-•- 



%ltM ihf Itori^oftul clwrn/uri ;ir4r only b«lf litt: l^ri^ia of th< 
Liif^ty tfid iiittiiiH '>fKff. Foi tti« two lau«r <'Mr^ ^ficritt'/ 
#c«4ip)r the whfik f^t |iriw««(i U^<; two li/f/^t^ a$ f'.vM in i Ik 
|^kr«, Builbitt direct ifiu i^ l'> l^c flij^ljr »<lUi^<l Co o/if^r 
irbik lh4'' {tmm te formmj( tbe cb^ia/^t^rf finely : v/li<;ii hf 
tAm\€% to pin the duira/ici » togcttwrr, t«> (//i m w;r'li« it w\\[ 
lif #ifrrfi tmt4tfi^fy to m»k« tbcm I«f9 1;^ f^M4U:r ti^n) tlfca 
i^imI fl;eis; fi^iMiinci' fAT cmt^Kukncti, mid ^^ ^nUr ti^i-'e 
(fom MccAry b m will be Aicwn fo if* proper pUce, 

Tliif ktUfff 4ii ltor( iMiMi, i* fmmi by «f 1 1 ficlii^ C|in^>e: 
lin'-y 'f rriMll <rj^niem of a cir<:U ; ir (lioiild nlwdya \)$ f($rtmA 
fnm the lop, wbkb i# m ib« k^A biiut » «i»4 ufiirfrblly I 
wMild sMivifef fhfr iill MH^biK^ 0od hori'^Mid UMfi$ be 
fivrnvMl ff^m lb« lift bind pirt, «• it if tbr twAi $^Mtuf$U 
Mttd wiU b« fo«Mi4 tb« ii»9ft ci^p»4Uioii«* 1'bi« Unttr m»y 
n\io U tife4 iQ fffprefi the w^dt /#f iy ''^^t ^ ''^^^ ; ''»^» 
wkh • AiPi t UmtjiI Arokr JMfied l/i tb« fore perti ii repreicia% 
ttteword ///>f#^ en4 cbe i^me Ar<Ae« wbeu pUired m tl^t 
fciiHirr pertf fi|f»iAe« tb« word V//W ^ i u fbrwn In iH< 
|4ete# Tbif letrisr ie 4*fo iiM to denote the iidciaiabU; 
prepoTuiofM Ar« #^« end 4^^ wImeii ^\m\pn% tit e word ; ae , 
^/#hev«» #i('<curet ^<^ h $Ab (oim§ tbe ieriiili/^i</i« /^/t^cmt 
a^j/ff lifMi fingu!«r end pluridi und ///; »>, r^nutka^I^fiUfr/r' 
MkU$t iod t'f^. 

Thi^ later U uot diAlogHiiMd b)re Ceparatc liiii^ixcri 
Un HI 6/Ufid (eiuBcpc btfoje h, wbkb k pf^HiJ^d foi) u 
cit^Mrr hirdf lik«i(( ^trOAf like #, f r ii, tl»«ief«/:«, irpic 
fcfitcd hjr th': oiM: or #/1tcr of chefe cbere^ers^ ^'.>L/i;di<(|( (q 
iu Ibimd. 

li. 



OP PENMANSHIP. ._ _ . 97 



D.. 

This letter ia the ferment of a fmn!) circle, with its two 

pc^ints (lownwnrd* : it ii begun ut the left hand point, as the 

lull. \^'heii ufrd alonci it reprefrnts the word <r«4^, ham/^ 

tkndenti. It nlfo ft.ir\di for the prepofitiont d^^ di^iih: at. 

4/fbaie, Hf-vide, #/(/-pute« And \% ufcd for Che terininatUm 

<«/.* asi turn-r^/. 

F, or V. 

This letter is formed by n (Iraij^ht, downright or upright^ 
Hroke of the pen (for it n)ay be nuide either upward* or 
downwards, as is found moll convenient to the writer) • 
\Vhcn it foDowi a letter thnt Is finiflifd nt the bottom, it is 
fomied upvrnrdi ; bin when it Ini'cccds a letter that Is con- 
cluded at the top» \t is formed downwards, that the pen be 
taken off the pnper as fcldom ns pofBble. It alfo ftanda for 
the n», which h a letteV'of nettrly the famofound, l»clng only 

t 

n Utile coarfer, and is, therefore, • not diftingniflied in fllort 
hand byafeparate chamftcr: but if it l)e neeelTary to dif- 
tinguifli it at anytime from the/, it is only mnklng the 
cbarai^cr a little bUcker, or fuller. This loiter alfo rcprc- 
ients the words /or, i/", <>/*, #^, and /I-Tf ; and tho inllpniaMc 
pre\v>fuion far: as, /or-^V'l- -^'^^^ ^^^^" ti-rminations />■, //>•, 
fuly :<v\^fHhtrs: as, de-/-, fani^-/;;V, fori^ety'///, forgct/w/zic/I. 

C, or J. 

This letter confifts of a fegment of a circle, the fime fizc 
as tl)e «y, but formed in a ditlcrent dircAion fiiim that IcUcr; 
thifl bcinj^ in a vertical dire«5\ion, running from the top line 
to the \iottom one. It is nlfo ufed for ihcy, which has partly 
thr fame found as the fofi if,, lint, when ufcd for the /, it 
fliould be written fainter, particularly tDwaida the bottom. 
This letter may alfo be bej>un either at ihc top or tho 
bottom, as is found mod convenient to make it join with the 
foregoing letter. When ii (lands alone, and as a jj-. it reprcfcnts 
the words a^ain^ «i<«'«^» ^rcaj ; and as a y, it lignifics the 
\vordiyW*f,yi^, join. Joined to other characters, it rcpre- 

VoL.L N ferns 



9S Of reKMA^aiitr. 

fciiti the word grand: ii« /rus^father ; and the tcnninationt 
^r// andyWii ; as, S'i^"f con-j0im. 

Thfr« ii no cbani^Ur to diftingiiifli this letter ; for, at k 
is only an afptraiton of the breath, iu infcrcion is not ncM^ 
iary to difcover the fiouod of the word; it is, therefore, 
whol)/ omitted. 

J- 

This is reprefeoted by/; as hath been (hewn. 

K, or C hard* 

This letter is fornied in the dune Oupe and fizc u thtJ, 
but in the quite oppoCte direAion ; it is always begun at 
the left hand. When k ftaods alone, it repreients the words 
cs^f unUi and whh a fliort firoke drawn under the midiUe, 
h fignifies unmn^ Ufed as a prepofition, it figmfies r#«r, 
/Mr, uyAcamira: aSf /Mv-pound, m«<ca1, aodMa/r«-ry; as 
a termination, it repreients «r/#, ieal^ and ick : aSf fpeA'^^, 
period«/V«/| and trx^icle* 

L. 

This letter 'is formed of a ftinight lineal (Iroke, like the/, 
bat turned a little at the top, towards the left hand. It is 
moftly begun st the top ; but, if found neceflary, may he 
made from the bottom. By itfcif, it rcprcfcnts the wordi 
#//, alnoayt^ ahej^eifjer ; joined to other rhara£Ven, it ftands 
for ionv^ laiur^ 2nd iafe: as, /wu-ly, latter Ay, lateAy i and, 
as a termination, it fignifies /^ .* as in low-//, latur-//, and 
late-i^ ; thus, two of ihofe characters rcprcfent each of thefc 
words ; and when thus ufed, (liould have its vowel point \o 
the firft fyllable. 

M. 

This letter is rcprcfentcd l;y a ftraif;ljt lateral ftrokc ; aod 
is always begun at the left hand. Alone, it rcprcfcnts the 
words am^ amotifjl^ my, mine^ me^ nxthom \ alfo, much or manj\ 
when made larger than comn»on, it figi)ifies l!ic word more: 
with a fhort ftroke acro& the middle, it Hands for the words 

t-MUt 



or mtMAvraiP. 




HwVv at «iK^ or /Wf# tU nwmi^i #r ^h^itk lit f MMiy^f i 
whh two i\icb ftrokfti It (l|iilif« Mnv ite#i «i ivmhK lie. i 
Ai>il with A dot pl«cf<i undtr thf ini<idlt| it linnda for A#/ #i 
;«v«<A 9Kt J and with two Aich doti pluct d luidtr it| it l|« 
uiflei tho word »^« With tht Mgtitivf ftrokt undt r il. )l 
fignlAci «fi mtn nH/9 mmA ^^^ J(^«d with oihf r chumAff^ 
it ri*prtl«MU« th^ prcpufitioni mv«/i Mid mii i as iMfii/4y« 
>wi>!oi tMn« i and «» a t«rii\inatloni it ftanUi lor mt9i or «w«#i ^ 

N. 
TMi \«ttfr Vi formod of a itralght llnfat ftfolie» with thv 
tup a iitt)9 turned towarda tho right hand, It it moftly 
t)9gnn at th? bottom^ but it may be fnrmcd from tha topi if 
iT^uifltf « Wht^n uf«d aiona, it reprtAinti tha words #•, ^ 
utt4kri ai a prapofitlon, it ttandi fcr #«m» #»#i, ^, /»##»s 
»ii4rf; aa» «ii>#<oad«nt, 4nM/*podei, i«*t^» /•##r.fogatHint 
«»;«(lffv.m\na, M a ttrfoination^ it Aandi lor #«i and 9^if a»| 
l^nrm«f«/| haMif/)« 

This Ifttor )• twm^A of an inclined cnrva linct laanlog 
taward« tbo rt|bt hai^. It i» alway* b«Hon at tb« \HAX\mu 
NVhw nfeti atunt^i ii fta«Ji» ft^ li^fi wpi a« «/#m Mud fimr. At 
rt pr^pofition, it it^prafent* ^t^ /'#* rtuJ /ki; ««, /*•# plr«, 
/^#*ta|^i a«d /«^ion|[« Aia tviruiuAtioiu it i« ttsldom or 

TWi Icttw b formed ut a ftrnijjht ftn^ke? in a Jincttl iliw- 

tion^ witb 'be top cnrl^d ijuite rouiui tt^waiija the left hami. 

It n^ay \>a JEK^gnn tithrr at i\w top <»v iho Inittuin, an in fouwd 

rooft convtnieot% \Vh«t* it flatuU alone, it (ijjnKift the woidi 

^k<yfi>« and |^Mi4/4fy i with a Oioi t AioU 'A\:ro(^ the luiiiJle^ 

h r^prefonti the phrafe •/♦u</iV ii¥^*<«w.A ; aiulwiihadoi 

placed \)nder It, it ftaudh Ivm /m// /^ ^ii<i«/*>v i with tht^ 

•fgative marl^ wnd^r it, it ftaiuU lor M<^t /^ y*i*j*/i/i. Whta 

joined to othtr charaften, it rt?pi«?fcnt«i \\w wonU h y«^»n». 

md a f««n ; ai« a f »wf#r of an hour, a yw<»r/ of wain . Ai 

a ttrminationi it ftandi (or ^«</>f ^ ai, re-^K/Vf, 

l^ ^ K.I i\if 






too c\y fANUANfiHlP* 

R. 

Thifi Ittcer is formed like ihe gf bur in an op|)ofiie dirtc* 

t)oii. It ihny be forriHrd either iipwardii or duwnwardsi ai 
moft convenient. When ufe4 alunc, it (lands for ar atid 
ctf}fr ; when joined to other Lhara^t(^i6, it rcprcfdhts r<f ; as, 

r^ folve. As » ternriinatiofii it (lands fur /rry* f^Mt ^"M** ^^^^ 
iff aSj dl-aryt cicecd-//i^, tiirn-/r. 

S, (bfi C and Z. 
This dura^cr ic formed of an inclined curve line, and i* 
moftly begun at ihd t)ottom. It ic|>rc(cnt9 alio the fofi c^ 
and tbriK/ but as the n bM a coarf«r fonudi it niiy be 
risprcf^nti^d hyabliM:k6r and fuller cb4ra/>«ir« Wben uliid 
aloruff it ligoifii9i /y/, #>, i^i, and jf#i ^ wlien ic i* joined to otbtr 
cbara^erft, it dandi for /nth^ circum^ A/^^t and fuh t a«, 
/MiS'iy^ fiiniim^ywi,jufin'f^m% fult-ui^^ A« a lerminatiofi, 
U ftandft ii>r t'm%j9\f% «nd>#wr / ai» gfa«^/#», wyyr^i whom* 

T. 

This Utter is formed of an inclined but (Iraight line, and 
SI moftly begun at the to{)» Alone, ic ftands lor ibi and to. 
At a p»e|)oOtion, It llandi for irtinf^ ai, trsHfAffft. A» a Ur« 
minationi it lignlAee ly or //#4 { a§, beau-/^, lieau//>i* 

Thl« letter is formed f^f a flraight but inclined flroke, liko 
thcr tormcr, but in the oppofift* diredi'^n. It is mollly begun 
at the li(»ttom* liy iifcb, ii fland^ for iu///, luilt^ luoyU^ and 
with a (liurt flM^ke dra*-vn uridc^r the middle ic rcprcfcocs 
ixjill naff ill- HvouU not. Joinrd to a following charaAcr, ai a 
l>re|i(ifi(ion, it (jgnifics W/A; as, nxjith'Osxl, As a tt^rniinacion, 
it llands for luani Aiu\ nijttl: as, ow\,-^arJf and holy-iW/, 

X. 

This lerrt'r is forn>ed ui a ftrnight lineal ftrokc, a little 
turried vx (he botroni cowards the righc hand. It is grndally 
fornitd downwardt, but it n»ay alfo b« formed upwaids, if 
found more convenient. Alone, it flands (or gjkUf/u^ /**//(//» 
HiA f.iJfj/ffu, Joined to other ctuiis^Urs^ itrtprcfent» t^, 

a iJctrHf 



OF PEMMAMtlllP. lOI 

#A'fr«f9 and#jrfrr«/: as, ^.v-pofc, r^/fd-urdiuar}', r.uW^ingly. 
At a terminaiioDi it rcpreiciui itx : m^ coiiip-/r«. 

Y. 
There ii no chara^Ur appropriated tu . tliis letter, being 
reprclciucd by the vowel mark for i. 

7 

This letter is reprcfcntcd by thr ch.iraif^r which (lands io 
comiuon for the foCt r, and j ; as hath been fecn. 

Hcliiics the chat alters appropriated to txprcfs the confo« 
i^nutd lin^ly, thcic urc three other charadlcrs tor three double 
confoaauts, yii, tb^ Jb^ tb. 

CH. 

The charaif^r ufed to exprefs thefe two letten, it a ftraight 
lateral tlroke, turned upwardt a little^at that end towards the 
left hand. It is always begun at the left bind point. Wbea 
it Aanda alonei it ligiiifieti raib^ which^ and jitib. At a pit* 
poiitiony it itands for ank; as, anb-'nviL 

SH. 

The chara^er appnipriatcd to thffe letters w like the 
forejjoing; but turned lUmnwards at the Uft hand point, 
luftead of upwards, and like that is always bc^;un at the left 
band. When it ftatuls alone, it rej>refciiti the words ./A<i//, 
y/'ti//, and Jh^uiii\ and with u fliori llioki* uiulti ihr iniild!r, 
j^«f//, Jb§mU^ or W0iiU not. As a termiiiation, it ftaiuis tor 
Jhip : as, V!W\\'Jbif, 

TH. 

The cbara^er ufed to denote thefe two letters, is alfo a 
ftraight lateral ftroke, with the end turned a little upwardit 
at the right hand point. This is alio begun :u the left hand. 
When It ftands alone, it reprefents the words th<)i, tbtm^that^ 
ibht and tb^M* 

There arc alfo other chancers appropriated to expreft 
feveral treble confonants, which frequently occur in worda of 
inoft common ufe* 

CHR. 



102 nr PEXVAKSnfP. 



CHR. 
The charaAer ufed for thefe three lectersi it two perpeinfi- 
ruUr lines joined at the top by a curve : — it i» moftly begun 
at the left bund point : and i^ ufed in the words CV-ii -, aad» 
with the Tuwcl point for «» in the word 4^.ir^Bier. 

LCH. 
This (harafter it formed like the two iUrs of a triangfe, 
with the point downwards ; and is nvoilly begim al the left 
bond ; as the forc^Ding. 

LTR. 

This charav'tcr is formed like the two ridci of a fi|ttre» 

with the conjunction of the lines at the bottom* aiul toward* 

the left hand. It ii generally begun^ like mod of the ochcrs 

at the left hand* 

LTH. 

Thh eharaAer n fcrmed like that for AA, hnt with tlie 

point upwards ; and » begun at tlie left hand point. 

This charaAer is a double curve, and inclined towards the 
kft hand, at the top; at which part it b begun. 

NCH. 

This chara^er is juft tlie reverfc of thiU for Jt^ nnd bcgnr. 
at tlic left hand. 

RCII. 

Thb chamber is coinpofcd of the two (iJcs vi a imiaie. 
joined at the top, towards the right h;un!, 

RTL. 
This rliarai^er is an inclined double curve, Iraniri^; towards 
iIk right hand, l>eing in the oppofitc dire«^tion to that ior mfL 

RTH. 

This chancer is an inclined line, Icaninj^ towards the left 
hand, where it is begun, and curled quite round at the top* * 

SMR. 
This charaftcr is alfo an incfincd line, but leaning towards 
the light hand, and curled round at the bottom. 

SKR. 



or' ritNMAMVHir. 103 

SKK. 
ThU chArftAcr it alfo an iucliitcd iinci IcAnIog lowank Uit 
I ight limuli ainl curlod rouii<l «t the cop. 

8TR. 
Thit clMira^ter it formed of two Aririgbt Itiirml lines 
joinetl together at the \tii hand cud by a cui vr. Tim Inter 
nuiik l)e bc|;iNi at the cupi and at tiie right hand. 

SPL. 
This charaAer confitti of the two fidci of a (i\\utr^ joined 
together at the bottom uf the rij^ht hand lldr. It ii aiwaye 
begun of\ tlva \tti hand. 

SPR. 
This charaAcr it formed of a douhte cnrw, and incVmrd 
to>vard)i the left hand, like that for mfi; hut the curves a(C 
formed io an oppotitc diieAlon. 

THR. 

Thu charaAer ia an inclined linei leaning towarda tlic left 
liand» and curled round at the botfouu 

Here it nuifl be notedi tlutt the diaracUM-a rv)r thofc tl\^ble 
i onConanti are to be ufctl^ though the coitfunants which tl»ey 
repiciciU do not fullow each other inmicJiatily i a» In tlic 
worxli wZ/a*, and ari/An^clic. 

When the lf«iner 11 pnfcv'^ly ^c^iualntcd with the conftruc- 
tion and full rjjjnifitMticm id cuch of thr foirj»oin/jt'lwrai*lci*p 
he m«v then pitK'crd to join thti. ch.\iaOtc*i^ tt»|;cihci, iu 
order to fonn wouls ) ohfci ving, th.U ciu h i-lmraiHci be nvatly 
joined wiih the forc^oini; one; lor whiih puniol'r, it ii oticti 
rcquifite, that many of the oh;u4i'lcr« W funucd IcU tlwia 
their real fuci as i\\t\y lu* feon in the pUtc. 

Of tk^ Vourlu 

Tl>e vowcU, in fljort hanJ, »ie icprcfcnted by dots. In 
the peipendicular anil inclined lcttcrS| .< i*i rcpicfented by a 
dot, placed on the left hand Cde of the Icttci , and near the top 
^ it a /| by a findUr dor, near the button), on the left hand 

fiJe I 



I04 OF PKNMANsnrr. 



iidc : /, hy a dot placed juft alx)ve ihc letter, like the little 
to a fmall / ; # is rcprcfeiitcd by a dot placed near the top, but 
on the right hand fide of the letter, juft oppoi'itc the place of 
a : and u is rrprcfcntcd by a dot near the bottom of the right 
hat'.d fide, oppofite the place of r. But, in horizontal cha* 
ra«5\crs the dot for a ii p'nccd nndcr the letter, and at the 
Lft hind point ; ihat for r, iindc; the letter alfo, but at the 
rij»ht hand end ; the /, over the letter, a^ before; the /», over 
the left h:'.nil end of th : letter, and oppofite the place of a i . 
the Uf over the li^ht^h.ind {)oint, oppofite the place ot r. 

Thisordtrof |>Iatiijg the vowcU ab<nit the charaflcr for 
any conlonant, is to be obfervcd only when the vowel imme- 
diately follows fuel) conlouant ; if the vowel precede the con- 
lonant, jufl the rcverfe takci» place, in placing the vowelt. 
When this is the cafe, the dots for the ti and e are placed on 
the li^ht hand fide of perpendicular and inclined letters^ in 
the place of 0, and ir, refpeflively ; and and u are placed on 
the left hand, where a and e are placed in the former cafe; 
that is, when the vowel follows the coi.fonant. And 1, ov y^ 
is always noted by a dot, plaied above the confooant it 
follows. In horizontal letters the rmic rule obtains, whether 
the vowel follows or precedes tin- (onli^nant, 

But the former method of markini^ the voweh, viz. by 
fettin^; the mark about I he (oiifoiiaut uhich inmiediately 
prcctilcs the vowel, is moie natural anil peifj/icuous; and 
(liould always be followed, if pofiil)le. 

To n)aik the doulde or treble vo.vcis, when neceilliry, a 
dot (liDu'cl be fct in the place of that vowel which is of the 
n^ arell lound to fuch double or treble vov.el : as for example, 
to cxprclb the ca in the word j^rcat^ we ufe the vowel point 
for (I : as, (init ; and to exprefji the tiij>hthoi)^ rau^ in bcauy 
v.e ulc the vowel j)()int for 0: a^, lo \ Lut for the vowels in 
the word baiuty^ we ufe u : as, />ufy. 

It is ncr.cfraiy that the Icarnrr, in his fiifl excrrifes in thiJ 
ait, make the chara<^er for every letter of whicrh each word 
is compnfcd, marking all the po nts fur the vowels. This ii 

iicccfTury 



at >.en. -- 

i o'lr..-. 7" . 
lar.K '■- . - 

it llr'v: 1* 



But -i r.t - 

"! exrtr-.;".:- -. .- 

* ■ ■ 

:er.t:v -iivo-;:. 
« expr?:re.: :v 



i«6 or raNMARiutf. 

gTWWWtL— -^ ^ggUW!*> -I ..A i ,. , ■» 

fbilowing one t i( they be joined in Any other manner^ m the 
wondi ^ ii6f No» t8| in the third teflbni or if they ft^nd 
fep«rateiy» they fignify wliole wordt, and not Angle kitert* 

RULE II. 

There Mt miny wordi whii^h frequently occur in writing 
upon «ny (bbjeft whatever, «nd nuiy eAfSly be recolleftcd by 
the writeri thou^ exprtAed ever fo ImperieAly \ Uk\\ wonU 
mty be written by only marking the llrft letter of the woi d| 
if It be ii eonfontnt i or the vowel point and the fir(\ confo- 
nanti If It begin with a vowcli at li often done In the third 

fHlbn with the WOttti m^Jt^/ly^ ^Miut^ f^fnt^ and im^denf^ 

and A|4^UW^ and imf^^iK^ 

RULE IIL 

When worda are thui exprcdVd by their Arft« or ftrft and 
feeond letter*, it i* often necelTary to dIAtnguifli themi ai 
being either fubfVantlveii adject ivei, verb«| or ad\trbi. If 
the word be a Aibftanttve, it ii marked by a dot placed agaiult 
the end of the charaAer \ If an adjeAive, hf a point ptaecd 
juft before or above the plaire where the Aih(lantivc point la 
placed t and if an adverb, by a point jnft l)chind or bclo^f 
the l\ib(tantive mark, that ts, on the oppoiStc fide to the ad. 
jeAlve point. The placet where the three points arc or flv)\iUI 
be fttuated, mud be in a ftrAlght Itnei which line mull \\c at 
right angle* to the end of the charaAer i ai fecn in the plate t 
(fee diltlngullliing polnti). When the fubAantive thua ex* 
prefTcd ii pinul, the Atbftantlve point ii to lie made a tittle 
longer than nfual. The verb ha* no point to cxpicfi it. 

RULE IV. 

When the fame ^♦ord i« reipili-ed to be rr prated with a 
prepolition, whether it be a fubftantive, adjrrtivr, verb, or 
adverbi It ii only placing another point after it* ruhrtantive, 
adjedivei or adverb i^oint i ai In fig. 51 fim ^fier $imi. 

RULE 



or vsifMANsiitp. 107 



RULE V. 

• 

Wheo tvro words are exprefled by their firft confontntfi 
and a prepnfition (houM be between thenii which is omitted^ 
they are to be joined together in the common manner, and a 
point placed at their point of conjundion ; ai io fig. 7 and 8» 
the Uvi ef moneys the thirftfor gain. 

RULE VL . 

When any word begini with any of the prepofitionsi it it 
to be begun with the mark for fuch prepofKion ; and, in 
generali the next confonant will be fuflicicnt. And when 
thfy end with any of the lerminationi, the firiV, or firft and 
fecond confonant of the word with fuch terminationy will 
generally fuffice to difcover the ibund. But when prepofi* 
tiont and terminations are ufcd, as tliey are joined to the 
other charaAers like fingle letter^ the word flionld always 
have at leaft one of its vowels* pointy to prevent confufion. 

RULEVII. 

Moft of thofe phrafes which contift of a word with a pre» 
pofitioni conjundtioni or artide, before and after li, may be 
written as one word, 

RULE VIIL 

When a pronoun follows a prepofitioni they are joined 
togctheri as the foregoing. And pronouns may always be 
cxpreffed by their firft, or firft and fecond confonanta, haviu^ 
the vowel point if iTquifitCf 

RULE IX. 

To exprefs the definite article the^ the confonant mark for 
/ IS ufed ; and to cxprcfi the article <f , a fmall point is placed 
at the beginning of the following confonant. 

The foregoing rules are all that can be fafely given j and 
if ftriflly attended to, will anfwcr every purpole that can be 

O a cxpcdkd 



i^S OF raNMAi«mir% 

expe^ed from thii art. I have avoidec) arbitrary characters 
for certain long words and phrafeit as I am convinced they 
arc not adapted' to every one's memory ; and from the j»reat 
number of m*ords with which our )angu:ige abounds, it is 
impoflSble that a few hundred charaAers to rxprefi fo many 
peculiar words can be of much utility to the learner, and 
particularly as the chief ufe of (hort hand is to follow a 
public f|)eaker, nuiny of whom poflTcfs a very extenfive flow oi 
language. Beiides this, the method of fubftituting a fet of cba« 
raAers for many words or phrafes is very burdenfome to the 
memory, difficult to learn, and is cafily and foon forgotten. 

I have thought proper to mark all the vowels by points, 
according to many of my predcceflbri in this art, though I 
have dilFered from all others in the order of placing them. 
Dr. Mavor, Mr. Angel, Mr. Mafon, and Mr. GurneTi *'fo 
exprefs the vowels by points ; but the method of the three 
Utter is to denote the vowels by points placed on the fame fide 
of the letter : thus, « and # are re prefented by points near the 
top of the charaAer, or the beginning of it ; / by a point in 
the middle of the charaAer ; and # and m by points near tho 
bottom or latter end of the charafter : whereas, in this fy ftcni, 
the points for « and e are plnced on one fide the charu/ter, and 
thole for # and m on the other fide of the charaAer, and the 
point for /, at the top ; which muft give this method a ^rtAt 
advantage o\'er the other. By the former mctho<l the place of 
the « and e cannot always be diftinguiihed from each other, 
nor that of the # and »; by this methodi I will venture to 
aflert, they will never be confounded. 

I'hough lome writers on this fubjeA'have given diffirent 
chambers for all the vowels, I have given the pittcirncc to 
points ; they give the writer infinitely the advantage over the 
other method, in point of expedition ; and by an attentive 
perulal of his work after he has written it, and while the Tub- 
jci\ is (Idl fiefli in his memory, he may mark all the vowcU; 
Mi^% will render ii intelligihle at any future lime. 
With regard to iho charadors for iho coofonants, I have 

endcavuurrJ 



tlvt 109 

^nilcfivotti*«4 to rcocUr ih«m ai fimpk m polBbIt in th«ir cua* 

ftrviAioHi xH ptrftAly different from etih other. Mod writers 

on thii in either make their charaAen t<io ci»mpii*x« or* if 

they make chtm fiftiplff ftirin the m fo much alike, thai thqr 

rnn eafily confoanded with each other, in lome modern 

fyft«m»i tho difference between different character! confifte 

Q\\\y in ono being a Ane and the other a blai^k ftroke 1 whicb 

diftinAiont writers of Oiurt hand have frldtim time to makei 

not to mention the other iimtlarltici between the charaAerii 

Cttch ati different charnAeii being of the f«me tt>rm, Utit of 

different ftieii with many other abiurilttim. Whilci on the 

ether handy thole who have retulerril their ehHia^vrt fulK- 

ciently vlifreix;nt| have I'orn^cd them lb c(Mt>plex, ui to give the 

karner no advantagCi in point of facility, ahpvr the contmon 

round hand. It muff be allowed by every one. that the mote 

flmpVV charoAcr it, the more cafily it i» formed. Wlieu a 

charaAer eonflftt of two lineii whether itraiKht or rurvei it 

requirei ahnoft twice an much time to form it ai to form a 

eharaAer confifting of only one of fitch linoitt and <-hura^teri 

which confift of two line* joined together at one end, \o mh to 

form an angle, require l\iil more \u%k to form them, Mr. 

>Villi«> wIm) pubiiliicd a iyllem of fliurt hand in the year iC^jH, 

ha» no Wii than thirtt*en i:lmradiet» in hit alphabeti which are 

fbimed with angle« in ihomi l)crtdei two wluch uit (\Mn|ilrte 

oval*, or circloi. And Mr. Mawd, who publilhed unothi^r 

fyftcm in i6js, han alfo eleven angled churttdtent. tuul thole 

for the moft part tukcn horn Mr. WiUti. Mr. skf Iton, nlfo, 

wlio in^provcd upon the two lormeri hai, in hin alphubeti 

pul>liliied in 1 6 <;0t fourteen veiy coatpUx chauMrniinumelyi 

ten angled tmesi thue cm led ut one end, 4iid one completer 

cncle. Uut Mr. Ku h, who publilhcd hiti iyiinw in 1669, \\m 

ooly foven anf^led vluirai^lnt, thice cut led onr», und one entire 

ciixle. Ui» fyUcm waii in j^reat repute for many yearn, ui\d Mr. 

L<K;ke recommendit it h\ hia triMtdc tui Udm\uion (hrooite 

there wai at thai tmie itune better). Vet Mr, NicholitK. vNho 

publiiUhl hli Iffftem thirty ycAia itfier Mr. Kiilu uuil evidently 

'j^ took 



fiV ormiifAaMiiK. 



mk moft of the diania .n in bU alphabet from thatp km 
aiaeaaglcd charaActit thret corkd onei» and om ctralv;> 

Mr. Nicholai» aUb^ inv the &< who omhtcd iiifaiiog fogabf 
chatiaff i for aB dM life fowelt, tboogb he hu uicd Moi^ 
f. For Mr. Willii hu dMina charaaen for every one of iho 
fowelfei Mr.lCawd hai charafiert for all hot i'aad e i Mi^ 
Skekon and Mr. Rieb have charaAen for them alU 

In Che jrear 1715, Mr. Lane ptibliibed a fyAem of I|mi| 
b»d voder bb own name I but bit alphabet, aswell^.tbat 
of Mr. Addjr, pobliflied fime time before, it tahC9 ^fmaOf 
from Mr. Rich; eacept chat Mr. Lane bat omitttd An ^Mr 
raCter far r, which Rich hat nfed ; and iniertad a 
for e^i which it not in Mr. Rich*t. ^ 

In 1707, Mr.Wefton pobliflied hit fyflem, wfaidt 
talsen for the moft part from Mr.Riebi but eaafMM «f 
more eomples chanciefi than anjr of hit predeceBM|^B|Hif 
thirteen angled cbanaerty four coded onet, and.a€Oi|MBi^ 
eircotar one. 

In the year 17309 Aahy Macauby, Eiq. pubHIiai Mt 
treatife of fliort band, which though more orighnd ta Iba 
conflrtidion of the charaAert than any preceding one, it, 
nc\erthelefi, very complex, at in forming many of the lettert 
tlie pen muft be taken off the paper before the letter can be 
finiflied, ai it the cafe in the m^ where the pen muft be taken 
off to mark a point to diftingtiifli it from the r, to which letter 
it otherwife would bear an exaft refemblaoce { the fiune cui 
be faid of the charaAer for the k^ which muft alfo hafo itt 
point. And the vowelt in hit fyftem are all exprelfed by cba* 
ra^ert, which muft render it ftill more tedioui to the writer. 
Mr. Annctt foon after publiflied a treatife on ihort band, 
taken from the former, but rendered a deal more fimple, or 
nither too (imple. For many of the chara6ten in bit alphabet 
are formed fo much alike, that it it impoffiUe for a writer in 
hafte to mark the difference : the charadert for tf, r, i, and yt 
are ail formed by a ftraight lateral ftroke, and only diftingntfli* 
ed from each other by their length, which muft neoeflTarily 

crc9t9 



OP PEKMAKSHIK lit 



create miKh confufion. The charaAers alfo for i and p are 
fimllar, differing only in length, as are alfo thofe for ^ and t. 

In 17539 Mr.Giimey publiflied hit treatifc of ihort hand» 
being an improvement on that of Mr. Mafon, publiflied near 
fifty )*eart before, and who was the iirft who made any con* 
liderable improvementi in the conftruAion of the charaAera 
fincc Mr. Rich. Mr. Gurney*i alphabet, though an improve* 
ment on that of Mafon» has, nevertheleft, eight chara^ert 
which have anglei in them ; beiides a curled charafter, a 
common round hand r, and a circular chara<ftcr with a 
ftraight ftroke before it, lilce the figure xo. 

Mr. Angel, in 1758, publiflied a fyflem of fliort hand, 
being an improvement on that of Mr. Gurney, and in the 
year 1 76a, Meflh. Swaine and Sims publiflied their iyftem, 
which WM alfo an improvement on the fame author. Each 
of thedMphabett contain flx characters with angles In them, 
one circular or curled letter, and one like the figure 10. 

Soon after this, Mr. Hodgfon publiflied his trcatife of fhoit 
band, taken chiefly from Mr. Gumey*s alphabet, but being a 
great improvement thereon ; his characters are more fimple, 
and, at the fame time, full as different from each other as 
thofe of any alphabet that had l)een made before his time ; 
he has but two characters which have an angle in them, only 
one curled one, and one like the figure 10; the otliera are 
fimple curves, or ftraight lines. 

TheRev. Mr.Byrom, A. M. publiflied his univerfal fliort 
hand in 1771, which, though confifting of no angular nor 
circular characters, has no lefs than nine characters completely 
curled at one end, which mull render his fyflem very complex 
and tedious. 

In 1774, Mr. Palmer publiflied a treatife on fliort hand, in 
which he fomewhat improved on Mr. Byro'm's plan, having 
only feven curled characters in his alphabet. 

In 1776, Mr.Williamfon publiflied his fyflem of (hort hand, 
In which alphabet there are alfo eight curled characters. 

Mr. Blanchfu*d, in 2776, publiflied a complete fyflem of 

fliort 






Ml OF rFrfMA?f<iifr. 

fliurt hap'l, ill ^«'hirh tlie i\inrkf\» rn are all fia'plf*, ^Tt\fhf, 
oi cm vl linci, eiccpt one ^ mlcd rli:ini^^er, one cirnilir on?, 
Aiict a Lio'.4«M.c. Hii alphabet !•, th^rrlnr^ m'ire fimp'f iinri fit 
fill pi:u'ii' r il-.an th.i! ot ^ny or .m4 |iiiH«i*n'ir% and the levters 
ML iuW'i.n.wly «l fferrnt tioni cvh orhrr lo prrvent mif>;ik». 

SiiKf.' Ml. ilUdf.liard imbliOiCfl In* fyft^m, frvt ri\ othcri 
lidvr ^\i\it ii'.'i, uhi( I) I )mvc tvt room 'n irenlW n ; fuftke tl 
111 t«iy, tiMT Imni that iicriud to th' prcfnit, moft, if nrit all 
ilir wiiicri on ilie aiC luve run ihto the oppofilc extrfme to 
the uritrii i)« tore hii tiiii'.*, uhirh i^, th.it of rencif rinf{ ihcir 
nl|.h:iliiti' ^1 f liflu/tcis tgo fimfilf. In niany modem alpbabetl 
ff/n r of ihr rhara^crs itf' Mililr e.v.l' otitcr fo nearly, xhwf the 
wf jfcr, (oinc tiiiic alirr hr h^i uiittcn his [nnt^ ii often at a 
iiA'i tri 'liicovtr rh'j i'cnfc of tlv: f^rca'cr p»it of it. 1 haveatet 
wiih ('.vcial wiitcis who have Icarnrd fmm Mr. TapHn*! 
fynfin, ^w\ hive ex pc I i*. need tliit dithi ii1»y. Mr«^aplm's 
a'jili.iUt hn« not tm': anii;k-rl or rnrnpnund rhnraAcriMid nnJy 
MiC hn.i!l * iicnlqr one for the hrttr i ; Uit then ho bat one 
(h UciMci f(M ivviioi' niofc hitters : tin:, /',y, ^, nnd v are ull 
rrpr(fenic'.i i>y i Arait^ht ffiolc! in the (iaiDc pofition, and 
flinin^Uinifl lioiii r..( h oth'.i ori!y l»y tin. Vdi^th or Iwi'lnfrfs 
*ifih'; M)ii ii'ttr : f'w f»:i.' nii«y !■«! ofi^ i v i] f/f »l_,f < hai;i<'^tt n 
'"'■ >ft /» '■» '" ' •*» vvii'fj ;nr aiio ih »',;'iJ li'tfs in th*: fume 
poliiiof! : i'lid ili'Mi.'h rlir (iiii' aiitv h't.' • ' n 'liolc- ;in'l o»ner 
fhir"'*'!'; i[i ih'it ;ilj)'ii''* iiuiy not |i«. f») >pn«neMt whfn 
vi!W«'i hiii;ly'i vt whrri hi'l* ' Ijir.i/h rq miv in r,onta''.t •litb 
oflins, it Id'"'. HI Jails -o pu/./Je it4 wr I'.n, rjitryx l^* ix: tcrjf 
(/invni.inr in r[iv ()[^ ni. 

Mf. THpIin's MK Tli'id '.( nnirkirif; th'* vft\^fU r- ff»m' time* by 
«lov, ;n.fl ('ill ' fur '■•: I y »),• fifij irfm 'if fifi" n» t| . ronfonrintS> 

I h iv: noiif'fl th«: ;f'p!i.(lrrti( li f fi:n;«''^» i • only of the 
foifjjoin^ wDfi r«, v. ii|;'in» ;w|v iriri}^ to rlr ir '"'h' r rhnrn^cri 

h»l r|/,i|Mc ,iM'l tirhl'' Ic'rfi-,, '.vol l-r, Mif| •ihr:if. s^ ni thofp 
0\ iTH^\i M I'M m til'- IJ ir' mH of r.i' h wr i*"i'! i\ihn\. 

( '(/O'"' I ninjj f h«- ;il|)h:;l»ft I li v: h' f 'lif honmir to propoff, 
( tnufl jiift oI>lci vc, rliat I h ivi: :ivoi'.!c'h*il ^^nji;"' ^r, v'.»mpound, 

and 






•t . 



>« «. «« - » 



. I iv ■ ■ 

rtnlh, :w\v. .-.'J .- . 

rai.i •%■■ iV 

I- 1 n ! Ml-.'- •/..;■ 
'1' ;i! iuu-.;\:".>i. \ 






-■,|.r -" I i>««i. ■ 

■ 

• •111* ■■' ■ ■■• 



114- 0» WiftM<IMiMt»i 

Ld&m ttt«>ir t mtn put to dcAnt Mitdtftyi I would oiU 
fti ihi t«ll#AirMi of «ti innemmyi mindy cM h«r when i mtn 
tmt commHttd in iftkM« ffN* which he eenf^iret himUlff or 
fiiif*ici f hit hi t« iti|wfcd to th« ct nrurt of others. 

For f hit rtifiMi i mill mil/ modeft it is much fo when he is 
itoot ii In ^ompiOXf ind it fulled to i blufh in hit dofeti At 
when the eytt of multHudct ii« Ufkin him. 

t do not ft member to hiire met with iny InlUnce of mo. 
difty wHh whkh t im fo well pleiMi it thit eelebrited otm 
#f the jrAttig tirlneii whofe fither« being i tributiry king 10 
the Roininti hid feireril compiiltttt liid igiioft him before the 
fimitey it i tjftint iod opptetfbr of hit fubJcAi. The prince 
went to Rome to defend hit flithcr 1 but coming into the fe* 
nitii end heering i mukitude of crimet ptnvi d umt him* 
Wit fe oppnH&Kl when It eeme to hit turn 10 (pcillWtit he 
Wit vneMe to titter i word. The ^ry tellt tH» thit the fi- 
thert were more motred it thit inftin«e of modefty end ingt- 
nuitx»then they could hitre been by the moil petlictic oretinn \ 
ind| in Air»rt| perdcmed the guilty fithcr for thit ettly proniiff 
of virtue In the fon, 

I tfike Afturittre to he the ftctitf)' of prtfff Aing a ntAti% f* U, 
or of faying end doing indifffrent things wUh*»ut atiy utitiih 
nefs or emotinn in the mind. That whith g^Mictnliy jjivcs » 
mnn afTurence is imoflcrete knuwieilge of the Huild^ Uit 
above fill i mind ffiwd and determined in itfclf tu <!•> itu(h*ng 
againrt the rules of honmu- and ilecenry, An open («iul «i. 
Cured bcbivk)ur It the naluril confequeoceof huh a kIuIm 
^•ttl. A man fhut armedf if his wotdsOr adiuiis aie ^it finy 
«)me miftoterprctedi retires within himfclf, and, frnm a '.on 
fc lutifnefs of his own integrity^ ifTumes forte c nnugli t*j *!• 
Tpife the little ceofuret of igmfrancc and malkc. 

l^flim tit*— Eveiy one ouglu to cheiidi and tDtcMirfl^^ id 
himlelf the moilcny and afTutaiire t liave heie mcntimiefl. 

A man without aflurante is liable to be iiiade iinrafy by t!»f 
lolly or ill-nature of t^try une he convcrfet with. A niftfi 
* Mhout mmlcrty it loft to all fenfe of honour and virtue. 



«■ 





tlief 

twees DnuxzuKSs a 
X fltaPFCpm Iwif" 
be botn XEncxst 
perv^to be 

people of 

they are nor ririe ^ 

tencewitboixc 

villanies or nacS^i: 

Such a pcr/cn ieena x 
in fpite of \k\w^\% 
reftraints bis 
way. 

Upoo tbe wiiole, I waQA 
maxim, dut the pradiceaf 
to grre a mcao a bemuuD^ 
Guilt always ieeks to 
and is 



••rf-rrrr? 



^"sac 




I have^ for the eaie cf ine icsr:ar?i ^^runzes.?:! 
of each of the ibregoisg irtfrgw:, aszi a f*:gs;ar 
prefixed to each word, or pcraie, ££ snmoer. 
bered ia the plate ; by whicn, ti^c 
may be feen at one yiev. 






li6 



Of PRNMAUfflllP. 



Ill tlM Cri MRm U laCirMd rmy ccmfiNiant biUmgliig !• 
iMh wor4| wlihlht poliic for tnry vow«l i which yitliw, 
■• WM brf ow ohftryfdt tkt Itariiir miift purfuti iM tekl 
v«ry fmdjf in both wruing, iii4 rMding, nil bit iMwIfcii 
Tbt Irfl 1011 w«rdi in thU kOua h«v« ibtir ch«niA«n fawwd 
fcpirtteiy from Mch Mhtr^ 

1^ t^ iiMM4 MRm no more Utteri In i vtrd avi lifcfti d 
dw art «Mfil«iitly nMtdivy lo difeoiftr tht found* Tbs fln* 
git epnfoiiMK nMrki im tlfo uiM for th< wordit pwBnirinnii 
«id MrsiatiioM tbiy rapraftnci and f bt chmAiMJinlit 
donbit tad imbfe Itittn. 

The third ifflbn it wrlUfln upon tbt moft Mfliod grip- 
ciplit of ibii ire, Aboyt $\i tb« ndvaougn «hie|i it po^ 
MSmi in CQBMRon iKiib cboficopd liflbui it bn^ m or mm ^ lU 
fbo abbfif iatlooft dollvorad in tba fort going rgtafc A|^bl^ 

US30N I. r^SM th^ Pk$0j 



t I know 
a no 

3 two 

4 words 
c that 

6 have 

7 iMirn 
H more 
Q Hbafed 

10 by 

11 tne 

It different 

1^ and 

14 wrong 

I c iiitcniretatioMi 

16 whicli 

1 7 are 

18 put 

19 Uf)0|1 

30 them, 
ar than 
aa tbefi» 

43 tWO| 



t4lfodtfly 

tctnd 

to Afliirance* 

t7To 

•« fty» 
ft9 luch 
30 a uuti 

3' ^^ 

3* a modeft 

33 n^»n. . 

34 loiiiatimeK 

35 indeed 
30 mffcs 

37 w 
30 a good 

39 (harai^tfri 

40 t>ut 

41 ar 

41 iilclciiC 

4:4 i'i 
44 ^«ry 

46 ulitd 



49 a incepifli| 
^o awkward 
^i fellow, 
$t who 

S3 bai 
IS4 neither 
u good 
{6 breeding, 
$7 poliCcrnclii, 
58 nor 

50 ^"y 

60 linowledgt 

61 ot 
6t the 
64 world. 
64 Again, 
6$ 4 man 

66 of 

67 afluranrei 
6H rhoifgh, 
69 it 



70 £f^ 

71 itonlj 
7s dcaotcd 

73 a peri<» 

74 of 

75 a free 

76 and 

77 open 

78 carriage^ 

79 is 

80 now, 

81 Tcry 

82 ofuallf , 

83 applied 

84 to 

8^ a profligate 

86 wretch, 

87 who 
88caa 
89bffpk 

90 througi) 

91 ail 



9^ 
^ aid 

97 

99 a bl::^ 
ool fbsJl 

01 endesvoiK; 

05 tfaecefbce, 

03 in 

04 this 
ojcfiajr, 

06 to 

07 restore 

08 tfaefe 

09 words 

10 to 

1 1 their 
la ttac 

13 meaning; 



rrr 



xsr 



ia4.diac 
125 <sf 
116 



SS7 vid 

ttg hiader 

130 m p ad mcc 

131 £niro 
13a pofiog 
133 for 
I34affanuice. 



LESSON 11. 



I If 

a I were 



3 put 


4 to 


5 define 


6 raodefly. 


7 I would 


8 call 


9»^ 


10 the 


II refledioa 


12 of 


13 an ingenuouf 


14 mind. 


1 5 either 


16 when 


17 a man 


18 has 


19 committed 


aoan adion 



21 for 

22 which 

23 he 

24 cenfurcs 

25 himielf, 

26 or 

27 fancies 

28 that 

29 he 

30 is 

31 expofed 

32 to 

33 the cenfure 

34 of others. 
3$ For 

36 this 

37 reafon 

38 a man 

39 truly 

40 modefl 



41 w 

42 as 

43 much 

44 fo 

45 when 

46 he 

47 is 

48 alone 

49 as 

50 in 

51 compan/i 

52 and 

53" 

54 fubjed 

55 to 

56 a blulh 

57 in 

58 his 

59 clofct, 

60 as 



61 



Qufii buofly in which lli» chiiniAi;ni iir« nU fifrtplr, flt«i|r.ht, 
or curve hn««« •xc«^ one c^iiilcd eb»rii<^f r* one eIreuUr fjnt, 
«i)d A cioUuoe. Hii Alplmbit t«i tb«r«for<:, mf>n fimple AOfl Hi 
{lit ftiiiiM tb»i> (hA( of ftfiy oi hii prcdcswflArit iod th« tctteri 
Ate (ufiUicitity (ttArent from «wh othtr (o prcvonr miftak«!«* 

biiKc Mr. Bl*(ii;biir4 pubhflicd h»» fyftrm« foHml 6tbrri 
bAve Ap|icAic(l« %vhicb I bjivc not roDii) to ircntkn i (uftr« U 
to Uy^ thAt from ch«i period to tbt pro(«titt nrioft« tf not «li 
the wtticri on the «rt ItAve run iuto the oppofttc untremi to 
the writcm I)tf0rc bii tbn^, which in that of rendrring ihf if 
atphal)€tical chiir4/tciii fta/mf^. lit mftny tnodorn ntphftboti 
fiiiiie of tlic (4MiniA«r» rciWsihle cAch otb«r fo n«iirly« tbif fbo 
wn«T, dfwe titne Ailrr be bA» urittcn hi* pic««i ii often at • 
lof » to ilKcover the tenfe of the grcAf cr pAi t of if* I hftve SMt 
wiih fcvcrAl wnceri who have IcArnrd fiom Mr«Tiipiln*l 
f>(lrin« And h.ive experienced tht« dilfi( utry. Mrg^ftpiln'l 
AlphAbet hA» not one angled or conrtpotind ctarAAert ind only 
one fmall ( ireiilAr one for ihe letter 1 1 but then bo baa one 
ch^rA^i fo>' two or tnoic Icttori '. tbuni //»/i f, ;iAd <v j^ all 
reprrfcmed by a ftreight ftrulce in the (aiua p^fitioov and 
diftinguiflied from riicb other only by tlie length or boldnvfi 
of the thai uAer i tfte (mwc mny l>e otifarvcd of t\^$ ehaia^terf 
ff^^ jtf J9 ^9 ^'^<1 ^* whkU Are aHo ftrAigt^t Unei in the fatna 
pijfaion: And tbouj/h the (ittii'anty between tiiofe and othei 
ch^ri/lcti in tlut HlpbAbcr mAy not be (9 ;ipptf rent when 
viewed finglyt yet wtteti (ucU chAr.t£lcr» coidc in cootaA w Ifb 
otIicrA, it feldijut foili to pui'iUi tu writer, encepl he be very 
c/mver(4iit in the (y^cn%» 

Mr* T«pbii% method ^'f mnrkiof; the vrmcU 't% fomritfiite by 
dotfe, and roinr.tiifirt hy iUn nitutioti of onr of tbc confenaAiA* 

I have nuticed the atpb;d)etiefti ('hAra/^cr» only of the 
foiegoing writerii without advcttiitg toitkciroihcrcharaAm 
fot double iiiid treble letter«, woids, ;ind phrafrt^ m thofo 
cb;«rA^tetii form the (Ian dard of e4(:h wt'utr'n iyiicm* 

Coneeioing the alpluibct I bavis h«re the bonf«ar to propofo^ 
1 mttft juft obierve, that I luvc avoided all attgfitar, coRipouiidt 

and 



ciF rKNMAKsiiii'; 113 



ni\d circular charaAeri, and ufrd only one curled onei which ii 
tV^rcheletcerf ; and I trnft Ihavemadc them TuflirientlydiftlnA 
in their formi. There at*e fome angled and compound cha* 
lasers, ufed for the treble Ictteri; Init then it (l)ould be re* 
memberrd ihat each of thcfr chara^ers with a vowel pointi 
will very often fcrve ft)r a whole won!, and I wai afraid by in- 
dulging too Kreat a limpMcity in thelc iharaAcrs 1 might de* 
generate into the modern uniformity. 

The methovl of marking the voweU by pnlnti, an 1 have 
hereadviCedi will l)e flmtui a vety t;rc;\t f»vingol'time. It will 
alfo afford thofe who can fo far depend upon their memory,' 
ati opportunity of entirely otnittinj* themi till the writing It 
Ani(I)ed 5 when^ by an attentive perufal,^he piece may have 
all iti mgtit marked ; whiih \%ill render it intrlli^nble to the 
Writer W^ future time, when lie Imi, pcrhupi, forgotten tht 
i\ihjeift matter. 

A PHAXISi 

OP THUFK MvSSONS, 

On MmitHy. 

LelTon L— 1 know no tw»iw(miji, tlwt have been mon* 
ahufrd by the dilfcrent and wron^* intripictrtti«»ns whiih .uc 
put upon them, than thcfc tWl^ MovlcOy wnd AfliuAiur. 'I\> 
fay, fuch a one it a mndcft nuin, fomciimc* indeed pwircs* for 
a good chararter; but, at preient, is very often ufcd to nj;nify 
a flieepid^i awkward fellow, who bus neither good breeding, 
politcnefi, nor any knowle^lgc of the wt^rld. 

Again, a man of artvinnce, tho\ij;h, at firft, it only t!enote«l 
a perfon of a free and opct\ earrinj;e, ii lunv, very \jfually, 
applied tt) a prt>fli|;aie wreteh, who t;\n brenk throuj;h all the 
rule* of det*cney and moinlity withovit n binni. 

I fliall endeavour, therefore, in this cflay, to reftore thrlo 
wonia to their true mcaninjt; to prevent the idea of Minlelly 
from being ci>nfounded with ll-.ni ol Shecpiflinefi, and 10 hin- 
der Impudence from paffinj*, (o\* Afluianee. 

Vot. I. V l.cdori 



or rtMMAmiMif^- 



:lo It ii 


77 (hill 




7I mlnrrf 


"ij ilui ihr prinre 


7<) MtKl Nf n.lc.1 
Bo inRflh«r, 


.14 il->" 1»rnti..(if.l 


iiihcr 


K )•■'«• ll'<l hnlh 


Bl mmpnfc 


Tin thrW. ijuallfii atiiiix In 


B^ »)Mt 


.'7 " ""T 


H4 wc «ndMV«|» 


•^B cmtticnt 


*^'3r 


39 "tfRrcf-. 


40 Wiihout Nfnirancc 

41 l« 


n I mcwrtl «(riirmut i 


41 wmiM nr^cr 


B9hvwhNh 


41 hnve iitxlctlnkcn 


^0 Wr MnficfHrtnrt 


44 «. f|K-*k 


91 ihf jiift nxait 


4c lirloic iltetTKiIt 
4* ""«'»« 




9ltMmful.Kf.nmtimmHlenr 


47 rifcmbly 


94 1 IhilUomliKli! 


4S in Ihr wnrltl ; 


gt wiihnbfcrvitib 


49 witliniii mmlrn/ 


9(1 thai 


(ohc 


97 ■* ihc rtinw 


it wotiM hiTC 


J, picirfcl 


99 m»)f lie 


f ( iImi tMfc 


loolmihino.ltlluMltfl'imil. 


((he 


toi f(i ii l< aim 


(i;I>ai1liiVr.i 


iciixitnuir 


(fi n|in.i liKii. 


11.M Im thr Uiiir 


(,ll...tl;;lt .<li*.t 


n* (wiLmi 


(B-Iiuw..! 


i,.i...|.<- 


(.,fV,T 


lod iMiih itiipDtlf nl nivl lofk- 



6( pliHi. 


1 1 1 •Hid 


^A thai iimilcrty ami iffmvt 


ic 111 him) 


6;afv 


It) of iniiiiurr 


(iR hoili 


04 in |iH.|.1ri.l 


ft., ami.l.lr, 


H-lrptaviM 


;<;«j...v 


1 1(> iixml* 


J.wywdl 


1 1 ; Rttil iiwan 


ijimrct 


t iHfiliiiaiHint 


■^imtbaf-mc 


tn(wh.\ 


;;kSS- 


iioih<iU||liilirr 


Iti ate nmalilc 


;^w... 


iitwmrci 



09 nNMAMIHIPi 



ia» 



(•3 a iniQ*i 
^ e or pfXMioiiMt 

iO a fCDtCQOt 

[•2 without coafafiooi 

laScan 

(•9 vduntailljr 

130 commit 

131 thegrta 
t3aTiUtQiei» 
[33 ormoft 
[34 indecent 
:3c t6tioni. 
36 Such a ptrfim 
i32 feemt 
[38 to have made 

139 a refolutioQ 

140 to do Ill» 

141 even 
[4a infpite 
i43ofmmfelC^ 
1 44 and in defiance 

14c of all 
s|6 thofe checks 
149 and reftraintt 
148 hit temper 
[49 and complexion 
^ofetm 



151 to have laid 
15a in hk way. 
153 Upon the wholti 
t54 1 would endeavour 



15c to eftabliih 

IS2 tni 

1 58 of virtue' 



thii maxim, 
159 that the pradict 



iC9ifthemaft 
too proper 
161 method 
16a to give 

163 a man 

164 ai>ecoming afl\irance 
16c ill hit wordf 

160 and actions* 

167 Ouilt 

168 always 
i69feeks 
170 to (helter 
t7iitfelf 
17a in one 

i73of theextremesi 
174 and is 
1 7 c fometimes 

1 76 attended 

177 with both. 



mm 



Vol. I. 



ciMP. 





I 



CHAP. in. 

Of VULGAR. ARITHMlme. 





t ■ 




u- 




« ■ • 


1. 


■•/ ^»l 




*'. ■ 




« 




■' . 




■ . . , • 




• 

• J 



SECT. I. 

MMTAtlON Of MUMBIM. 

Arithmetic b tht mft necefaryor aU the 

Fixmh henoe we ma/ «60iittt'for the pcrfeAtelD wUchM 

part of literature b bcought, above any otiier hrailciV 

mathematical fcieact. ^ 

Notation, (Iri^ly fpcaking^ is that part of arilbiiKtit 
which teaches how to write any number by iti proper cbi* 
radters, or figures, and confequently in their due placet; alia 
to read, or difcover, the true value of fuch number, wbeo 
written. J 

Ail numbers, and the various combinationi of them, ait ^ 
noted by thcfe ten characters, i one, a two, 3 three, 4 feoff 
5 five, 6 fix, 7 fevcn, 8 eight, (> nine, o cypher or nothing. 

£ach of thcfe charaAcrs, when ufed alone, Hands for im> 
more than its own imrin&c value: thus, 1 flands only foe 
one in number, 2 for only two, &c. But when any of them 
are joined to other fij^urcs, they together Hand for moretbta 
meir own real leparnie value : thus, i and a, joined together 
thus, la, (binds for twelve ^ 6 and 5, joined together, ftands 
ioit&lx ty*five, 9cc. 

Id 




In order to diitAj^cr tbt rsLimt of sttf coofmaoie^ '"T^Vri 
it mcft bedbfcntjd, ihaimmm^boF fboesl m llKfirftpboe 
towardi the rigiit hand fiaadf for so snre dnB in »l 
intrinfic rtioc, bat sacreaies ia v^^loe in a toiilsy propor* 
don by every reoKfrc tcnrardf tlie left bsid? liu», id die 
number 1799, the £rS £gDrt 9 fiandt ibr 9«iif; tbe iiscood 
figure being i%tbe ^somJ piace uwamif ffe kft band, ttt 
▼aloe is iocneafed tenMd : ^mm k n prti iiti imttj^ or m 
times nire ; vbicb, s itb tbe foiegoii^ 9, lasda ior innetr • 
oioe. AgUB, tbe fifore 7, vbidi iapdi in iht dnrd place 
towardj tbe left band, it uxxaicd to lea cinKt tf amdi as k 
wcKi'd be if it flood io tbe oext urfenor piace, vis. vbere tbn 
la/l-fiieDtiofied 9 iiaods: that k iiqir^feiiti ietm bnndrcd ; 
wbich, wkb tbe two fcfv-»eDtiooed Bgarc^ §Mid §or iemen 
boodred and n'oetj-nine. Tbe %iire i, wbicb ftaods id tbe 
Coords place, tovaidf tbe left band, if aHb incaeaied ten tiioef 
in valtse to wbat it would be if k flood in tbe next infetior 
places wberelfie 7 iipbced; in wbidi caie kfroold lepie- 
Imt one baodred, vbereas, io tbt fakm inftanoe, n ftands 
(or one tbooiaod ; and witb tbe odier figntes repreilEm one 

^ tboniand, ieren bondred, 2Bd aioetf -nioe. 

This defcnptioo of tbe four forcgo^ni figures may ierve to 
g;ive tbe oninSonncd an idea of the raloe of figores, acandiag 
to tbe diferent places they occupy in a oompouoded Dumber* 
For every remove of a figure towards tbe left band incrcaiet 
its value to ten tiaies as mncb as before ; as wiU more folly 

^ appear by tbe foikming rable, called tbe NmneratioD 
TaUe>- 



a^ 7& 




I« h ^; 



43. 

a. 



Mk 



SIO^ 13B.4J4rS» 

• 7fiwS4S, Sl<lk ISS' 

4««C 7S9.09a^7C4 

43. 310^ 1S^4<4 

7>«9ak9S7. XA 

3 1 I. Ol 9, S4'S 

C 7. S 9 o, 9 S 7 

f>. 3 4 3, 3 I O 

1 3 3, 4 5 6 

7 8. 9 O 9 

8, 765 

433 



III ocikr to read any number with facility and eafe, Hi> 
fiecd&ry tint the learner have ill ibe aamcs of tbe nunben 
a the head of tbe table perfc^y in hit memorj, that he naj 
apply tbem to uiy ocher nnniber be may have occaCoo fivj 
calling the firit figure, en Ac right hand, nuiti ; tbe fccoad, 
tan i tbe third, hoDdreda ; the fourth, tbouiaiul*, &c. u in 
flie table. 

Thot, tbe bottom figure in tbe table, fliading undo' the 

place of nniti, ii itfrlf an »'*. pr a fingle Mr- The next 

2 higher 



kigb e i fHynbcr in the tabic o e nfifb of two^giim, i aod o; 
thefirft wfaereo^ ttmdJDg m ds |ibBB of 
ten, being cxiif a hgast out; ^bt dhar 
cjpher, and in the place of imits, flmcb f (ormdiing, oroa 
wotttsz tiiele tw9 figvre^ f1iPfrfiine> cvprefs anhrten. TIk 
next DiBBfaer ooofiAi of die fignnB4^; tSie foBr laiu^ ia 
tfaejrfacgof hnadird^figirifieiibnamy iiu o Ji g di ; die tkne^ 
as manj tens; and die two, as manf units ; and is das cs- 
piefled : four hondred and dikty-tipo. T*fae foaxdi nmwihrr 
in die taUe oonfifts of four figoics, die firft vbereof fiandi 
in die place of dioii£nds; diis monbei^ d mcfcii e, is das 
csprefled: a^ dKwfend, iertB huu dw Ld , and fiat3F4m. 
The fifdi mmber Ibb its iiigheft igane iadiejilaoe of teaa 



of dKMifiuids, andktfaps entlui s ievcoij-c^i^ diavdand, 
MK Imadre^ and aine ; it kiviatg a cypher in die place of 
tenSy wfakb iaads iv ■arhing. The fijcth number confiAs 
of hondrodsof dwnfinidtj and is tims czprefled : onefam- 
•drod and twentf -duoe thmifinMii £rar iumdredy and fiftf-fia. 
The higheft i^ace of die ieiCDtfa iivDber is tliat of ic'diiacis ; 
k is czprefled thus: fix aulfioD, fife Imndxrd and fortj-duce 
dioufimdy two hundred, and tea. The eighth number con- 
fifts of tens of millions, and is thus €zprefl*ed : fizty-iewa 
miilioo, eight hundred and ninety thooiknd, nine hundred 
and eigbtf -iiBven. The ninth number hss its higheft figure 
in hundreds of aailfions; h is ezpreflcd thus : throe hondred 
and twenty-one imllkxi, twdre thouiiuid, three hundred, and 
ibity-fifc* 

The fix other nmnbers are ezprefled as follows:— The 
Ceoth number : ieven thooiand, eight buodred and ninety 
millioos, nine hundred and eighty*ieven thoofaod, fix hua* 
died, and fifty-ibur. The eleventh number: fbrty-tbrBe 
thouiand, two hundred and ten ininioo, one hundred and 
tweDty«three thoolatid, four hundred, and fiity-fix. The 
twelfth number : four hundred and fifty-fix thour;4nd, firvea 
hundred and eighty-nine million, ninety-eight thooikiid» 
ftvcn huodrcdi and fixty-five* The thirteenth number: 

nine 



• 



f ^ OF TVMAtt AatTSMme^ 



siM nilHoQ of iiiWiooi» •ight hnadrad nwi fct i wy y iji 
thptifcwd, flw handml api fei tjr*tbrw milltoPf two hwn<iii 
•nd tea ihiifanfli om bondroli and twtntjMhrto. Thi 
fe urtecmh minbcrs ftity*tlirce million of mttlionfp mo 
bottdred ind ten ttumfeodt o^ hundrtd and twcnty-thioi 
mtlHooii fMr bondrcd and Rfty^fix thoufud, fevan btto* 
dred, and eighty- nine* Tbe fificecmb hombert one bondiid 
and twenty-tbree millioft of miUigoti four bundled «id Mfi 
6% tbonfandy Ctveo hundred and etghiy-otne milliooi^ MnetjN 
eifbC thoufaod, Icren bundre4, aod fixty-five. 

I havc^ fai iba laUt, diftingolflitd erery three fgnrea by a 
pofaMi or coiDma« beginning at the right band^ aa it ganarnlly 
dane M public oCcet, aod by moo of cxteoiva bofiiiaiu 

Tbii siatbod aUb affiNda an aafiar vay of aaoaaaraliQg 
noarfiant than by tbe foregoing table, ai oieryihraa %Hiaa 
may have a oommon fumame nifroiMiniJinrJ^^ (Infitnad 
in iialica at tbe bead of the tabic)* befidai Ihahrnnmaiof 
nolti^ tenf, and bondredtt thni^ when tba iMmar can ano* 
meraie tba irft three ignrea in a number, and kaovt tM 
proper fomaoM to apply to each three figuretf be may ebik 
meratc any number, however large. The firft three figures 
on the right hand have no fnriianie, as they (Und fiaipiy for 
vnitf, tenft end hundredi ; but the next three figaret have 
ilie fumame of tUu/ltn/it ; the next three have the furname of 
miiltoni ; the next thiee, ihou/ands ofmiUUnt ; and the other 
three figure! have the fumame of miUi^Ms #/ miUi^tis. Tbut| 
to repeat the highcd number in the table, beginning at tbe 
left hand, 1 fay one hundred and twenty*three (to whlcU I add 
iti furname of) niillioti of million! ; four hundred aod fifty* 
fix (with iti furname) thoufandf of millions; ieven hundred 
and eighcy-oine (with iti furname) millionf; ninety-eight 
(furname) thoufands; feven hundred, and fixty-fivc. 

1 liave been more particular in the defcription of the Nu* 
4neaation Table, as it if generally found the moft dtfiicuh of 
flA the. tables in Arithmetic to a learner; aod fevcral pcrfooi 
viho bane arrived to a tolerable pro£cicocy m thia Icieoce, 

arc, 



OF VUUSAB.. ABtTBliBTIC. 



1*7 



are, neverrheiefs, very iniperfe^y acquaiosed with thb moil 
dCmcial part. ... 

Befides the foregom£.tea chara^ers u£ed to ezprcfr niuii. 
ben, therr are alfb leaers exnplored for the faiae pnrpofe^ 
crffed Miwrricat Letten. Tbit waa die apggot mtrtiBi ot' 
eiprtCng mmben ; and is iliU iiwiig afeof fnqucottjr, in die 
tide-pages of books, aoil is fmatgai oioeMicDn ia Run— 
hiiiory;, tii expicis iIk dtfe of tbc year. 



I, fbnds 6ur one* 

V,five. 

J^aeo. 

Cm an hmdacdL 
A or ID; five hmidrecL 
M, or CID» a thooiaiicL 
I30^ five dwuiamL 
CCIDG^ tea dumiaiid. 
lOOC^ fifiydumiand. 
CCCCI3CO0, a hundred 

thottiand. 
IO0O33, five hundred 

dianfimd. 



CCCCCIOODOO» ten hon^ 
drcd diooiaad, or a imU 

llOfl. 

The letttn MDCCCTll 
expreif die munber 1803, ^^^ 
dsne of the pn&at year— 
M fianding for one thoniandy 
D for fire hundced, CCC 
diree bandied morey which is 
ei|^t bnodred, and III chcee; 
rogedicr one thotTfand, d^t 
hundred, «id three. 



If a l etter or letters of inferior value foilow cmt of fnperior 
value, dicy are ro be added thereto: thus, VI (i|ptfv fix, 
VII levea, VIII eight, and DCC ^e^•en hundred. But when 
a letter oi infercr value is placed betorc one of fitperior 
vaine, it is then ro be dedo&ed therefrom : thus, iV ^ffufy 
focr, TX nine, XL forty, CD &ur bundrdd^ Siec* 






#. 



ttt W TOtaAm ARITfllfBTICii 



SECT- IL *•• 

or ADmno*« 

AMmM k tfM pirt of aritbinctk wMdi tadM la«« 
iM two or noit mmbcrft or fimit te|itlMr9 fai oHtm tr 
dUcovcr ilw Mil, or vatoe of cbf trhelc* 

AikHiioa of whdc oonbcn k ftktdfOty dMdii iMo mm 
fmu t MiMljry Addition of nuoibcn of one dMoaiMtel 
and Addkioo of owibtn of divert donomioMloMi 

Addkion of nmnben of one denomination cedUb in add- 
ing lofetbcr fimple numbcn or figures ; in widdi it mndt to 
•riftlj oliferved, tliat tlie vnhi are to be let diraftljr «dar 
eacli other^ In the ftme column ; the tem^ in lito iBaonarf 
noder eadi otiier I tliebundredt alfoundtfWhoclMri the 
thottfandi alib^ tent of tlioufaodt, and tfcefc ot off iy » 
art all refpcAlfeljr to be placed in tbdr i i i^ i tt f phea^ 
from the right hand, to which their rank eodllei thani ift - 
in the fettowiog esamplct t*» 

««473« 
64«W3 
ra6j74 
810973 

861413 
963670 

J4Z2^ 

4479^7 » 

The feveral numbers to be idded together being fet dowii 
in a regular order, at feen ihoYt, they iire to be added to|^ 
thcr ; beginning tt the bottom figure on the right hand, and 
proceeding upwards, till you ha^ added all the figuret in one 
column together ; then place tlie fird figure on the right 
liand, or unit figure, of the Aim io found, under the fame 
column, carrying the remaining figure or figures, if any, to 
be added to the next column 1 having difcovercd the amount 
of the fccond column, place the unit figure alfo under 

the 



ai 


»7' 


la 


^39 


33 
»7 


7«3 
604 


49 


830 


54 


»?« 


aa 


100 


108 


i7oa 



OF VULGAR ARITHMBTIC, 



129 



the fame coiuain, addiog the other fi^e or fi^rrs- to ilte 
next column, proceeding; in this manner till the whole be 
finiihedy and fetting down the total amount of the laft column 
tmder the f^ime. 

ThiUy in the firft example, I fay 2 and 4 il 6, and 9 is i j^ 
and 7 IS s»9 and 3 i» a$, ^nd » is 17, and i » 28 ; this being 
the amount oi| the iirft colnmn, I Het down ft (which is the 
figure in the p&ure of nnita) undier the fame column; and cany 
the remaining Igure a to be added to the next column^ faying, 
• and ft is 4,ai|d $ is 9» and 4. is 13, and i i» 14, and 3 is 17, 
and f is idy and % is oo, the whole amount of the laft coliunn; 
wherefore I fet it down under the column, and the total is 
thus found to be fto8« 

Proceeding in the iame manner, in the fecond eaomple^ I 
bj ( and 4 is 9 (for the o ftands for notbinf^), and y is 12^ 
an J 9 is 2f, and x is as ; wherefore, I fet down the a nnder 
the cdiimn, and carry the remaining ft to be added to the 
next colnmn ; faying^ a and 3 is ;, and 3^9^ ^nd t itf- f)4 
and 3 is la, and 7 is 19, the ^moimr of the Ibcond column ;^ 
wherefore I fet down the 9 Mn<\et rhec^^hMimv s>*^ ^^<y ^^^ 
remaining figure i ro he added to thv; next ^oluh^in, fnyin^, i 
and r is a, and i is 3, and ^ Is i r, ami ^ is 17, iind 7 i? 14^ 
and ft u a6| and 1 i^ 27, rhc ptmor.nt of the :^(V nolumny ^n(i 
ro l)c fet under the fair,e; wh^trcfor'i^ the total is 2';j% (:-x:> 
thouCiml fcvcn hun()rc<l and ninety- two). 

Irt the fajne manner the third example 14 wronjjJ>f ; as alfc* 
the three following; in which the ri^><;raticn is pnrpof*-.-/ 
omitted, for the |^t'a<ftice of the learner. 



GalUns. 
17964017 

437^/>i»3 
94ft 1 8740 
ft09<;i8n 
5*997152 

Tot i«l ^oonooioo 
"4^036^83 

/roof^ 00000700 

VoTTj. 



Yardt. 

«*7^4^ 

64^6^(161 
fto 1 07(^36 

7 29706 17 

T ota l ftftSu/U 7 

at ^652779 
Proof 228447147 



1^7 29420 

z 2090736 

67^42617 
742.>^>64 

ft9</ft^>72 T 

4 739 4<:>* 

Total 24f220</>0 
2244V ',^^± 

Proo f 24122^ -? 
Jllerr 



Ija 



oP irtJti%Afi AftiniM#.i*fr. 



m^um 



Hcie it imift lie noted, that when the amogfir of iny 
ctftimin ni any fnm Imi a cypher in the pl4ct of utiiti, fbch 
eyphf r li to t>e placed under the cOhimn ; a» in l!hc lirft of 
the three lafl cxam)>ie<. 

The tKree )aft examples are prated— vrhkh 9i done in this 
manner s after the total in fonml acc<irding to the foTef^ing 
ruteiv and placed in the firft of the three botfMi t)nei| fM 
fop line of the fum it to he fcpar.itnl by a line dravm nndfT 
ir, the reiminiiifr part (rf the fvm caft up, and tlie emomif of 
it plxcd under the aforcfakl total i this lali anioniily and ihl 
top line o/ tlie fum, are tlien to be added together f and if tht 
amooatof thefc two lines be eqiiai to the total inthellrl 
bottom line, the fum ii lightly caft up | OCheiwifo ffOI* 

All other fume in addition are to be peofod hi fl llmUar 
manner, whether Ihey be of one denoiflioatiMi or of dhrcri 
dcnommationiA 

Addition of divert denrmitnationi confifa m ad d w i g tngi* 
ther mimbcri of ditferciit denominatioMi whether they be 
^ooney, weights^ or meaftwei. 

Before tlio learner proceeds to addition of moneyt k ii 
necrilary that behave the f(/lioMrinf{ tables by heart; cMled 
t!ie Pf/h^ Talflff .nid rite Sl^illm^^ lable. 






riiu 


Ptna- Tul h\ 


TJkc Shilling 


TaUe. 


20 




20 


iliillings is 


1 


y^ 


— a 6 


3^ 


— 


I 10 


v^ 


'i 4 


40 


— 


n 


«:o 


4 2 


'i'^ 


— 


% 10 


Co 


S 


(}0 


— 


3 


70 


- ^ 10 


70 


— 


3 «o 


Ho 


6 « 


Ro 


— 


4 


«/'5 


^ 7 /, 


90 


— 


4 «o 


!'/> 


« 4 


100 


— 


5 


no 


Cy 2 


no 


— 


* 10 


no 


— 10 


ISO 


•« 


6 



II 



c4Pta«M^ and Acv aane or M«% fpocollj 4t tlK tap*. 
»4ddiiiaD4tf<paB^tibepoaQdsare|ib^ in onr nnlTiPn, 
wkh m £ m dietop for ifha, dv Lmp voi>d fcr frnmiii 

khM^ M MKMhcr coluoMI* wttli a ^ «t dK tap fix* ^^Sraani^ 
itmhgmiut f€wu\ woA iwnrtieca the&Afabifp afc fboai 
ip a fcygPBic frinwai, with ay« ac die top fcr f aiiJ^iaf ; biS 
ibe 0ioft fnMBrd mk «» a^ place tWn munodiatdjr irfter Aa 
pcocciy a* a Iradiap of a pcBDf ^ liuii|| for^aefciirdipait 
0f a poMff Pf qoe hxtimmg ; ^ far oor luJl^ or a hairpmaf ; 
I fitr dvce fcavtkf nf a pecsff <ir dHce fartbiflip : ai is tte 



X- 


«# 


X 


£' 


$0 


A 


/. t. i. 


^ 




a 


»7 
13^ 


9 

4 


Jfil 




17a 9 a 


i^ 


"S « 7i 


I 


6 


19 


i*4 


21 


3, 


144 '9 " 


o 


7 


9 


7^ 


7 


9i 


176 12 loi 


•9 


fC^ 


4 


i^/. 


'9 


lo^ 


»'^8 17 11 


3 


^y 


;c 


I'ji 


7 


«f 


/'i^ K 7| 


a 


7 


» 


tc 


C; 


<>i 


?Ji^ 17 i© 


^. 


'V 


M 


5'r 


jc 


6 


ViJ7 c> 


^* 


• > 


30 

r 




'S 


3 


344J 11} 


^7 


7P 


^ 


'/i7» 1' v|r 




'$ 


io 


77^' 


S 


7t 


-3^45 ««* 



Is addaioD (jf otavberf ^f <£«<» ^dnsoBUQitjonr, tlai it tj>e 
0K«rai ri^^ — To bcgia at tiie n|^ loui caiJajiui, or tke 

4« iaiid ii^'jaui to^btr^ ajjd ciideryiag Lciv iiasT/ aoiti 
Iferr? lit «« £ o^ ti^ £K«t S%Ur (X£>vjxau:*ir^ aod Jbciw 
^•cij <>>itfp;#»; li*^ ovtrprsA n v> tx fc lioniii w>dtr tie 

? a ai^ 



( 



132 ^V Vtll.OAn ARITHMCTtC. 

mIIo be ncitcd Iio'A' rn.iny units tbrre nre in ic of the next 
Irgtftr (IciK'ininatiun, nnd hnw niiKh overpltii : theovrrplut 
M ti> l)r phird under hi own rolninny and the units of the 
next dcnomiintinn add'-d tr> the next cuinmn, as before; 
411(1 fo on to every new column. 

Thn% in the fir ft of the three forr^ing exampict, 1 begin 
uith tlie unit fi<;nrc!i of the lowed ficiioininati' n, which k 
penrr, Tiying, 1 and 3 is 3, nnd 1 t4 4, and 4 if 8f and 9 it 
i 7, ami 1 is 19, and 9 is zB ; to which I add the tcni in the 
f.iiiM: (oinmn, flying, 28 and 10 is "^8, and 10 it 481 and 10 
i-* |;B ; now, hy the Y^i\r^ table, I know that jo pence is 4 
fliillin^fi ami % pence, thrrrfnrc ;9 |K*ncc it 4 fhillingf and 10 
pence: tJius, I imift fct down the 10 pence, which is the 
•vfrplus under xVr fume rohimn ; nnd the 4 fliillings, which 
are 4 units of the next ]ii;;licr dciirimination, I cany to le 
a.ldcd to the next (Iciioriiiii.ition, i.iying, 4 and 9 is 13, and 
7 is 10, and ; is 25, and 7 i<i 31, and 6 is 3S, and 7 is 4;; 
tu whi( li 1 add the tens laying, 4^ and 10 is ${, and 10 it 
6;, and 10 h 7^ : no.v, |iy the fliillin;; tiible, I ^\\i\ that 7$ 
iluHinf^s is 3 pounds r ^ niillinf;s ; the r ^ fhillinj^s arc to be 
ft;r uixUr fhr roliimn of (lnlliMjr:, ;i')'1 i!»r -^ povindf?, being 
ii:ii:ii of tlir nrxt (Irioin :i.:li(»r:, '.1/. j»fM)nd', iiP" to I -c a (I '.led 
th.ncfd: and flMj p^iiind';, Ik in;-, ti.' I.ilt .ind in^^htri dcnonii- 
n.itifiii, an: to In* jiIcImI r«igttlar .n l'fiiij»lr iiMnihcrs of one 
dfnoinin.ition, .tnd the to' il |il utd uud' r tlic finic: thus the 
total is found lo Ix i^z/. i :;«. io</. 

In the next cxnn)|J/ I l)r;;in with th»; f irtliings, Ixring of 
the |(;Wrll (!i rioiiiliiafu):i, f.iyiii;;, 2 l.irfhinr,'' and 2 is 4, awl 
\ is 7, and i is R, and 2 is \'^ \ ro f tirlnn;;«; is 2 pence and 
2 f.irthin;;s ; the 2 fatthin^q is to lie fti iindcr the line as 
overplus, and the 2 pence i*; to he wM^^^^ to the column of 
prn'-e, which, added np, anu)nnr«« to 4^ pence, which is 3 
(l)iliinr;s inrl 7 penrr ; tiio 7 pence is lo Ik* fct inider the 
folnnifi of penrr, and the '\ fliillin;;^ is to he added to the 
rolnmn of (liijlinos; in whicli eolnmn, with the 3 ad'lcd, 
there is 7c; niilhn«;s, or \ |K)nnds m^ flnllings; the 1^ ihii- 

111);;* 



OP TTTLGAS ARlTHllfiTXC. I3J 

Hogs • maft be placed under the ihlUingm and die 3 pounds 
added to the colooui of pounds^ and the pounds added 
togfctbcr as before, and the total placed undemeathi ibns the 
i^moaot of this film is 778/. 15/. 7!/. 

In the fame manner the thirds and every other foan in ibm 
put of additioo, is to be vrougbt. The fums are all nadf 
pnmred, for the eaie of th^ learner. The Hoe under the total 
ibews the amount of the fum without the top line: the 
bottom line (hews the amount of the line juft over it added 
to the top line of the fum, and proves the work right, by 
being equal to the firft total. 



Mare Examples Jhr the Learner's Praiike. 



£. i. J. 


£' 


/. 


d. 


I' 


s. /. 


47» 7 44 


176* 


9 


H 


179 


9 9i 


19 2 


ipoo 


3 


ft 


184 


19 oj 


145 19 ic| 


JO 


10 


^i 


soo 


I ^T 


701 


2A 


9 


3, 


301 


8 lof 
6 4t 

8 7* 


10 6| 
«7 8 > 


>»3 


4 
18 


o| 


401 

SI 


30 7 9i 


1*9 








33 


oi 


145 4 


7» 


6 


9i 


ift 


i» oj 


3Pi 10 10 


4' 


2 


II 


1 


4 4 


29 7 2I 


7 


4 


«i 


8 cl 


660 


8 


8 





6 


12 io| 


118^ a 


3'«3 
1421 


16 
6 


.1 


1368 
1 189 


'7 ^. 


712 12 9i 


7."^ 


1 1 S ^ 2 


3«»3 


16 


s^ 


1368 


<7 9 



jiddition of Avoirdupois Weight. 

By this weight are weighed all kinds of goods idiile?er| 
fxcept bread, gold^ iUver, and prepous fiooes* 



Tbt 



n* 



09 vuMAn AfLirnumc. 



4qtMrt€rii 

|6 dnirn« — • 

til poiiAfU -"• 
4 qimrteri *« 
to ItuiKlrcil wcigfct 



Tfkff Tabid o/AvmrdupoU might 



I drtffif — mat fc64 ^fri 

I poufidi -^ W. 

I qujii Mr of i huiHlrtd wria^iU fP» 

% hundfud wviKliCf '"^ /^ 

I too, — — 7; 



Aroirdupeii w«igbt i« dlvid^4 if>t^ l^wo ptrtif catl«il liif 

greater und the lah, Avoiidii|Hiii ilir grcAtcr iii»ri(li q( 
liiindredjii quarttrts, and |N)undfi; av/nidiipoii ttte Ufii »• 
dtvidcd into {luundiif ounccHi and dr^mn* 



I* 





4 ftS 


c. 


^r«. /^. 


*4 


* 4 


10 


9 





1 to 


•4 


f Q 


:0 


3 *« 


4^ 


f 


50 


1 fft 


40 


ro 


^a? 


a 1 1 




r:.~at ;: 





16 


16 


M. 


6«, 


'//■. 


9 


9 


19 


00 


«1 


»4 


.17 


11 





49 


4 


7 


6a 





( 


10 


7 





. If 


6 


7 


«4 





i« 




WW- — 


■ — - • 


»'? 


6 


\ 




•— ^' 


T"*"' 



4«« 
C| yri. Ik, 

7 3 '* 

9 

• 7 

1 o 

» 7 

40 o •<j 

I 3 o 

9 7 



Thc& «xumplefl {iif wrr>uf{tit In tlu? Oiitie mamtcr At the 
foniMffi but having itfgird tii th^ avoiidiipoic (ablei inftc4d 
<»f ib« pciiut lublc. And itwi number of unlti in tu\\ 
c^ltimni wbi(:h coni|)or0 ah unit in tk nr:iit liighfr column, 

it placcfd ar the hr^d of the aiUiti.n i thub, in tliefiidcx* 
onit^lr, A* atl i« the number of |)ound« whuh form oiip 
quurtrr of iin bundrc^l, it i« plmed over tlm cohimn of 
priund6( and 4f which i& the nuintter of i|uafter« contained 
In an hundred, i* pUced over the cohtmn of quarrcre. And 
in the l«lt t«amf>Ie, ifi l)ebig the nundier of drami cofirained 
in »fi ounce, it \% pUred over the eiihimn of drams \ and, «• 
i6oanc'C0 ft^rm « pogiid, i6ifit)i(ced over the Milumn of 

Oinicci; 



- ... . 0> tttdA* iMTflllfcTtC. 135 

o(iAc«i; «nd the like ii obfefved kt addition of other 
weight! and iMfafurei. 

In the flrA of thefe examples the number of poundi in the 
wA column 11 6a» whkh is a qnarlcrii niHi 6 poundi over 1 
the 6 it to be let under titc potiiuls| and the a quartera adde(l 
to the column of quarteri, which, with the amotint uf the 
whole columoi is 13 (|\iai'tciii| which is 3 liumfrcdi and 1 
quarter ; the 1 quarter is to he fcr under the quarters, and 
the 3 hundreds added to tlie next columni and the whole 
amount is found to be i93»^'. i^r. tii, 

AJiiVitloh iff Tvoy llVighi. 

By this weight are weighed breadi gold| filver, and pre- 
cious ftonea* The t^Aial denonritiationi afc pounds, otinces^ 
l>ennyweighti| and grains* 

■ ■ 

The TtGy IfVtghi Tatlv. 

' >B4 grains Aiakt i penny \^ eight, 
•o penny weights 1 ounce. 

tft ounces i pound troy^. 

Exam[)Us vJTnuj Jl'tlghf. 





la ao 14 


is. 


•s«^v.fr. 


4 


9 > »7 


m 


7 »9 7 
17 fi 


7 


I 


a la 9 





10 14 ao 


4 


II 10 II 


7 


4 3 » 


aH 


10 19 a 





\% 


ftO 94 


ih. 


CM. 


ptif.gr. 


12 


I 


1 1 ai 


« + 


la iQ 


»9 


1 


U) 8 


•0 


10 


7 7 


7 


II 


6 lA 


H 


10 


IS 


i« 





to \t 


oa 


K 


8 93 





11 90 ft4 


/*• 


04. /^tp. iy». 


:<» 


(> ft so 


M4 


ft 1 


47 


Ii) ai 


:<^ 


ft 1% 11 


249 


4 \o 10 


347 


7 i> 
t9 I 


1 - ■ ^ - • 


f> 6 1 



^UBCM; ana nch itivX into 24 cur&ts* ; ana each catut into 4 ^ttilni 

Thcfc 



1^6 or VULOAH AtlltHMBtrC. 



Tfittff vxnmplci are wrought nccoiding to the general rule 
gtvrn in the former p^rt of this lev'tion» and in the f«n\e 
manner at adtiUioo of stvoirdupoii ; but pnying a Av\(i 
rrgarti to the taUlei or the iigure« nt the head of each coiun^ 

ihf^ That the pound avolrdupoit U heavier than the 
pound tmy ) but the uvy ounce it heavier than the avoir* 
dupoia ouuce^ for itf«t#a« ta/io. troy ii equal to a |iound 
a>^irdupoti | and a pound troy ii about tjaat. i^r* avoii^ 
dupolt* 

tt it unneceflkry to give examplea of the other parts of 
addition, conteming apothecarlei* weighty iiqutd» dry, an4 
long mrafure«» jkc* ai the fame method fervet for all of themi 
having rcf|)eift to the tabic belonging to each* 

The Tabh ff Jpofhttcnrm* tfVf^hf. 



to graina 
3 (crtipici 
8 drama 


make 


1 fcruple, 
t drans 
t t>\incc^ 


marked f). 
J- 


ta ouacea 


— 


t i)oundk 


V,*, 



By ihia weight apothecaricK mix their drugi ; but thry ai a 
bought nnd iold by avoirdu|K)i» woighr. 

7 pounds makit t clove, 

a cloxcii, or 141b. 1 iWc. 

a ^mf, or aSUi. 1 tod. 

6 tiHl and a half t wrv, or iHalh* 

ft tvry«| or 364U>. t lack. 

ta iacka -« 1 lai^ or 4)68 lb* 

440 Ibt — t {vtck of w^dol. 

. Kttf* That \ Aonc it generally t4lb. in n^oft parts of 
England 1 but antoiig the l.ondoii butchert it ii only 81b. 



or VVLOAH A&XTSMinC. 



»37 



lU Table of Cloth M^Jitre. 

» 

• 4 na3% or 9 inchei make i quarter of a jmrd. 
4 quarten, or 36 inchet 1 yard. 

$ quarten, or 4; inchet ; 1 elf ^nglUh* 

6 quarterii or 54 inchet \ ell iFrenth. 

3 quartert, or 1 7 inchet 1 ell Fiemifli. 



TAc Talle of tFine Me/tfurt. 

B {Anlt make x gallon. 

4aga]loot — 

63 falloDt — 

84 gallona — 

ft bogflieadt — 

J pipet| or buttt 



X tierce. 

X hogfliead* 

X puncheon. 

X pipe, or butf* ^ 

X tun, oraji galloni< 



N§te. That Areet oil hath only 136 gallpnt to the tun. AD 
Kquidt are metfured by wine meafure, except beer and ale. 

Ale or Beer Meafure. 

8 pintt xnakc i gallon. 

8 gallons — i firkin, 

ft firkint — i kilderkin, 

ft kildcrkint — 1 barrel, 

x} barrel — x hogQiead. 

The ale and beer gallons are the fame ; but the beer llrkin 
contains 9 gallons; confequently, the kilderkin iS, the barrel 
36, &c. 



In M JumefWtnrthtri au^ 
ft pipes, XMT butts. • 
6 tierces, 
tji gallons. 
504 pottles. 
1008 quarts. 
SOX 6 pints. 
Vol.. I. 



In a Pipi^ or Buttt tbtfisn^ 
ft hoglheads. - i 
*i tierces. 

xft% g^loni. 

ft^ft'pbttlet. ^ "'^ 

iK^*<iiiwi. \ ""* 

X008 pints. 

In 



84 niloni. 



(n ttftltoni. 

* lifijpoMlff. 
• CK ntiftiti. 
564 'piiiti. 



/• Marr^i^/Sfff tb^0 art^ | U <• B^nft »»/ ^-//^ /Arrr ##iy. 



ft kildcfltinit 
4 Arkini. . 

i44i|tifir|At .' 



\ 



ft luitltflklM^. 

64 po((lc«. 
ft|6 ptiiii. 



r^# r«^A^ e/* /)ry Mp^iu^. 



ft plniA i|j«k9 

ft qu«rtt -~ 

ft poitloi •^ 

ft gftlloiu — 

4 pffckt -^ 

Sprrka — 

3 buflicU •— 

♦ btiflMli MOT 

4 quiirirni i— 
{ quiif im — 
• wtji •^ 

4 fafi or wtfr or 36 bitaicl|i 



f 
I 
I 
f 

I 
I 
I 

t 
I 
I 
I 
I 



A^#^#. Th|^ if yrli^l flnur (here 
Afft peek! to |)ii^)^. 



potetcr. 

ttuniHi IahiI niralillc. 
buAllfl, WAHrr MiraliJic. 
fAik. 

09fi)tH or biili quarirr. 

<|Mftrici. 

thitlilrofi. 

wry. 

Iiillt i\T 10 (jMAnftn. 

UiftUffin. 

Nrr atwAyi flvr biinirli tn 
bcapcdy gr dir Utrfr ftf' 




yULQAlt AMTM 



H'l 




Im L4f/i ikn mtf 

k ■ « ■ 1 1 

X • » ■ 111 

10 quirtert. 

flo b\itfiel«. 
Sto pecki. 
ii8o pottlet. 
3 $6^ quarts. 
$iiopiQt«. 



In UTty ihifi mif^ 
Squtrten* 
40 buflieti* 

t6o pecki; 

* 

3ftO gillODS. 

640 pottki. 
iftSoquarti. 
•560 pints. 



Long Meafure. 



3 biriey^ohit make' 

I a inch«t — 

3 feet , . , -" 

3 lett% 9 Jiichci ' — 

SfeeV- 

6 feet — 

5^ ytrdf — 
40 polcs^ or perclies — 

8 furlon^t * — 

3 mUci — 



I inch« 

J loot. 

1 yard. 

t ell Engliih. 

a geometrical pace. 

I t'at))om« 

I ^ei j)erch| or rod* 

1 fi^rlongr 

I Ehglifli iMile. 

I league. 



In M Afile thtrt art^ 



8 furlongs. 
3ao poles* 
1760 yards* 



$180 feet. 
6)360 inches. 
190080 barlcy«coms< 



Land Mca/ure. 
make 



.t»i 



54 yards 
4^Tqlian6 'potei 
1 60' fiix'i^r^ teller' - 

e6't>ii([U^n tenglh^aAd a in breadth 
40 poles in length, and 4 in breadth i acre. 
•4>irei'tn^icncth — - -»-- 

idVhifJi^lhlength, and 1 in breadth 

Sa 



I pole, perch, or rod* 
1 rood| or quarter of 
X acre. [aoi4cre. 
X acre. 



I chain. 
I acrt. 



Til 



i 



or irmAM% AMiruuwttc^ 




The Talk of Ti/nie. 

M feconds 0Mke 

60 mihnUf , «r 

S4 hottrt -^ 

4we«ki -^ 

13 mMfiM^ f diyi and near 6 bourt 

iW Tior thn srif 



f minute* 

f hour* 

I dajf, oatural* 

X week* 

I tnontfi^ (unar. 

I folar year* 



13 fponthi, 1 (!byt6 boors. 
52 weeks, s day, 6 hoors# 
365 dj^s, 6 hours* 



8,766 hours. 
$15,960 minutesi 
3 1,557,600 fccoDd^ 



y^te. The fcAMtyezr U dmded into 19 unequal months, 
called calendar months, according to the ancient verfis, which 
may tcrrt to imjireis the number of days each month con- 
tains, 6n the memory t 

Thirty days hath September, 

A|>ril, June, and November ; 

February hath twenty^eight afone. 

And aH the reft bare tbirty-one* 



SECT. III. 



OT SUBTHACTIOK. 

Sv art ACT tow, irulgarly called Suhflra^i^n^ teachetb bow 
to take a leTs number from a greater ; and (beweth the re- 
mainder, exceCf, or difference* Thus, if I take 7 fSmm 9^ 
there will remain %. 

RuU. Place the leis number under the greater \ obierfioii 
that the figures of each denomination in the left number And 



OV VWLOAK AMTHMHTir* ^4^ 

direAly undtr the figures of the fRtne denomination in i\\m 
greater numberi that \^ the units under unitif tena unileT 
tent, and poundii flulHngtf pence, ounces, drams, &c, ku 
dxttMy under the lame, as in addition. Then, beginninK at 
the righc hand, or the leaft denomination, take the value of 
each figure in the leTs number from that in the greater num- 
ber, which Ihinds dirciftly over it i fetcing down the remainder' 
undcrnuth. Proceed in this manner till the work lie tininied. 
But if, as U frequently hap|)ens, any Angle figure in the left 
number be greater than that in the greater n\imi>cr, fioiit 
which it is to be taken, an unit is to Ik U^rrownl from the 
next figure towards the left hand of the greater nun)l>cr| and- 
added to the uppermoft figure, that the botton) figure may be 
taken therefrom i which l)orrowed unit mull be paid, or 
added» to the next figure of the Icfs number on the left lutud. 

From 6954 1719886 370190^70 grrntcrnumlwrs. 

Takej44^ 1098907 iaB4Q;<4<)t lels number. 

Rem. iju 6309 79 «4 1 HH087H 

Proof 69^4. 1719880 •^7oat)0^7o 

To flicw the ufe of this mic, I f.iy — Svip]V)le ;i nicrduint 
owed 6954/. whereof lie has p,iid ^44^* : 10 know what re* 
mains to be paid, the liims nrc to l>c fct ottlcrly on4 tuuler 
tl)e other, according 10 tl)c fore^^ning rvile, ami us fcen in the 
examples: then, beginning with the unit fi^'urrs in thr full 
example, I fay, take 3 from 4 and there reniaitu 1, which i 
fet under the line ; next take 4 from f; and tiietc renuins 1, ' 
which is alfo fet under the line; a^\atn, take 4 fioni 9 nnd- 
there Kmains 5, which mud be fci down as bclarcj and,' 
kftly, take $ from 6 and theiis remains 1 : thus there rcni.iin* 
dtieijti/. H 

SublraSion is ptx)ved by niiding the remainder to the icl > 
of the two given numbers, juhI if the total of ihcfc two nun»-i 
hers amount to the cxaA fnm of the greater ntHuln:i, thci 

woik 



I/I (mm lO'ih Ok. fit 'J ligHK; I /.lyi I) f»^^/HO fH iifMi l)fi$fti M« 
iMy Ml'^Vfiyn h«. iliiHr: wliKil iUt ^Wn fifp^^H** Hfi- fti<i l^fVlK) | 

t'll/l • i Miti^ 111 i fl*. trtMii: ff po'itf* f in ^\t^ \\\h ') ^ «4fH|lf»^ i Irtyi' 
ihftrft! if-ffiiiina i', . ihth f Ifiti f )><«»M.'Vi'1 ar;«1 >; io I'/, I'rtttitit 

iUni I tiMM'ru/i't ih'l .( U \i ', li/|if> n I l'«hiMi^ i*H* *^ itnth 1 1 

iitftUUijI^) \ <>ilM»'|t| \nH ^ IfiiM I <« «f rift 1 1 i^f*r tHli«M»« 0) *^l^*^$ 






Of VIM « AH AlirrUMKTlC. I4J 

tUfvovt*vt*l by t«l»fvtti*lin); \\w Mr ol the vcai lUc cvcm |j»»p- 

NV4Hi»1ii\vi> »V- ii% »y* 

|*hn^ »*ot ISM I'*"! 

iamc |»i'ihri|k)r m« Iuti04«*lhui ut fuutibi*niot 4M\i- tlt'n«thtiu:(tioh. 
OUVrvio^^ i\\M wWwAW \inii ii hunoxvcil t^t ihr nrxt )\i|*t\c) 

uttttniiV v^hir. iiiul \\\\\\\ W \i\\.\U\ to ilir lown fi^uir of the 
tkmr ilrtimtuntttmiu «» will l*r Iccii in ihr Mlowin^CXJiU* 

id u 4 i^ «•> 4 

•-^— |>aU 10 u) f»| m 10 *jt 



..A 



htvf 17 Li A iM i» /4 

I v. 



^Wtivll t IrC UIHlrV i\\P r4l(tuni<- . (lu-it (01 die Ut\i( I lHiiHi\v<-il 

u' ihr |M?iit'r» J n«M 1 to iltr c«. mmu)* o m\y\ 1 i* ; i now 7 

nentalt^l 4 ; Ittlllx, !o tuM\i I*' A\\x\ i\\c\c \v\\\:\.\\^ 7 ; llius lh<' 

la (he TcxMUtl r\(tiu|>lc» I Uv» 1 t;«itluni* honi t ;t)ul ihnr 
it'tUi^UU ^ iAi\\\\\\^'.^ 01 (tu li(tll)»rnitv , ultult I UM down in 
iCl pu^l l^JdtVt \t^« luitlci tlir (liiwxniiuiMoii ot t,\nliiii^« 1^ 
(hc^f) S)tUUl) 7 ) iMuuttt, wlu-irt'ou* luMioNxut^ ( ihiDiii); (uuii 
(Nr 44)Ahit (tJilin^ it to ihc 7 i>oiuvt wliioli mnko ig jVhii', 
II^Vi t$ tivni to M\\\ \\\t\^ irntdut^ 102 \\\^\\ I that I t'oi 

l\»\VCtl 



^(44 ^^ VtftdAR ARITICMSTICf 



rowed And 19 U 2O9 10 from 14 1 cunnotf wlierefore I borrovir 
I pound from the poundi, wbichy Added to the 14^ makci 34 
fliillingi ( tbereforet I fay, so from 34 And there reinaini 14) 
then I thai I borrowed And 1 is t, a from 3 And there re> 
mAiflf 1 1 und I from t And there remAbii 1 1 thui, the An- 
fwer to tbU Aim If 1 1/. 141. io{//. ( Aiid iti proofs under tlic 
»n(Wer| flicwi timt it i« ri|{ht. 

■ 

Mora Exampleu 

}o 1 1 4 10 I'z 4 xo I i 4 

/ft it d» £9 i» dt £• u d» 

Pg« 174 JO 9i 14$ 6 io# IA94 19 10^ 

raid 99 1; 10 no ii rif 1001 19 10] 

RemAini 74 ii iij ^4 1^ ni 19^ o o^ 



I'roof 17 4 fo 9t 14$ 6 loj 1194 9 io 



If tlfomgneypekl be paid aC icverftl timei, the fiimf fo 
paid Are to be added togetlierf and tlie total fiibtroAed from 
the ium /Irft due* 



Due 14c 19 6 Received 



I'uid at f<^veral I 30 9 8 Paid to feveral 
timck I o 10 6 pcrfoui 



F«id ift all ^ 9 o o Paid in all 

Keufdue tt6 re; 6 Reds due 1064 19 o 

Proof i4(; k/ 6 Proof iiao 10 o 

■^ ■ I » » ■ I ■■ ■ I ^^ I ■ I ■ M ■■ II mm 

m- ■■ ... — » -» •*"^^"»'' , - J 

lixa^nplea in AvoirdupaU tVtlglit, 

4 a8 4 a8 16 16 

Fr^m la % ao 147 a 9 19 9 14 





'I* 



Jiikc io % SI ii6 :) m la 






Rfihuini A o A7 ;40 a a{ 7 o ii 

figof la 3 AO 147 * H. 49 9 »4 



I 

i 



09 TVioAii AiimnfiTie« 145 

Examples in Tmy Weighs 

fto 14 

190 19 aa 



From 


•47 


12 to 

10 18 

11 19 


•4 

ao 
at 


Remains 


^8 
3?^ 


10 18 
10 (8 


aa 

ao 



aSo^ 16 a^ 

3in 16 »i 

Thefe examplet* and all otheri of other denominatiQns, 
treivrought in the famp manner as fubtraAian of money; 
liaving TtfpeA to the table 1>elo'ngtng to <Ke denomination: 
thuii in the firft example of avoirdupoii weight| I fay, take 
• X pQUndf from ao I cannot, wherefore I Uurow 1 quarter 
of an hnndred from the 3 quarten, and add it to the ao« which 
makes 48 pounds; then I fay, a i from 48 and there renuins 
17 i next, 1 that I borrowed and a is 3, 3 from 3 I c»iuu)t, 
wherefore I fet down o, as before hinted; laAly, 10 from la 
and there remains a« 

The figures at the head of the columns ihew the number 
of units which each unit of the next higher danomination 
contains. 



<muf 



SECT. IV. 

OF MULTIPLICATION. 

Multiplication is, perhaps, the moft nccclTary rule in 
lUrithmetiCi for bufinefs, on accoynt of its difptch in relolving 
lieverai long queftions. 

Multiplication teaches how, from two given numberi, to 
find a third, that ihall contain either ut the two given num* 
bers as often as the other contains units : thus, 3 times 4 is 
It ; here 3 and 4 are the two given numbers, and la is tho 
third number, or produ^, which contains 3 as often as 4 
contains unitSi vix. 4 times \ or it contains 4 as often as 3 
contains ^nita^ 3 times* 

VoL.L T Thcu 



t4» 



M WMMII AMnmWt¥h 



0Uii««it <4' df Hfiii I mil^i into ymdi. hpu bm l«»y-isorim f^« 
8«e€iiuUy« lhviii|{ iht^ Unnifc niut bri^di i»t a |iUiii lur« 

Thirdly. Hivfhg ib^ rut* w vulw pf *ny «!»* iWm^, w* 
ki^w tlH» rM« or vaIu* of Mny number of (\i(^U things, bow* 
i^v«r KfMt. 

Qmi [iphrp tbf tfunifr f 9A h^gin thU riili>, (t It uMblutidy 
it^^Aiy tbiit hi» bitv<» ib« follow in| tiibl(» tn^ifeAly by b^nri i 

Thp MuMplimlim Ttikk. 



3 - 



i ' < 



{ 



I 

10 



n^ 



10 — 

It '=' 



ft 
•4 



aiifiit)* 



3 ~ 

4 — 



9 
(* 



' 



I- 11 



<o 



itm^M 



i tiUH^li 



■ l i-M 







9 — 



Jli 



M ll«i#t| 1**^ 



«• tlfAtu i« i* 144 



Tb# 



0» vviLOAii AKivnity rtc^ t4| 

The ufe of tMa mMe i«, to And xht firoduA of any two 
immUm} thtt^ 10 fliut th« product ot 6 timet ;» 1 look \i\ 
th« hrftve whkh ha« 6 at the polut, ami iu the line which hai 
7 at the hcigii^ulpy» oppolite to which U x\w produft. which 
U 4e. 

The table ia h» he thut i^«»d i— 

B«l^iAnlng with the flill biDce» I fay— a tlmea e it 4, t 
timen 3 \% 6, • timet 4 ia 8t a timet ^ it 10. a timet 6 It la, 
• timet 7 it 144 t tinvet 8 it 16, a timet 9 it i8« a timet i» 
ta tO) a t\mea 1 1 it aa, a timet la it a4. 

Theoi |iroceeitii\|[ in the lame nmniieri 1 hc|;iii with the 
{QQWiii hraee, fi^ i(\s, 3 timet 3 It ^ | timet 4 i« >•» 3 Umea 
S ia ij. 3 timea 6 it iV, j tinm 7 it ai| 3 tinvet 8 it a4t 3 ^^ 

tiipet 9 it a7t 3 tlmci 10 It 30* 3 timet 1 1 it 33. 3 timet la ^^ 

U36, 

A||^a\i\i 1 begin with the thkd bracei faylngt 4 tinvet 4 it ^ 
i6» 4 t'unet { ii aOi 4 timet 6 it a4i 4 tluust 7 it a8| 4 tit^ea 
t it }9t 4 timet q it 36* 4 timet 10 it 4O1 4 titpet 11 it 44^ 
4 timet ta it 4k 

Then* 1 (ay> j timet 0« «S> S ^1"^^* ^ ^* J^^t S <^*^^^^ 7 i* 
3S% S <i<^^t»a 8 it 4Q| i timet 9 it 4S> S ^^^^^^^ ^^ ^* S'S i ti^«^«« 
^ t it ^^t ^ timea la it 6ot 

Then, 6 tioiea 6 it 361 6 timet 7 it j^%» ^ timet 8 it 48, 6 
tifnet 9 it S4i 6 timet 10 it ()^| 6 tiu^et 11 it 66, 6 timet la 
w jat 

ThePi 7 timet 7 it 4i>. 7 timet 8 U 5;6, 7 timet y it 63, 

I tUnti 10 it 7Qi 7 tiiDet u ii 771 7 ^'^^^^^^ ^« i* ^4* 

ThfA 8 tifiwa 8 it 64, 8 timet si it 7a, 8 timet 10 it 80, 8 
lUnea 1 1 ia 88i 8 timet la it g6. 

Again, 9 timet q it 81^ (> timet 10 U qo, 9 timet 1 1 i» 991 
^ timea la it io8. 

Then^ 10 timet to It loo, 10 timet ti it no. 10 timet la 
U iao« 

Aiui, 11 timet 11 it lai, u timet u it ija. 

Laftf/i la timra tiii 144* 

Tt hi 



t 



t4t Of TirtOAR AIIITBliBTIC* 

y ■' I ■ » !■! mmmmmmmmmm^ 

In multiplicattoa there are three termi : viz. 

The Muliipiicand^ li or fum to be maltiplied i 
Mult I flier i 10 
Prtudu^t 120 or refiilt of the i^hdle. 

Multiplication confiftt of two parti t muhiptication of 
jinmbcrsof one denomination, atid Aiutfiplfcation of divers 
i1enominai)un9. 

Mtiltlplication of numb'eff of ofie (tenomioMioti \i either 
fingle or compound.' 

Single mtiltlplieation ij, when the multiplicand and mul- 
tiplier, confill, each of thehif of only la, or left than la ( 
and may he pei'Fornled by oMe operation, and with one pro- 
clud. Hence thi {^reateft produ^ that can arife by fingU 
multiplication ii 144, ai that ii the produ^of 11 timet it. 

Compound multiplication fi, when the multiplicand or 
multiplier, or both, confift of more than li, and require! 
ihore th&n one operation. 

Rule, Place the multiplier under the multiplicand, in the 

natural ordet of figuret, vitt uhitt andcr units, &c.; then, if 

the multiplier conHft of la or left, multiply every figure of 

the multiplicand by the multiplier ; beginning at the place 

of imiK, mi J placing the units of the produdt right under the 

\inits of the multiplier ; carrying the tens, <5r tens ami hun* 

ilrcds, if there be any, to be added to the next produA* 

Proceed In this manner through the whole, and fet down the 

v.'liole produdl Jl the lad figure, as In the annexed example; 

olHcrving, for every ten that ii carried to the next prodkiA, 

an unit is to be added thereto ) and for every hundred, teti iH 

to be added* 

Multiplicand 1S09 
. . . i Multiplier la 

Frodudl 14508 

In this example, the multiplier being la, I fay, la timet 9 
it io8| wherefore I fet dowa B| the uniu of this produft, and 

cany 



Of VUL0AR ABITtllfBTlC* I49 



carry 10 to be added to the next product, fayingi it timet o, 
or It timeaoothing is nothings thu« I have no produA from 
this figure^ wherefore I fet dpwn the unit figure of the 10 I 
carried to be added to this produA, which is o, and cariy tbo 
remaining i to be added to the next product ; faying^ is 
times It (as the two next figures in the multiplicand is it) b 
144 and the 1 1 carried makes 14$ ; wherefore I fet it dowOf 
being the produ& of the Inft figures. And the whoJe produft 
of it09» multiplied by it, is x4SoS. 

But, if the multiplier confift of feveral places^ after having 
multiplied the mukiplicaml by the firfl, or two firft figares* 
as before d'ire£M, multiply it in like manner by the next, or 
two next figures, if they be it or lefs, and in like manner by 
aH the other figures ; placing the produAs below each othcr^ 
AriAly obferving that the piodudt of each new multiplier is 
to haye itt unit placed exaAly under the unit in fuch new 
multiplier, and the fubfequent figures in their regular order 
towards the left hand ; and then the different produds added 
together in the order in which they (land ; as in the following 
examples : — 

Example* Proof, 

Mu\t\p\\cand 109 701 2 Til ft tnuUipliianJ !'''() 701^ 

Multiplier 1104 H.tlf the muhipliM (41 

4J8K04J> "7'>r.;oS4 

987J108 4^SSi'4S 

131^144 6<;^?. 7\ 

HM^7??^8 iMva proau.^. or 1:0,^00764 , ^. . 

pn>uuv*t J — - 

In this example, I begin with tlic fird figure in the mul* 
tipUer (as the two full arc niorc than 12), I'^iying, 4 times x 
is t times 4, that is 8, which I place in the lirll line of c!ie 
produf^, add under 4 the nuiltiplier j then 4 times i is 4^ 
winch I alfo fct down in the next place ; ihcn 4 times o is o, 
or nothing, wherefore I let down o; next, 4 times 7 is 18, 
therefore I fay, 8 to be let down, and carry a ; 4 times 9 is 

t 3^ 




or TOlAit MlMMtTie. 

mmmmmmmmmmammoBesBgmm 

36, tml a that I carried it jl, 8 and carry 3 ; 4 time$ o is 
nothing, wherefore I have nothinf^ to ict down but ttie 3 I 
carried ; agiiin, 4 limes i is 4 1 thus I have done wiih the 
firft figure In the mtiltiplior. Beginning with the next, 1 1'a>% 
9 timet a or a timet 9 it 18. 8 and carry 1 ; the 8 it to bo 
fet evaAly tinder the multiplier 91 then 9 timet t it 9, and t 
I carried b iOi o and carry 1 ) 9 timet o It 0| wherefore I fee 
down the I I carried ; again, 9 timet 7 it 63^ 3 and carry 6 ; 
9 timet 9 it 8i« and 6 it 87* 7 and carry 8 ; 9 timet o it o» 
but 8 wat carried ; 9 timet i it 9 1 thut I have done with 
the Acond mtlltiplitr* • The nestt aiKl laft two figuret in iht 
multiplier being la, I multiply by them at by one Agure^ 
placing the unit figure of the firft prodiiA under that of tbt 
multiplier, which it the a t iaying^ ta timet a, or a timet i^ 
it 14, 4 and carry a ; la timet t it la, and a it i4» 4 ao4 
carry 1 ; la timet o is o, but 1 wat carried 1 ia timet 7 ia 
84« 4 and cnrry 8 ; la times 9 is 108^ and 8 it ii6» 6 and 
cairy II : la times o is o, but 1 1 wat carried, therefore I ftt 
down I, and carry 1 ; la timet 1 it la, and 1 it 13 { which 
being the ltd, I fct it down. The work being finiflied, aM 
the fevcml produAt are added together, and the total is the 
real prOiluA. 

The woik it proved by dividing the multiplier in half, and 
multiplying the original multi}Jicaud by one half, and the 
piiHluC> thence aiifing by ihc number a, as fecn in the fore* 
lining example. Uut if the multiplier cannot be divided ex« 
aclly in halfi ai is ihc cue when it confifts of an odd number^ 
then u number that is an unit lefs than the multiplier is to be 
divided in half} and the multiplicand multiplied by the one 
half, and tliat produ^> by a, as before, and the original 
muhipltcand added to the bll product, as in the following 
examples:*- 



jlaV^MMft 



or WLOUi AinmutTie, 



SMWfii. 

-iat' 

7it9»86i04 
[1 38989 156 



379*430» 



1 64005 ;()B464o 



Ifl prwing thUntwnple, I cannot divide the multiplier 
43*1 cXi^ff m htU, becaul« it containi in odd number in 
the pltce of unin ; I therefore take a number that ii an unit 
left, vii. 43aOi and divide it in half tbui 1 layint;, the half 
of four tbouftnd it two ihoufind, and the Italf of three hun- 
dred tnd twenty it one hundred and flxty ; which, together, 
iaaibo for the firft multiplier in the proof; the product of 
which li again multiplied byt, and that produi^ added to 
tbo itSc mulliplictnd, whioh giwa a prodiiA equal to th6 
pwduA in the example; which prove* the worli ri,>;ht. 

When eke multiplier lui cypheri iiuentiijied with tli'- nther 
figunh the figniHcant fif^rei only arc to be regarded aa 
mulliplieri, obfcrvinf; the dire^ions txfore f;ivcn, to place 
the unit figure of each produA under that of the multiplier t 
M in the feJIowinn examplei :— 



' 


tl'!l: 





J;i.;|; 


Si$:^ 





SBloHI'moKl?!')! 


:!2 



Mil '!" 
>|,I>,|(.|,Ib|,I,Io.. 


♦ ♦ 

Ho 


TtTtH" 


» 



5l7|ol4l(^t»|o|»l7i2l61o 



WJwn the mulltplier, or multiplicand, or boit^ eonfiH of 



||| M VinOAR AKITHMRTIC, 

r))ihru lowartU iha ri|lil liaiul, aiMfignlllcNHi Ayu>'i« 
will |)lii'e4 40 ibt riftht lund of ilie jiioilufl ; u liilli)w& i^ 



• «l 


6,|,|. 


ir 







<> 




Ju' 










^ill 


i2^'* 


i^ 


^ 


■ 


B 




|n ih« jtroAroflhe Uft i)iiiirn|fl<^t >l«> intil(ij>ll<'*ini] )■ «diletl 
(innot ba d|vi4(;4 Md^ly in Inlf. 

J^ulfifili'iitkii ^ iiiv'ti Dfrnmht'iimt, 

Mulitpli'Dilnti flf 4ivt>i« ilennminMiimi i* p#rti>rnihl hy 
miili)|>l)ing Mcli (lennminiintrn Ity ttw iniilii)ill«r i toglnDiog 
wiih iha UiA dnmininaiiAn, anil rnrrylng ihn iitxri ol rtic 
Kriri tlrm)inttHli<iii M be Att,k4 tUrrent, mi hi miMIikhi aI 
ntaney 

Mul(i|tticti)i>ii af (liven (l«niH»iiiiiiiiHii ii eirlin tinjiUor 
rflinpauiitl 1 litl^lr, wlwn ihr nm)t)|)lkr i'iinli(l« »( li or 
Icl'i, anil U ptir<wn)«4 liy nn' i)n)lii|ilici' i t-iNii|K)nnil, v.\ien 
ttx innliiplirrfMililli lit mure iliin i«, cinil leijiiitca mm* 
iluin one uiuliiplUr. 



I. ,. J. 



/w/. 



g -i— ' 



OF TVIQAR AllTHMITIO, I5J 

In th)f exanipie I begin with the pence, laying H times S 
ii 64, which ii 5 Ihilhng!) and 4 pence i the 4 pence 1 lit 
down undei thepcnc^, and carr)- (he j lhilling» to be added 
to the produA of 0)illing« ; iayingi 8 timet 10 in 80 and $ 
U 8^, or 4A ji. the S flnllingt 1 let under the ihilluig:!, and 
carry the 4 pouodi tu the uexi produ«lt : then 8 times 9 i» ;» 
and 4 is ;6. 

The woi'k it proved at the former exainplei. viz. by 
dividing the multiplier in half, and multiplying by one halt, 
iMid that produft by a. 

But in compound inultiplicati«m of divert denominationti 
or when the muhiplier it more than i»« the multiplier it to 
be rc(o/ved Jnro irt two conimenlurable |)artt| if it l>e a com- 
menfurable nuntbert and the multiplicand multiphed by one 
of thofe parttf and that prcnluct by the other p.u-t : thns| if 
the multiplier be 36. I multiply by 6« and alfi> the prinhu'l 
thence artfing by 6| which are the two commenhuable 
partt : for 6 timet 6 it 36. 

But if the muhiplier be not a commenfunnble number, ot 
one which caunot be relolved into partt exai^tly« then the 
next lower number which is a comntcnlurable luu*, is tu he 
taken, and the multiplicand multiplied by the two pait:iai 
before* and the multiplicand multiplied hy the overplus, ami 
that pi'oJuf^i added to the lull prinluA : at in the number 46, 
Thia number cannot be relolved exactly into two, or three 
commenfurable partSi there \>c'\ng no iuch number in the 
multiplication tablet wherefore 1 take the nc^^t lower eoin- 
m^ifurable number 4^, beoaul'e <; times i) i> 4^» and multi- 
ply by thei'e two numbers, and the multiplicand l>)- 1, whivh 
rouft be added to the produ(^t. 

1 }^fry. What is the amount of 36 piecrsi of cloth, at 
7/. 14J. 6«/. each piece '^'— lleie I multiply by 6, and that 
product by 6. 



Vol. I. i: r^amfl^s 



i|4 <»f yuLOAm AaiTumric^ 

Example* Pr9§/. 

7 «4 • 7 «4 6 

* 3 

46 y o 

6 




a^H t o 139 I o 

1 f "ii: m 



%fi ft o 



a i^. Whit ii the amount of 46 fcore of fti*con)^ iC 
38A iBit Oi^ per fcore? 

Ex€m^. Frnf. 

39 18 o 38 18 o 



5 3 



194 10 o iti 14 o 

_„ 9 7 



1750 10 o Hib 18 o 



1 789 8 



m mm^mmmmmi^mmm^ 



o 



77 t6 o 

894 14 o 

1789 8 o 



^ 



In the firft of thefe exunplei » the work \% proved by mwh 
tiplying by 3, and that produft by 6 (which it equal to 
multiplying by i8| halfthe original multiplitr)i and the lift 
produd by i| at direAed before. 

In the fecond example, I multiply by j, and that prodilft 
by 9i which tt equal to multiplying by 4j, and for the othcf 
one I add the mukiplicind to the laft produA. In the proof 
of thii eximpic, I multiply by 3^ iud that produft by 7^ 
which being equal to 1 1 , wants t of half the multiplier 461 
I therefxire multiply the original multiplicand by t, and add 
the produa to the laft produft | the whole of which I liftl/ 
multiply by a. 



1 

1 



or rvLOAa AAmmnc^ 




EsampUi iu AyQirJUtpok liVhghi. 
3 9u, What ii the weight of 107 chefis of tet; each 
cheft weighing (bar hoDditdy three qoarcen, and twenty* 
two poundi ? 

ExmmpU. Pr9§f. 

C ffs. Ih» C. frt. /!• 

4 3 a» 43 a* 

10 t 



49 


to 


49* 


1 16 




7 


34 


• «4 


^•9 


I • 



•4 


• 
I 


16 
10 


•47 


8 






3 


H 


3 


10 


a6» 





18 

• 


5U 
5*9 


1 

1 


8 

a 



In thit enmple too it the neireft coiimMnfimMe number^ 
but the multiplier it 107 1 I therefoK mnhipfjr by 10 and 
to, and the original anultipUcand by 7 \ whkh laft produiSt 
M added to the other. 

In the proofi becaufe 107 is an odd numt>er| I take the 
half of 106, which it 53 ; multiplying l)y { and 10, for $0| 
and the original multiplicand by 3 ; then 1 multiply the 
whole produA by a^ which doubles it to 106 ; audi laftlyi add 
the multiplicand to the product fi>r the 1 that was wanting. 

By tbele examples it may be icen» that there i3 no occafion 
to have always a commenfurable numberi or to come very 
near one; foTy if it want ever io much| it may be worked in 
this manner; always multiplying the original multiplicand 
by tlie overplus, and adding Inch produd to the other. 

It muft I)e obfervcd, that it' the multiplier, in this p;irt of 
iriultipllcationf confift of more than 144, it muft be icfolved 
Into thite multipliers at Icaft ; and if it conftft of more than 
IJ2^^ it mufi be rcfolvcd into more than three. 

U a 4 ^- 



.156 or TVlOAlt 41tmiltlTIC% 

4 :(«r. Whut u ihr fupetAcitl content of m puce of gtxmitdi 
whofe biTa<)th it 10*74 feet* «nd Ict^gth t4f>40 ? 

•4^40 
Hcit I multiply the ien|th b/ the bte«dth 101^4 

(whtth it die general rule in luperAciul >.v ^i- 98^60 

fute)| and the pixxiuA uiSJtjij^o fqiMre 17*4^0 
fccti foriht«)rwtr. t4?^*o^ 

5 :(»• How muny folid feet does a piece of tImlKr 1 ocw 
tain. thAt ii forty feet in Icngthi four in breadth, ami three 
in d> {ith ^ 

Here the general rule i«, to multiply the length 40 

length by the hieadthi and that produi^ hieadth 4 
by the depths Aod the produ^ ii 460 

ibiid ftct| for the anfwtr. depth 




Multiplication teachen alfo how to multiply diflcrentdeno* 
aninationi of meature by different denominatiomi, called «i^l 
mafr^iM/iM I of which I (hall \\yt$k in menturatuMu 

Multiplication alfo fcrvei to bring great dcuivmin^ition^ of 
money, weight*, or meAturei, into fmall <meii but this nuuc 
proi)erly bclo(\gt to the rule of rcduAion. 



m 



SECT. W 
OP DtviaioiVt 

DiviatON teachetji how, ftx>m two gi\xn number*^ to 
And a third) that fltall l>e containetl in the bigell of the 
twogtven numlH^rii' af often ai the fmallctl cont.iuu units 1 
or the third numl)er contains uttitii as of\en as the hmikft 
ol the two given numl)eis is CfintaineAl iA the other. Thus, 
U I ^ wf lie to l>e divideil by 3, the anfwer wo\ild bo ^ i lor 3 
Is cohtainetl in i j, 5 tintes i and j is i:onta«ncd in 1 s, j times« 

As muhiplicattoii teavheth ho#tobiing gi^ai dcnomina* 

(iolU 



or vuLOAi^ AMTiimno. 157 



tioni Into fmall ones 1 and having the rale or value ot one 
thing I to know the rate or value of many ; and from the 
length and breadth of a fuperficiei, to know Its contents 
dtct fo, on the contrar}-, diviiion teachcth how to bring 
fmall denomination! into great one 1 ; and from the rale or 
valu€ of many things, and the number of them giveui 10 
know the rate or value of one ; and from the conicnti of a 
fuperficieti and the length, to find the bi-eadth ; oKftom tht 
iu|)erftcict, and the breadth, to find the length ) and in^m 
the contentt of a folid| and one dimenfion thereof, 10 find 
the other two. 

In every fum in divi(ion» there are three parti which are 
to be particul;irly rcmembcml, viz. 
The Z)mV(f/ii/, or n\m»ber to be diviiled. 

J)ivi/0ff or nuiitberby which we divide. 
ji^araffVff/, oi nniwer to the work, which (Itcws hotr 
often the dwifor it contained in the dividend. Thuii, in the 
before^mcntioned inibmce, 1 5 if the dividend, 3 the divifort 
and 5 the <|UOtient. 

Hcfidea thefc three parts, which are in every (urn, there ta 
fometimet a remainder, when the woik m iiniihcd, which 
will aiwttyi happen w*licn the dividcud docb not exaoily cun*. 
tarn the divifor a certain numhci* of tinK*s: a>, il 1 wet c to 
divide 13 by 4; here 4 the diviior is ront.unai 3 timca 
in the dividend 13, and there is a icuuiiuicr oF i; and in 
diviiion of divers dcnoininntionH, it nuill l)e noted, that 
the remainder is always of the lame denomination wiih tl»e 
dividend. 

Divifion is cither finjjlr, or coniponnd : finale divifion it 
tvhen the diviior docs not con (ill oi nioic than 12, and the 
dividend of not moic than 144. Any ({neiiions of this ibrt 
may beanfwercd at once by tiic luuliiplication table, without 
fetting them down : thiiN, it it wcic nqxiircd to divide 1 10 
by t0| by that table 1 know that 10 times 1 1 is no; thus to 
is contained 1 1 times in 1 10, and 1 1 is the quotient. 

Compound diviiion is when the diviior contains more 
than IS, or dividend more than 144, or both. 

In divifion the dividend ii to have a crooked line placed nt 

each 



\ 



r 



or VVlOMi AlllTKMBTIC, 



cjfihtrt (owanU the riglir liam), *nil li|[nkltnnt <{|[uru igaj 

ffird* ibt kfi. 'U(b cyphtri arc mtiitwil In tbe < 

wid f>li(ril on lb( tithi liiuxl of llie iiroOuA i m fuUomt- 



i)«l7l«4;9lo|7|« 



nv. 



tU 






l)«?'*[^ 




In ih« proof a/ the 1*1) runi|>lc, iho niDbljttkMid ii addccl j 
to the prodiifl u Ixfnfi: ilirr/>cil,wli4:nltour(j(lnill mulli^illrr 1 



AtulliplhOtiou nj linn* iitnnmintitimu. 

MulitplirnHnii nf divru (kni'mitinHon* t» ptriitmnl bf 
miillil>lj lfi([ r«li (len'iminititHi \<y llir mnltijiller ; bf|{tnfi(it|( 
wiih ihi Ifift f)r mm In HI ran, mil rnrryin); iho uniMnf 'I'" 
Ttt%\ iltnnrnln^ti'in to tx ndiltd tlirreio, m in MtJIllon ef 
mnnvy 

Mulilplieiiiivi nf ilivrii riKmiitiiriiil'pni it titber fin|tl*«r 
roinpoiiiiil 1 finjjlr, wlitn thf m(ilri|ilh!r '■nnflft* of ii « 
Itft, *n<ll* p«rro>m«(l t'y nne tnullijiltcri cninpoiinil, whtn 
th« inultifiltfr rnnfinii.l niute iliiii i>, xitd leijiitru muri 
tlun one intrltipli«r. 



t. .. J. 



/',»/. 



]LJ^ 



i 



1 th«rf foro ptaec 6 in thd qtiotittUi tud multiply tht clivtltir 
7 th€t^]r« and th« pruduet 4t i lot und«r tlit dlvUhmd 4i| 
tu bt AibUfiAtfi thtfi efrom i «nd lo the rrmaindtr 6| 1 bring 
Oown the neit Mgure ;» of the orlglnni dlvltlMidi thui I hav« 
tff9t% nt w dividoniU Then 1 ntk how ufttn 7 it contiilii«4 
bi 67, which 1 And i« 9 timet \ 1 theivffii'e pnt 9 in dw 
^uotirnti und mialtiply th» divirur thrreliyi Mid iho praduft 
i$ 1 piuM iimfer« Ami tubtinA fmni, the Ui dlrklond) nnd It 
th« ittnaimioi* 4 I bring down the next und Inft Ngnrc 6 in 
the (U'lgtmil dividend, whioh makr« 46 for a n^w dividend* 
Tben 1 aikhnw often 7 U contained in 46. which I And it 6 
limt II 1 place 4 in the t|notionr« mul multiply die divUtir 
thereby} tll•p^MiuA 4a 1 Aibird^t fntrnthe latl dividtnid ^ 
and theiY biing nn more rig\ire« in the oiiginal dividend #• 
bring dnwnthero it h letnainder of 4 After the woik It Knili- 
ed| and whieh remainder it Mlway« iefi th^n the divifoti if 
the work ba rigitc. 

The remainder, iniy be fet over the divifor At a fraAian 
of an unit I thui in the nnfwerto thi^ queltiun 1 if 4(1 tM. 
were to bo divided etpiAlly among 7 men. whAt wt^nld each 
nian'i A\are amount to ^ JmA 6iA'* ^tul 4.7th« x^i u |ii»und. 

I^iviflon it proved hy nutlti|du*Ation: thut \\\c taiejt«mig 
^ttm\do it imiN'vd by muhiplying the quotient by the dlvU 
n>ii »ddin|[ thereto the rrumtnder, luul if the produdt tie 
^inal tt^ the dividend the woik u li^lu \ othrrwiic nut. 



8)6iallo(76nv5 


ii)i»7«7Vt7(^t 
11*" II 

77 »'*7*y 
77 

• 


4« 

4« 




O.Ti 





In 



l6o OF Vl/LUAE ARITHMETIC* 



In the firft of theic two tkiuiiptcf ^ I ray, if contained in 
6ft 7 timet | and 7 cline9 8 {« 561 which I plicr under tiut divi- 
dfndy and lubtra/ted from ir^ there rtiU 5 ; to wiilch i liring 
down the *! ivhicii make« j* for a new dividend, i in 59, 
6 tii»e« { and 6 timef B h 48, which, fubtrit^ted trom 59, 
lliere rtAi 4, which with the 8 brought down it 48. 8 in 49, 
6 timef i oiid 6 tjmei 8 if 48, which ^ulnra^ted ^rom 48, 
tiiere reamiof o; to which 1 bring down the next, und lad 
iigure o, 8 in 00 no times, wherefore i (a o in tha Uii place 
ill the quotient ( and thuf the work if fiaiflied hghdy ; as 
fl&ewn by the proof* 

Ttie iecotid example if wrought in the fame manner^ fif- 
ing 1 1 in 18 once; and 1 1 iubrra^lcd from i8| leavef 7, whicii, 
with the 7 brought down, if 77* 11 in 77, 7 timcf { and 7 
timef If if 77, which fulMraded from 77, reftf o; to which 
I bring down rlie •. 1 1 in ft, no timef ( therefore I |>tac<; o 
ill the t^wd'iLiit I and o t'lmtft 1 1 j:: o, Which fubtra/tcd from 
9 tliere reUf ft, and 7 br/Hjght down iti 27. if in 97, 2 
timef, and ft iime» 11 ii zs, which fuixruAcd /roiii a/, ilKir 
remainf 5 after the work u cudul. 

From iltefc: examples it may {jk fcen, tliai there muft lie 
alwayf one Hgure, or cy|4icr, biou^^lic down ar a ninr, und 
no more than onej and tui' tvtry one, in brougfit dov^n, ^ 
figMre or cyj^fier miilkitt placed in the ijuoticnt. 

l^hough the foregoing method ie> ihc regular way of |>er» 
forming divition, ytt tlurt h a more cxpcdiiiou* nM ihod, 
when the divKor ioniidi of no niore lUan 12, by pUcjng liic 
4{Uotient un'krthe dividco'l, und ^Mrrforniing the fut/tra/tiou 
in the mind; a(» iu the ^yllowing rxamiikt : - 

:ii^'«« ^'75IS 7h^7.i 

RcuiahiA ;j KciiuLi.;) 7 Keijuiai Ii 



u 



09 vuiOAm Aimiifftno. i6i 

1q tbt flrft of thf fa emmplti, I r««y, i ia conutnid in ay, 3 
tlmift und tlitiv rcmnlni 31 th»$l phcr undtr the y ia tbt 
dividMrtt und tht $ which rcmAlni J ini«|in« to bt piMid 
bofiiri th« q in the dividfpnd« which muliei jg fur t new dlvl« 
dond. Then S in 39 it 4 timoi, and rviiminit 71 tb« 4 1 phm 
In the quo! trntt tnd the 7 placed before the (the iirat ^rt 
In the dividend) gives 70 ii>r a new dividend. Then H in yoj 
8 timeii aiul remain* 6| which, with the next figure 8, makt 
ti* S in 68, 8 limett and renuilni 4. which, with the lall 
^S^^i 8^^* 4} <nr the laft diviilend. And 8 in 43. s timafi 
and theie remaini 3 at the laft. 

Proceedinif in the lante munner in the next example! I fa/i 
II in 74, 6 timet end there rcniaina 8. Then 11 in 83* y 
timeii and remaine 7, 1 1 in 6o« j tlmeii and remains {• 
1 1 in {0| 4 tiiMi^ and remains 6. 1 1 in 6ai s <>*^*» ^^^ 
umalai.yi 

This la the mod eipeditioua manner of dividing by a Agurt 
Wder le I and ia generally done In publie oAcea, ihop- 
boukaiAiC. 

But when the diviror conflda of more than la, the work 
muft be performed atvitriling to the regular methtul firft laid 
down, aa the divifor ia to be multiplicil by each antwer 
pkced in the quotient. 



ait-*o 






7ui 



JtlAt 



In the firft of thefe examples, I mark off by a point the 
thn^ilift figmea on thf left hami, bccaufe thcie are thrre 
figurea in the divifor j ihen I alk how often i\w twv» firft 
iigurea in the diviior are containeil ii\ the two 1ki\ %urei of 

Vol, L X ^^i* 



|M» pdiiitwl off dlvMinili whkb I flnd to bt tw((i« { IhU muUi- 

'f iytog ihi dWliiir bjr o, tlw procltiA h jfOf wblt h i4 gr«if«ff 

'ikMi tit* flttt dUMtnii I 1 fhvrrfim plsot i In fti0 qtiotUnff 

'Mid plftfr ihi divlfer tindirr iho dividend (ni i will not Inrrmfa 

^fc by Aiilfi|>liMtlm)>9 whifh 1 ftibtruM from dm divldRodv 

iftd to the ri^miilodcr I bring down the ntn^ flKitre s^ whirli 

miiliiNi jARft for h new dividend \ then rrpeAiIng the qneftlopi 

f pi^oeerd In the fiinie m4nner throni^ont ttie whole. 

When the divlibr eonflfti of feveml flgnredi the tnoft e»- 
pedltleuii And nt the fitme tlmi; ti\m\)y fnfet mctluid ii| tii 
mAkr 4 tutde of the divifori which may conteln the dlfferant 
|Ht>dMA» of the dlvifoTi multiplied by tv^ry itvmber from t 
lo 9 inelttflve i ni in the following cxemple t 

nth lifih DM/0r. 

»o<i<eo*^6 V «|iot)ii'.is6 

Thr fiirr|foin)S tntile t*^ Iciimrd hy rtitiirijilylng tlir dlvKor 
hy ihr O^jillii HMt W^wirn liom t to ^i oi h inny Ims fotmrd hy 
4'l<lin|{ rrM li Ia(I iiitnliiH fi» tlir ill (t . lliun, thr itfuuM mimlHfi 
U\ fitr ifttilr in (gitnnil liy (ltiut>lin)( (hr liifl ^ ilir third miiiitici 
to iMMtinl hy rtddiiig thr fncMul tii the Hill | ilic ffiiiitti mun- 
\ft hy ftilijin)^ ftu' tlittil to (lit* ihn I thr ftfiti |iy ml(liii|( lite 
IftuWU ill ittr lii(l,ikr. i ititd lltfi uU\r inny be piovrit, by |fttll< 
li|ilXiti|{ tlir hill nilitihri (e';H74;(gt|; by g, ntid il tlir ^tih 
dun br ci|iMl idtho tfiilmitnbci (a08HOH7';»)i the tfible it 
»i}^tti 



0» vqtOAIi AUTHMlTlg. |6j 

Th« ufii uf thia tabic l»t lo liiid h«w uKtii th« dUtlor b 
tcmtalncd in any puiiivul<ir iliviJond i ihui| iii this f amitpit, 
after having puintcil tM \\w AiA nine figurci in tkt divMtikl 
•43098849 (hccaultf (he liril eicla iigurca are left than tht 
clivifor), 1 caft my eye on iho tahlCi and And that tiM neat 
Uh number it •3<i^9944^4i and which 1 find by tha tahhi con< 
tains the divifor 8 tiuie»i I iheraforr place 8 in the quotienti 
and the multiple of 8, taken from the tablei I place under 
the dividendiand fubtrae^ ii thertfrum| and to the remaitxder 
bring do^wn the next A^^ure \ fur a new dividend 1 tlu:ni by 
the table, I find the divifor ii contained in tbU dividttul |ul 
imcTi I place 1 In the ipHitienr. and fubtraA the mttlllpk •< 
I (or the divifor) from Uu h dividend ai baforcf awl to ite 
ren^aituler I briit| down \lw neat A^m't 7 «. in tiiia diviitetl 
(by the table) 1 fiod the divifor u (XMMaincd j tia^eif which 1 
place in the quotient, and taU tha mHUi|do ol' j from the 
tabic to be fubtra^led iron) tite lull dividend, to which re- 
mainder I bringdown the lad &^u\x a : and» by the table, I 
find the divifor b contained in x>\c laft dividend 7 time*; tind 
the m\dtiple of y brinK fnlurai^^eil from thU U\\ dividend, 
there rem<iin» noo^i*;t» .»ttrr the woik ia ended. 

When the diviloi hcu a i*vpl)ei' or cypheii towiiiili the rij^ht 
hAiul, t\^e d\videml may l>r ilivided by the lif{nihv*ant li)(\iies 
4inly, and the cyphern fe|Mrutril fiou) the diviUu' bv a <h(»ke 
of the pen: In whii-h cule iheie in\tft Ik* ai nuny ti|;uie» 
ieparated fnun the li^hi hand of the dividend, an ihrir tire 
feparatetl cypbeis ttnd inch fe|iaratrd tiguve* are to be fet 
down at the lal\ av u irinaiiuler : and if there Iht any othrf 
remainder, the fepamted tigurea air to be fet on the ri^ht 
hand thereof. Whm the divtfiu tiati an unit only on the left 
hand, with nothin^ but cyphers on the li^ht hand thereof, 
tht diviHon it performed at (Hu*r, by cutting olf u« nmny 
figutt» from the vi^tht haml ot the dividend as there are 
cyphers lii the divitor : the lentanuler of the dividend is the 
4)Uotlcnt« See the following* etiamjdh :^ 

Xa ' ia,o) 



► 



■64 



Of ToiOAK AmTtftrane. 



i»,o)»704.3( 

•3* 

Rem. lo) 


44- • 

IS 


1,00 5[(>fl47'»4 
Rem* ^4 



Div\fim pfdivwu DinMiUfiaikm. 

DWiilofi of 4hftf% denmnififttlwii t« performed by di vidiof 
«ieh dciiomiiMtkMt in the d^ldend hy the divifiir, pt«cing 
*• qtMient of eidt denoffiituition under the fame denomi* 
•Mion <n the qiiotieoft and ctrrjing the overplui of eick 
denominfltton to be added to the next^ m follow* t 

Difide 437/* f 91. loA among §4 men. 



^4)437 
•4 

«97 



-12 
»3 




In thit examplci I firft divide the 437A by t4t the quotient 
of which it f 8/« and there rfrrtaini 5/. which, added to the 
19^ make<( 1 19/. for a new dividend; then the divifor ii con- 
tained 4 times in 1 1^1 wherrfore I fct riown 41. in the quo* 
tient, and aji' remains^ which added to the lo^. make aSM* 
for the next dividend; in which the divifor is contained 11 
timeti and there remains at/ or 88 hnhinf/^, in whi< h the 
divifor ii contained 3 timet. Thm the quotient it 1 8/.4i. 1 1 J/. 
and there remain* 16 farthingi* 

6umi of this nature may alfo be more expeditioufly wrought, 
if the divifor he a rom0»enfurable number^ and ran be re- 
iblved into two part%, a% in the following example ; — 



OIF TutaAiK Amrntfirrio. t6% 

j^tt. I. If the ekiirnlf of a country fieaft be ui^f. lOf.ML 
to be piM by aS ftcwarth. what mull each ftewanl pay f— !• 
this rxaiiiple I divide by 4, and the quDtienr thence arifing bf 
7i which ii equal to dividing by a8, and the anfwcr b femi 
to be 9/. 8i. •</• for each Reward to py. 

:^«. a. ir a gcnilrman f|)rnd 347/. 1 (i. qi/. hi the fpace of 
one year and eight wcck», it i» dclircd to know how much it 
b per week on an average } -Here 1 divide tlie whitle liim by 
5i and i\vt qiH>ticnt ihrncc aiiliag by 6| and that quotient hf 
ft \ wbkh \% ti\\\9\ t(i ilividing by 60 ^tbe numlicr ttl' weeka 
in one jrear and eight wccki)| and tlte anlwcr is ;/. iji. iiif. 
per wcek» at in the example, 

J^ar. 3. Iff the capital ftock. oF a tontine amount to 
437aA 141. Of/, and there l>e in it 160 fliaret, what will tie tho 
amount of each iharc ?«— In this oiample I divide by 4« and 
that quotient by io» and the quotient clience arifing by 4« 
which it equal to dividing by i6oi at 4 tintes 10 it 40* and 4 
timet 40 it i60| and the anlWer it ujL &/• yJ. for each (hare. 

/• i. A £. J. «/• £• u lim 

4^ab:\ IP 6 0<47 '< *) f \l.^7» Jl_?_ 

7^ ^^ W 7 * ^) N t" » 4 lojio*)^ i 6 

98a; a ) 1 1 1 1 10 I 4) 100 6 4 » 

ssssjsssm ^— j^ "■ • 7"' <> 7 "^ 

To ind the exa^ remainder in fumi where there are two 
or more diviforti at in the foiYgoinj^ onn, the rule i« to muU 
liply the Arft dlvilbr by the UA renminder, adding thereto tht 
firil rennainder« if any« and the produ^ will be the true re* 
maioder t at if it had been divided by the long method i thut 
ill the firA of the foregoing examplrn, 1 multiply 4, the lirft 
flivifori by {1 the lali remainder, which produces ao, to which 
adding a^ the firft remaiuderi the true remainder it found to 
be aat which nnay be proved at Iciiurc* 



l66 or VULGAA ARTTaMBTir, 



Jl^. 4* Them it a piece of l«incJ| having 4 rulci, containinp; 
I3q8 Acrei, 3 roodsi 3$ ptrchcii and a40 feet in brcadihi it U 
dcfircd to know how many feet it ii in length ? 

j^. {• There ii a piece of timber, the folid contcnti of 
which is 600 feet, its length ii 40 feet, and its depth 3 feet ^ 
il is required to know its fuperficial contents f 

Sfu^hn 4. 

jf. -R. P. ^e/lioH 5. 

♦ )'396 3 35 , 3)600 

^) 349 • 3^ 3 —:^ 

10) 58 I t % .ii. 

5 3 ^* ^ 

In the fourth queftion I divide the contents of the IaikI, 
flrft by 4i and that quotient by 6, and the next quotient by 
10, which is the (kme as dividing at once by 940 ; and the 
mfwer is found to be 5 acreii 3 roods, and la peKhes, for 
the length of the piece of landt 

In the laft queftion I diytde the folid contents of the piece 
of timber by 3, the depth, and the quotient aoo feet, is the 
fuperficial contents, which if divided again by 40 feet, the 
length, would give j feet fi)r the breadtii. 

In the fame manner as the foregoing examples are wrought 
divlHon of other denominnttons may be performed, having 
refpcA to the table of quantity belonging to the fame. 

H\it in this fpecies of divifion, if the divifor l>c not a com- 
menfurablc number, or one which cannot be divided into parts 
exactly, the division muft then be i>crformed by one diviibr. 

DiviGou alfo tcacheth how to bring fmnll denominations into 
great ones { but as this part more properly belongs to reduc- 
tion, 1 have deferred treating of it till I come to that rule. 



SECT* 



i 



OP yULOAft AKtTHMETIC. 167 

— ' ■ ■ , , I I 

SECT. VI. 

OF REDUCTION. 

Reduction is'only the application of the rules of mulli** 
plication and divifion, and teacheth how to bring numbers of 
one denomination into another denomination without altering 
their value. 

ReduAion is either Aifitndlng or afcenMng. Redu£kion de» 
fcending is performed by multiplication^ and ferves to< bring 
great denominations into fmall ones ; as pounds into flnllings, 
pence, or farthings ; hundred-weights into pounds or ounces, 
lee. Redu<ftion afcending is performed by divifion, and brings 
fmall denominations into great ones ; as farthings into pence, 
ihiUings, or pounds ; drams or ounces into pounds, hundred« 
weights, &c. 

Rmii* In redu£tion defcending, multiply the number by 
the number of units of the next lower denomination which 
make an unit of the next greater, and multiply fuch produ£t 
by the number of units of the next lower denomination which 
make one of the next greater ; and proceed in this manner 
till t^ie number be reduced to the denomination required. 

ExAMPLB I. Reduce 250/. oi. od. into fartbingi. 

In this example, I fiift ajo 

multiply the 150 by 20, Shillings in i pound _2o 

which is the number of units Shillings in 2 50/. 5000 

-. . , , . Pence in i Qiillmg i» 

ot tcie next lower dcnomina- „ , / ' l ' 

, . , , . ^ Pence in 2 CO/. 00000 

tion which make an unit of Farthings in i penny 4 

the next higher ; that is, the Anfwer 240000 

number of fliillings contained " 

in a pound, and the produd (hews the number of (hillings 

contained in 250/. ; which product muft be again multiplied 

by I i, the number of units of the next lower denomination 

which make one of the next greater, or the number of pence 

contained in one (hilling, and the product gives the cumber 

of 



|6t OP rUtOAH AKITHMBTIG. 

•f pence contained in t^o/ii which protluA, aj^ain multiplied 
by 4« tiw number of farthings In one penny* the piodiiA givct 
the number of farthini^i contatnetl in a $o/. ; or the anfwer« 

Rtik. In rcduAion afcending. divicH: the given number by 
the number of units of that denomination which make on« 
«f the.ncxt greater { and di\ide that quotient by the nuifiber 
of uniti of the fame detuMnination which make one unit of 
the next higher, and proceed in thii manner till the whole it 
tttiihed. 

Thut« u in the foregoing example I reduced • {o/. into 
•40000 farthioga ; fo it.vcrlel}*, here I fayi in 040000 far* 
thiogti how many pounds ? 

Farthings in 1 penny 4)040000 
Pence in 1 flulling la) feocoo 
ShiUmgs in I pound ao) so^^ 

In thisextmplei 1 6rft divide the given number of farthingi 
hfif the number of units of that dcnominatitm which arc 
contained in an unit of the next higher denomination ; or il>c 
number of farthings cont^incil in one penny, and the quotient 
gives the numlvr of |Knrc contained in 840000 f.irtlungs ; 
which qimticnt i« attain divided by la, the numlKr of fienre 
contained in one (lulling, and that quotient give* the number 
of flu lings cotituincd in tlie given fum of larlhinj;* ; aiul Urt'y, 
thefe ftiiiling* arc ag;4in divided by ao. the number ot Ihillinga 
in one pound, and the quotient i» a ^oL for the nniwer. 

Thus it nuy l)c teen, th.)t reduction aicending and deiccikU 
hg prove each other. \\n if the turn Iv- |>er formed by re* 
duif>ion dcfcending, it mull \k proved t\v i-educUon ;)fcending, 
as in the two fotcgoing c \a10ple5 ; and d' it be in rcdu^^^ioa 
afiTudingi it mull be proved by reduohon ddleiuling. 

In reduelion dcfcending, when the lum lonltlN td fcveral 
denominations, the numl>er in each denoniiua(i«>n, after the 
llrftt it to Ik addeii to the dcnoiiunation to which it belongs ^ 
M in the following example ( 



m 

J 




OF VULOAA AHITHMmc, 169 

SiMUi^ S« In A39/. loj. bii. how many pence ?— In thii 

txiunp)c» after having iH^iucetl the pounds 139 10 6 
into (hiiliiigi by muUiplying by ao, I add to 
the prodiiA the 10 (hillinKi which ftand in 
the place of (hillings) and having induced 

the MUngs into pence by multiplying by 1 1/ ^ 

I add to that produA the 6 pence which Aaml ^^^go 

ia the place of pence ; and the anfwer to the 6 

work is thus found to be 571486 pence. $V^^^ 

E^mplf 4. Id 84 tons, lo hundreds, and 3 i^uarters, how 

many pounds?— This is performed us the 94 10 '\ 

foregoing, but having refpe^ft to the table of ^2, 

avoirdupois weight. 1 therefore multiply '^^^ 

Ae tons by ao to reduce them to hundred 

400 
weights, as ao hundred is 1 ton. and to the ^ 

produA I add the locwt. I then multiply by "^oo 

4 to bring the hundreds Into quarteri, to .< 

which I add the 3 quarters i Hud, laftly, nuU- 196 4 

tiply the quarters by aS, the number of |)ounds ..A^ 

in a quarter: the pit)diK^ is 54964 for thr ^,^^'1^ 

Oliver. 

ExampUs in Htdui^iiun ^(llrnJin^], 
Exam/it 5. In a4,tJ4o,74i unnutcj., how nvAwy day>, 

hours, and minutes ? 

£4*1141^/6. in 47v<i)8 graiud ol' iioy wcii;hi, how nunv 
ounces, penny wcighu, m\<\ ^wwut ^ 

Exmmfii 7. In a9,474»9H6 Itjuurc pnvlic:; o( Luul, lu>w 
many acres, roods, uud pcichcsi ? ^ 

EjMim^t 5. Kaviw^*/** 6. /.\v.i«^V 7. 

6,o)a4(>4g7»,i_^ a)47,5_^)^ 4*^^^-; )47»<)^*^^ 

• ) 4icBa8.4i 14)^^1) ^)j^jh^i^^i^ 

ia) ao^4U 2.o)'u)7,4Ci iS4ei^ 



17117,40 t)S u 



80 



!:. 



• 



\ 



» 



In (Iff firft f^ tliele exsmplci I (Nrkb the miniifn bjr 60, 
to hriii|s them into hotff«, hf eufting dT the o from fhe 6, 
An'l fUvkVinffby 6 /ifily, m fiifigbf hi dtvifldh, und the qdcMlent 
)« 4 (oSsff hotiffi flfld there trhtnittn 4 minntift whMit |»lfie«d 
fr fore the f c}rt crfT from the rfivMenrf, mikei 4f mittutei fbr 
a rcmAinder* Thf» f|iiorfetit I npin divide h)r ft^ iirid thit 
quotient by f t, whkh h e#|(iiil fo dividing hy 94, the fiiiffiber 
of hottri in i dty, and the ^iiMfiefit in 171 17 dajrui flfid thefe 
T€tnnm$ f^i fnit to And the trtie rerfMinder^ 1 miiMpty th« 
lOf the laft rcmsihidcry by z^ the firfl divifor of the honrty and 
the product ii ao for the true remainder s tho» ths anfwer to 
the rpieftion in, 17^ 17 days *^ hours, 41 mimttei* 

ff] the ftcofifl example, 1 divide the grflini by a anri it^ to 
bring them into penny weight!, a% 14 grains make i penny* 
weight ; the quotient it i(;74 pennyweight*, and la grainf 
remain. The pennyweights 1 divide l^y ao, to (^ing them 
into oifncf I, and the quc^tient ii 98 ouncen, and i pennyweight 
remains to which 1 bring down the 4 J cut off fro:n the divi- 
dend, tind the laft remainder ii 14 pennyweights; tfiiis the 
anfwer i« 98 /itinrf»f 14 pennyweights^ ami ai gr^iris. 

fn thr laft rxjimple, I divide the perchrft by 40, as 4'/ 
ltcrthr% nnkr i i(K;d, and the quotient is 7'/>8a4 ror**!*, Hr»'f 
2^ \}rnhr^i fUn roods I divide hy 4, to Uit*/, 0»«-rn ifit/# 
»u rr « ; iuu\ fhr ;tnfwer is found to he tJt4,a'y^ 'U rr«, »T.d a^ 

Kediii'tiofi, U/th afccn'lin^, »iid dcfcendm^, m^iy i»f j»ef- 
formed by rme divifi^ or muhipher: thtit, to bHng fsirthiof^a 
info pounds, tiie pounds m9y be divided by /y6o, the number 
of farthin^.<; in a p^Mind, and the quotient v/ill give tbr nTim- 
har of |»ounds, and the remainder (if any) rrtufi l»^ refoNe^l 
into tlir inferior denominations. And to rcdire hundred- 
wetgl)ts into finglc pounds, they may i;e multiplier! by ifs, 
the pOimd<; in an hundred-weight, and the pro'lti/t 1% fhe 
jnfwer. UiH the method before laid down n tlir n»or? 
jTgiiUr, And at ftie fame time the moreexpcditioni way of 
pcrfoiming this rule* 



# 



Q9i vvimAh AigmmiTxq^ 17 1 

Examples of both Kinds for Pra£ilc9. 

Sjmm^ 9k H 4^0 piecei of cloth contnin 84tQ cUi Fletnilhi 
itb reqiiiNd to know how many ellt fioglifli they contain) 
^Arf. $o$i cHt fiogHlh. 

SMm^ 9* In lao puncheoni of rum how nuiny hogf* 
beidi f^^Atifi t93 ho|(heft(lf« and tt gallons remain. 

EjtMmpb lo* A filverfmhh hath 1000 ounces of lilver to 
be made into fpoons, falts, and tankards ; etch fpoon to 
weigh 2 oi, la pwt, each fait 3 <A and each tankard 300c, 
and to make an equal quantity of each, it it defired to know 
how many he can make of each h — Am/. aS and 64 pwt« 
femain. 

Ejcmnple 8. Example 9. EtmmpU lo. 

MB. /Kf/. 

I410 aao • la 1000 




880 t% 7tt)aoooo(i8 

17^ 3 '4M 

7) 18480 ao ST^'O 

9) 1645 7 to 5^. 

*93 3 30 ^'** 

ao 



ai 



— 600 

in the firft of thefe examples the 8420 ells Flemtfli are 
reduced into quarters of a yard, by multiplying by 3 (as 
there are 3 quarters in an ell FlemiHi), and thcti brought 
into Englifli ells, by dividing thefe quarters by 5, the number 
of quarters in an ell Englifli. fl| 

The 9th example is wrought in the fame manner : vis, 
by reducing the aao puncheons into gallons, by multiplying 
by 84, and bringing thefe gallons into hogdicads, and by di- 
viding them by 7 and 9, which is equal to 63, the gallons in a 
hogfliead. 

This method of reduAion filwnys takes place when the lefs 

Yh denomination 



i7« or Ynicum AKirmnerie* 

In the loiK «iiini(>W I reduct Iho wtt'tgh( oi i fpo^m i iaM^ 
and I tankaixi Mo pennywir^titt. by inuUiplyuig by »^ and 
thti\ add iKnn U>^th«r i and bv tW Ivxal 7 it» 1 divide tK« 
1000 ounctt Qi &\ytu whWh U aU<» rtduc^d into pwu« ai^d 
il 4U\»t<« alt ^' eacht and 64 pwDu rtimun« 

By rcduAioA wi» art eiMMfd 10 vtdnc^ the cc«n ol ^« 
country into thai U* an^bec* wiihoMt having recourlit to the 
r^ ^ thrtt^ or eiL^hange%9 

f ^am^ xu What U the ¥altK» in £p|^UGh cwi> of 3|o 
dnc4teR at 4A« a4^ per ducat ? 

£4M4ifir la. In 446/, i8U% U^ Fleaiifli money^ hov n^uch 
Si>(^HO^— tfie QiMri'e qI* exctanfe beii^ ^oi. tJ. per pound 
flerling f 

Sjwk^ t3« How much money Kn^ctiih U there io 44^^ 
piccee of ei^ht» the conrle of exchat^ff Umoj; at 49^ fterlu^ > 

le i >4i it 4 



i^X^MI^ II. 



«>o> i4^»(t4 



\} f JM«fi% 1 1- 

)4>)\yA'>'iyi4i 44^0 44«» 
.<»» • ' 5 4J 




t« 

3^*)»S*4(4 
t4f4 

4 



^ lilt ili. 4}. 



Ot^ VULOAK ARITHMRTIC. 173 

la the ifth example, I multiply the 3j^o ducatt by 50, 
to bring them into pence, and then divide by it, and it 
quotef 1458 (Inllingi and 4 pence : I then divide the diillingi 
by ftO| and the quotient ii 7a/. 18/. 4^/. for the anfwer. 

In the I ath example the 346/. i8i.6i/. Flemifli money it 
vcduced into pence, nnd then divided by 366, the courfe of 
exchange ; and the anfwer is 161/. i8x. 4)1/. and 1 14 farthinga 
lemain. 

The 13th example is wrought in the fame manner as the 
iitb: v\z. by reducing the pieces of eight into pence; and 
for the fradion f of a penny, I multiply the given number 
of pieces of eight by j, the numerator, or upper figure of the 
fraftion, and divide the product by 8, the denominator, or 
lower figure of the frn^ion, and to the qt^ient I add t^he 
pence contained in the pieces of eight, and then reduce thiif 
whole into flnllings and pounds, by dividing by xa and ao, at 
before, and the anfwer is 913/. 1 8/. 4//, 

This method of reducing foreign coin into Englifli may 
ferve for thofe who arc unacquainted with the rule of prac- 
tice; for pra^ice performs this much nwre cxpeditioufly, at 
will be flicwn in its proper place. 

Thofe fums in reduf^ion, in which both divifion and mul- 
tiplication are ufod, mufl be proved by multiplication and 
divifion; as, for example, that part which it performed by 
multiplication nui(l be proved by divifion, and that part per- 
formed by divifion mud be proved by mu.tiplication. 

The foregoing; examples, perfe^ly utulerftood, will be fuf« 
fieient to give the learner a complete knowledge of this rule* 
and the various ufes to which it may bt applied. ^M( 

It is abfolutely neceifary that the learner b|p|>erfc£Vly le* 
quaiated with what has been delivered in the Foregoing part 
of this chapter, as all the following rules in arithmetic are- 
performed bpone or more of the foregoing rules; 1 have 
therefore been w^tc explicit in the former part ; being the 

bafis of the whole. 

* 

> SECT. 



174 09 VUMAE AMTHMVriO. 



sucT. VI r, 

r»8 QPiPSN AVUl 0«4 ilNOtK ftUI^K OP TilABC 

OlAHCT. 

Thii rul«i vfhicht for iti miverfiil ufe m moft partt of lUc 

ff^^tUm^ brcAufe ibt? number fPMi^bt b^jini it Kxxxm \ixu^x* 
tioii 10 une pf tbp numUsri niv^n. 

It ii called Iht r«i^ #/* ikriu bt^Milft U c^nfiftb of thr««( 
lIlvtA nmnb^rii frcm^ wbiob « foui tb numbisi in tu be fuund, 
whtehi ia the dir«A rul^i b«ari the feme firopurtiun to th« 
ftcond number ai the ibird doei 10 the Aril* 

Jt«/h Midti{4y the ftcuiui and third oombeife tugether, 
and divide the proditA by tl\e iirft nvtitberi end the iiuoiicni 
ii the anfwer foug^tt w the fourth numUi . 

Mxmmpk I. It ,) ydf. of tnuflia f^U ie«. hIuiI will (j yiti. 
coil at that rate f ..^ 

Here the fourth number or ftiifweri ^6, be^ft the (amo 
|jrpp(jriion to the feconi) nuii)bi:r le, a» tj ihe ihud numheri 
hUPi to the Arfl^iuniticr 3, th'U if, it lonuinii ii tbieeiimeii 
or ir bean tlM fame |uo|iortioit to ibe ihu<) numlier 9 a« the 
Cieond number le dciei to iho tirtt number '^, vu, t:uiiuii|a 
it fcur timet. Thii proportion is called #//r/^ |jio|Mirtion 1 
from whence ihii rule it called liie rule of time iiir0^t and 
it always performed at above. « 

But when the fourth numbw bears the fame pro|)ortiiiii u» 

liic 



or vnLQikn Aiimii^iBTir. 17^ 

tke ibeoikl at the firft deei to the third. It it than mIM Ai. 
Wivr^ proportion. Qyeftiona of ihii nattiro belong to ihi uettt 
rule, called the rale of three iwvn/^^ of whieh hereafter* 

In order to know which U the ftcond and third mmberi it 
muft be noted, that of the three numbera which are in every 
qneftlon In thia rule, that ntinnber which aika the qneftion 
muft occupy the thint place, and 11 called the thini number | 
and that number which U of the fame nature with the fo\irth 
number or anfwer, muft be the fecund numl)er, and confe- 
quently the other nunther nuift be the flrlh The fei^nd and 
fovirth numbera are therefore always of the fame nature 1 ai 
are the Arft and third. Thuit in the forc|Soing example, the 
nun\ber 9 adii the qucftion, for the queftion ia, how much 
will Q yardi coft ^ q i« therefore the third number, 1 a is of 
the ftme nature with the fourth numberi being money 1 it 
muft therefore poflVfs the fecond place 1 and 3, the otiier 
number» muft be the firfti which is of the fame nature with 
the thinii vii« yards. 

When either the ilrfl or third numbers coufift of different 
denominationsi they muft both he reducnl to the fame deno* 
miui^tion ; and when thi- Icoouil numU'r cunfiiU of liivers 
denonnntitionii, it n\ull ^lU* he rrihurd to tlio loweil ;— 
thia redw^um nuift be peiloniicd l>ctoic the* woik tan be 
wrought ; ami it m\ift he obirvvedi that the fourth numberi 
or anfwer ti^ the work, ia alwavti of the imxo iU-uouuitatiuu 
with the feconii nua^ber fo rcduceil. 

The numbers being fo rtilucnl, the taoiul aiul third num- 
bera are to be multiplied to|;ciher, anil the imnluA diviilcvi by 
the firft, at before direv'\ed i and the fourth numl>er m- anfwer 
muA be brought into the proper denominations icquireM^ 
redud^ion, and if any thing remain after tlie iinnhuis of ?ne 
fecond and third muuhcrs are divided i\v the tirll, fuch re- 
mainder muft be reduced into the next lower drnomination« 
and then divideii by the firlt number, a^ before ; and if any 
thing Ibll remaiui it i\\\\\\ be red\iced mto the next lower 
denomination (if there be any luwer)iand divided by the Hrll 

'^ number; 



I«p6 OP WLQAR AHlTHMETie, 

•unber ; proeecd in chb manner till the rtmaiadcr be 
bfougbt to the iowell denonination. 

ExmmfU n. If it gaUoot of braodj coft 4A lof. what will 
no galloiit cdl at that rate } 

If It fallotta coft 4i«iOf. what will lao gallons coft } 

ao 00 

90 It) 10800 

t»o ^ 90i>o 

III ihli example (the numbers being placed as before di« 
rc^^etl-, the fecond confiding of iwo dcnonninatioos» vix. 
))Ou:d» and fliiP ingi, it muft be reduced to the loweft 
denomination (fliinings)» and the produ^l i ^ ^ fliiliings : the 
queftion will thon be, if ca gallons coft 9aj. what will lao 
coil } 1 therefore muhiply ito the third number^ by 90 the 
fecond number, and divide the produo) by i z the firfl nuro* 
bcr» and the quotient 900 U the fourti) nuuiber, or anfwcr to 
the queflion. which, becaufe the i'eci>nd nuii|^-r is reduced to 
Ihitllugs is fliiliings alfo, and is divided by 20 to bring them 
into pounds, and the quorieni is 45 pounds, the liue anlwer^ 
or price of 120 gallons at tiMC rate. 

Tht^ Proof. 

There arc fcveral n^erh \!s of proving qneftions in the rule 
ot* thicc, biu the trucft and moit improving to the learner is, 
tv'k buck tbie the queftion : thus, to prove the laft eiamp!e» 
J ftate the queftion b^ckuMr*s, making that number which 
was the fourth number in the queftion the firft number in 
tte proof, and that which u :is the third number here I make 
the fecond, %Pd the leoond I make the thinl. 

Fr^t>f\ It 4j/. purchaies lao (;allons, wlut will 4I1 lOk 
puichalc? 20 1)0 

WOO 9,00} ioK,oo 

I a 

^ There 



T^ 



wmmAa\aiwww iTio , t fj 

:Ib lli€. pioif of thb nxnplt, I ndiio^ t)M fli4 iram^ 
iDto^fliiJiiogff becaufe the third number 4/. xoi. muft be fi* 
duotfd JillD ihiUings, confifting of pounds and AiHKn|i ; and 
then multiplying the fecond and third numbers togetheif^and 
dMdtng bjr the fttH, the anfwer ii la gallonii at in the ex* 
ample; it therefore proves the wotic right. 

E^mfli 3* If the income of a perfon be 3 farthings a 
minul6» bow OMicb- is it per annum i 

Say, tf I min« produce 3 farthingS| what will 365 days 6'bouci 

produee? - 51 

1466 

730 

E766 hours 
60 

585960 roinutca 

^ -2 

4)1^77680 fiirthin^ ^ 



J»frmr 1643^ xai. 6^ 



^• ) 394470 P««ce 
•| 0) 3a87»a — 6 
1642 



ftort Ibe 365 days 6 hours are reduced into miniifes by 
multiplying firft by 24 and then by 60, the product is the^ 
liiuMplied by 3, the fecond number, and the laft produ6k ia 
the nniwer ia forthings, which is brought into pounds and 
iUlKngs fay divilion, and the mnJvHr is 1643/. la/. 6^. 

In the foregoing eiample the iirft number is an uniti 
ivhen thii is th^ cafe, the work is performed by multiptea* 
lion, and when the third number is an unit, the worMs 
wroi^ by divlfion, for 1 neither multiplies nor divides ; 
quefiions of this fort, therefore, properly belong to reduc- 



Xwmpk 4. If the effeas of a bankrupt amount to 
8796/. loi* and his debts be 9990/. lai. it is re(|uefted to 
how much he can pay in the pound ? 
Vol. I. Z 3ay, 



Say* if 9990/. i$j» pajr ioi. ih tb^ poundt what will 1796^. loi • 



T^n 



55930 
10 



i998u)iiib6oo($ 
999060 

IX9J40 



i998it) 14^4480(7 

1398684 

3579^ 
4 

14^' 84 



In ftating thii qu^flioo» I 
fa'y^ if 9990/. lai. t)if whole 
amouiu of the bankrupt*! 
debtfy will pay %os. in the 
poiin^y ai it ceiiainly wiUt what 
will ^796/. ici. the. net value of 
the (lanVrnpt*!. property, |^y t 
•*And the aufmnr ii 5j. 7//. in 
the pound. 

In perfbrming thii example, the iirft and third numbers 
are reduced in^o (hillingt, and multiplying thi! fecond and 
thira'numl)er» together, and dividing by the firft, the quotient 
ii ji which is of the fame denomination with ilie fecond num« 
ber,* vi2. (billings; apd there it a remainder of 1 11/540 (hiU 
lingi, whioKia reduced into pence, and then divided by the 
fit ft number iis before, and it quotes 7 pence; and there yet 
remains 35796 pence, which, reduced into farthings, does not 
Contain the divifor once; thcfe pence^ therefore, remain over 
Aad above the $/. and 7^. in the pound which the bankrupt 
fays- 

. ?Thc foregoing examples will be found fufEcient to inftruft 
ihe learner in the nature and method of working this rule \ 
I (hall therefore give a few examples for praAice, leaving the 
Operation to be performed by the learner. 

Example {. If 56/^. of indigo coft ii/.4i. what wiU 
ieo8/^. coft at thu rate ? 

Ssy, if 56/i. coft sa4i. what will looStf^coft?— >ifa|^Mr 
403ti. or loi/. I at. 

Example 6. If a debtor ovves his creditors 593/. lai. and 
compounds at 71. bd. in the pouod| what will fwgr bia crcdi* 
ton at that rate i 

4 <Vf 



or rULOAft AR1THMBT10» 1 79 

Sayt if tct. can be piiid by 904/* what will pay liSyai* I 
mm,Amfi»fr%t%L its. 

E4Nmpk 7* If too/, gain 6/. intcrtft in la montha, how 
much will 340/. gain in the fame tinie at that rate of interaft) 

If 100/. gain 6/. what will 340/. gain i'^Aii/kver to/. 8i. 

£jtamfU 8. A draper bought 6 packs of cloth, anch pack 
containing ta pieces, for which he paid 1080/. being Bu^b 
per ell FIcmifli < how many yards were there in each piece ^ 

If 1001/. purchafes ^qrs. what will ajgaoor/. puuhufe ^— » 
Jtfffwtr 7776fri. which divided by 7a, the number of ptecca 
in the whole, it q\iotcs 10 -^r/. or 27 yards in each piece. 

The general ufc of this rule isi from having the rate, 
value, propoition, pnxlucc, interc(Y, gain or lofs of one or 
any other number of thingsi to find the rate, value, propor« 
tion. produce^ intereO, gain or lofs of one or any other num* 
Uer of tho iame things iu a dircill proportibn. 



SECT. VIII. 

or THB SINOLK HULK OP TlfRfiR IKVKRSfi. 

Thi rule of three inverfc is that which teaches how from 
three gi^^cn numbers to find a fourth, which (liail benriht 
fame rate or proportion to the fccond nuii\ber as the firft 
does to the third ; or the third number beais the iame pro* 
portion to the fecond as the firft docs to the fourth. 

SnU. Multiply the firft and fecond numbers togcther|ind 
dividle the produA by the thiixl. 

The method of placing the numbers in this rule is the 
fame as that of the rule of three dire^, and therefore need 
not be rapated. 

. In order to difcover whether a queftion belong to the direft 
* or inverfc rulc» it muft be remembered, that iha fii ft and 

2 a thud 



iS# or V0MAB AwnmmwnCi 



iwtf a u a i b cft tne cilfed the cstreocf ; if, thercfort , the 
fcuftb oonber be grcarter than the (ccoad, cbe iciii otiMit 
mot be tlie<HvMbri bot if k beleftf the greater cstfwie 
imift he tke ifiviiiN', 

Aad when tbe irlk Moiber b the dtrifiMv the work be* 
loBgftoihendeoftbreediMft; buc frben the third mmiber 
ft the dMiiNv k belosfi to tbe mle of three iorerie % m la 
tlie UUommg €XMmfU$* 

Bmm fl i f* If t mm perfem eiijr eerttki jkuelmork 

m 6 4$ff%f horn aaof men will perform theCMiie woih in } 

dejrtf 

If 6 dsfi rogoire 8 meo, whet wiO j dejri rtqakt f 

6 

3M(i6 AMfmr t6 men* 

In tbif eiample I cootder^ diet if to do the work b 6 deye 
k rtqotret the laboitr of t meiif rtien, to do the firnie work ia 
3 dayff ft will require more meo^ conleqae ittly tbe fourth 
muDber will be greater tfaao the icoosidt therefore I divide the 
prodttA of tbe Mt and ieeond nttmben moUtplied together 
bjr the third iMsmber (the leaft extreme) , afkl tbe quotient is 
j6 (men) for the anfwer* 

The ytnof of qtieftiom in ttiif rule, at well at the fore* 
gofog rule, n performed hjr baekAatiog tbe queftion ; but 
it mufi be obfcrved, in all qutftiont in the direft rule, the 
proof If wrou|^ bjr the rule of three direA ; and in quef* 
ttont of the inverle rule the proof if wrought bjr (he rule of 
three tnwtrfe^ 

Thua, to prove the foregoing example, I fiiy, if 1 6 mea 
require 3 dayf to perform the worfc^ how manjr day* will t 
men require to perform it f 

If 16 men require 3 dayf, what will 8 mes nquiicf 

.3 
8)48(6 Anfwn 6 dayi, 

ExampU %. If a loaf at a certain price treig||^h» wto 
wheat if bt. per bulbeli what fliould k weigh when trbeiC k 
4/« 61/. per buftel ? ' 

ir 



or WLOAK A M IT BUM la |8| 

If-^d, per bufiiel give 9 Iwlf Un. what will 54^ give f 
J4)646(i« 



% 



10 w 

lot '^t/' '* ^^^^ ^** ^ ^"'* 



Id thU example, T multiply 71 pencei the prioe of tlie 
bufliei of wheit, by 9, the number of the btlf pounds m the 
lo«f, and dWidhig by 54 pence, the price of the bufltel of 
wheat at the other price, the anfwer is la half pounds or 
6 pounds jor tlie weight of the loaf at that price of the 
wheat. 

In London the price of the loaf it varied, and the wei{k 
continues the &me. Queftions which concern the price are 
wrought by makhig the price the fecond number. 

Bxa$i$fU 3* If a board be 8 inches broad, how much b 
ieogrb will make a fquare foot ? 

If xa in. in breadth require la in. in length, what will 8 in* 

In breadth require ? if 

8)144.(18 Anf.i^. 

E xamp k 4* How many yards of (halloon at 3qrs. wide are 

fufficient to line throughout the garnoents noade with 1000 

yards of cloth at 7qrs. wide ? 

If 79n« wide require icooyds. what wall jqrs. wide requije? 

7 

3)7000(23331 A/ »333f yards. 

^, 5. If 1 50/. be lent for 9 months, how long iboM 
fol. be lent to gain the fame intcreft at the fame rate?«^ 
A^fiuer tj months. 

Hn^ 6. If a colonel be befiegcd in a town with 1000 men, 
having pMnfions for only 2 months, how many mud he 
difmiis, that the proviiion may ferve the remainder 5 months.^ 
-••Jim/wi^^f^ and retain 400. 

j^. 7«' If a perfon perform a journey (travelling at an 

ttiifiEMm rate) in 94 dayty by travelling za hours per day, 

how 



lit er vnoAH Aiimf«nmc» 

■" ■ ' ■ ■■' 



\ 



bow long will it take In perform the fame journey by ira« 
irelling t6 hours per Hay at the Cirrc rafe f—^n/, i8 dayv. 

j^a. 8. If a carrier carry lacwt. ;» miles for 5/. how 
many miles will he carry i8cwt. for the lame money ?— 
Jbif^mr 48 miles. 

This rule fcrvrs to find a fourth number to the giren 
tbrce* ill an inverted proportion. And it pailiculsilj aiifwcrs 
feven Ibria cf queftioiis: vii. i. Having the v^luc of two 
different forts of coin, it fluwi ho%i mary pieces uf the one 
are rquat in value to a given number ol the other, i. Froni 
two fliffcrcnt valuci rf one commndityt and the va'uc nf ao 
article iiMff? from the fame crmn»o(l"y ^t one value thcreiif* 
to find the weight, m-.afure, &c. of the fame article i or, nn 
the contrar)'« from the valuc3 cf the comntodity and the 
weight, mcafure. Sec. of the anirle, tu find the value thereof 
(the id example if of this nittirr). 1. Fmm the breadthi 
of two equal re^angnlar figure*, and the length of one of 
them, to find the length of tSe other ; nr, from the two 
lengths .v'd cnc breadth, to find the oiher breadth (nf thia 
nature are the third and fouith rxampte«). 4. From the 
gtvcri \vii^h», expciire ot cnr-ii^---, and numhcr «»f milf* «::^r- 
f -a^ '>f any g'^uls, tn find fhc num*'cr of mi'e^ any other 
wrigMt c»»nld hr rirr»rd for fhft f^me pure : fri»ni a g»ven 
weight and pH-'e, and two dit>inrr=, to find thr wcij;ht an- 
f;vcra!'!c *o the ntbcr dirtanrc (nf th < nat'tre is thr eiijlfh 
rjUcHi"*!). ^. From tw » him i-f ironry l-.nt, and tie tine 
f T which • •!'' rii th;'ii is kn'. to find the lime Tir i» hirh the 
other Ih'iu'ii be lent ; or, Ifin the two diffcrcpt timet, and 
tlie Aim which is lent fnr one of thcin, to find the fitm whidi 
fluMild be Ic'it for the otbr? tlnv^ {k^\ thi< niturc is the fifth 
eximplc\ 6. Fmm the q»nn*ity nf work which a g^ven 
numlier nf irrn can pertnnn m a given tini|^ tn find tbe 
number of men that can perform it in any other given time ; 
gr, ti^mi the number of men, t<i find the ypie any otiicr 
given number would require (of this nature 11 the fiift ex- 
ample). 7* Frotn the qitaniit)- of firovilions, or nioncjr, aod 
• • the 



Of VUtOAH ARItHMlTIC 






the niimh«r of mrn, or other crvaturf i, it would fcrvc a 
: ccttain tiinf^ to fimi the nutt>ber of mm, or other crmtorei, 
it would fcrve any otlier time ; or, from the quantity of jpro- 
vtflon and the fmm!>er of confumcn, to fittii the time it 
^>\\W ff r\e •ny other number of confumen (of this natuit 
it the fixth example )• 



.J ■■ Ji i.. jgaaggn 



SECT. IX. 

OP THR DOUDLK RUL£ OF TtIR£B DIRECT *• 

In thU rule there arc five given numbert to find a fixth» 
wMch (hall bear the r.mu* propoitiou to the produA of the 
fourth and fifth num!>cr^ as the third number bears to the 
prodtiA of the fiiil <itui fecond. 

Quefiiont in this rule arc refolvcd either by two opera* 
rioni in the finale lulc of three dirc^i or the mh 0/ tbrtt 

Each quetiion in thii rule confitU of two partSi the fnf^ 
^thm and tlie dem.tnJ. 

Rtrie !• By tu^ fi/hfafioHs. Pl;\ce that number which is 
of the (iime nature with the fixth number, or anlwcri in 
the fecond place in the full opiMntion ; and the two other 
Rumben in the fuppofltion hi the firft place, the one over the 
other; and the two tuimhns in the demand in the third 
pface^ one over the othrr, in like manner as the two in tht 
firft pla«!e ; obfcrvinf^ that the bottom numbers in the Srft 
and third places be of like natme, as will alio the top oties. 



t 
* Some modern wiitf ra compound th« two 4imbk lulei of three 
Into one I 1 l|U[c» howcvrt, gwcn them diftiuAly, being morcctm* 
tMUint, to thrtiut throiy of ictenoe. In the ne»t Sc^ion iii| never* 
ttcUCit Ihf WR an iotallible method oC workin| both by one rule. 

Tht 



I . 



l$4 09 VVLOAR AiaTSMttlC* 

The work it tben performed by two operalioBt in ibi f«g1c 
mle of three direA ; the anfturer to the Urtt operalioii fomiiv 
the iecond number in the fccoDd operation. 

e. By 0i9i 0pir4Ui§n. Multiply the two irombert whioh 
fcod one over the other in the fuppofitioni together« for ti» 
iirft number ; the two numbers in the demand for the tkiid 
number; and the fccond number in the flrfl qoeftion will bo 
alfo the iecond number in the work. Then the anfwer b 
found by one operation to the fingle rvie of three direA, a» 
in the following example : 

Example I. If too/, principal gain $!• inlereft in i yeaft 
what will t^ol gain in 9 monthi^ 

Tin ^iJlhMj/siieif. 

If too/, gain $/• What will 140I. 

in la montki, g^in in 9 oMmlht ? 

In thii examplet the numbera ioo« 5, and it belong to 
the fuppofitiont and 140 and 9 ii tbe demand 1 for the 
meaning of the work it, fupptfi too/, gain 5/, intercA in i# 
Btonthi, (then follow* the demand) I iimmnd to know bow 
much 1^ will |atn in 9 months at the Dime rate of 10- 
tcreft ) 

Thus the quefiioni are dated according to the foregoing 
(lire£ltoni : the j/. being the intereft of the nnoney (and of 
the fame nature with the fixth number or anfwer) muft be 
the (econd number ; and the two other numbers in the fii|h 
■porulon 100 and la arc placed one above the other, 0% are 
the two numbers 140 and 9 in the demand. It matters not 
which of thcfe two numbers is uppermofti provided that tbe 
mimbers in each, which are of the fame nature^ occupy tfae 
corrcfponding places refpe^ivcly : thus, in the fuppofitiov, 
the pounds principal is the uppermoft number^ fo it is in the 
demand, and the number of months is undermofl In both. 

ThcqueAion being thus ilated, the work ia'Wrought by 
two operations of the fingle rule of three dlre^. The three 
fippermoft numbers are the numbers for the ipft operation, 
and the fourth aumbcri or anfwer to thefe forms, the Iecond 

number 



OF TYYLQAR AIIITHMKTTO. 185 

Buaibcr fmr liM fec«iiHi op«r«tion ; the bottom number of the 
AippuQtion fimm the firft number, aiid the bottom number 
of the dcoMnd the third nuiuberi then the anfwer, or fourth 
number 0/ ihax facoiid operation, ii tlie true anfwer to the 
qoefiioiii aa ill ihe following example, which is the fore* 
foing one at large. 

If'ifto/. gain $/• what will 140/. 

5 

• - t ,00)7*00(7 

•1 

SfcoHii Operation* 

If ta months ^in 7/. what will 9 months ? 

7 

1"-.- M^J- ' t ' ■ •* 

The anfwer would have been the fame if the number of 
monfAl Itwd been ^he np|X*rmoft numliers tnAcad of the 
pounds 'principal; In which cafe the firft qucftion wouUI Ik, 
it' 12 months give 5/. intcMTll, what will 9 iiioiuhs ^\\c ^ and 
fhe anWrer {s 3/. t jj. ; then the ferond cjucftion would be, 
if tt>o/. gain 3/. t^i, what will 140/. gain ? and the anfwei ' 
is as before, jA jr. 

-Wy one OpfriUion* 

If 100/. gain 5/. what will 140/. gain) 
months 11 g months 

laoo 1200 

\ 

J 
"•••■. •• i»" <revniiini ySi 

so 

ia,oo)ft o>oo 

..J "^ ibillings 

VU-I. A a In 



i86 Of ruMiAm v^miTHMSTic. 

Ja rbit exaifiiplc« the work is iUtcd m io the former i the 
tiro firft numbers to the fuppofition are multiplied togr* 
theft and the two numbers in the demaod mw ilio moU- 
plird togetbeff then thefe. two {iroduitfare made, the one 
the firftt and the other the third numbeff and the fiseond 
number in the firft queftbn is alfo the iccond oomber. Tbii 
rule is the mod fure |nd pra^cal method of proving the 
double rule of three direA, .when wrought by two finglo 
ones. 

The forrgoing example worked both ways will be fnffi* 
cicnt to inftruA the learner. 1 fliall, therefore^ give a few 
queftionsi with their aniWerSt omitting the operation. 

^, %, Suppofe 468 men confume 17 j quarters of wheat 
in ]6d (Iflyfl, I clcmand how many quarters will ferve j6fe 
men 58 days ? — jIm/, 714 qunrterfy and 4tf)| of a qifarter, 
or a little more than half a quarter. 

^. 3. Suppofe So acres of graft be nv)wed by 8 men in 
t4 dflys^ 1 demand hoW mnny 9crt% %% men will mow in 1% 
days }—/!fi/, 940 acres. 

j^. 4* Snppofe the wages of la men for 6 days amount 
to 7/. 41. what are the wages of aj men for 40 days ^^^An/m 
tool. 

j^. 5. if I jo/, principal put out to inftsreft for 9 montba 
be increafiedt piinripal and intereft, to i{6/ti{i. 1 demand 
how much is tliHt per cent, per annum )^^Anf* 9/* 



SE(3T. X. 

or THK JDOUBLft KUIUS OF THIISB IIIVRIiaie. 

Tm» double rule of three inverfe is when there are Ave 
given numbers to find a fiath, io an inverted prefortion. 



OF WLOAR AHtTRMVriC. 1 87 



Rmli. Plice the numbera as dircAed in the Uftfc^tum. 
Multiply the lower number of the firil pLice by the upper 
one of the third, and iiKike the product the firft number; 
next muitiplj rhe upper term of the firft place by the lower 
one of the third, for the third number : ihcn if the iiiverfe 
ptxiportion be found in the three upper numbers, the anfwcr 
is given by one operation in ihc rule of three dircrt ; but if 
the iiwerfe proportion be found in the lower numbcrr, tlie 
work is performed by the invcrfe rule (for of every ium iu 
this rule one queftiun is diretiit and the other inverfc). 

Exmmfk I. If 100/. gain $/. intereft in xa months, what 
principal will gain 5/. 5/. in 9 months ? 

5/. 100/. 5/. 5;. 

' months la months g 

The pounds intereft being reduced to fliillings, and mul- 
tiplied by the number of months, the quellion will (land, 
and operation be performed as follows : 

xa6o 100 900 

too 

9,oo) ia6o,oo 

140/. for the anfimtr. 

If the number of months had been made the upper rcnns, 
the upper proportion would then have been dire^, and 
ivould have been required to have been worked by the dirctfV 
method. It would in that cal'e (land thus : 

11 ICO 9 



* The rule laid down in this fe^VK)n will 1)C found quite ^^mu'i;i1, and 
fuflEiciciit for working all qucRiotis iu the duuble lule of ihuc b.uli 
direct tnd invecfes and is (b ubvious» as to ici|nire no dcmonaratim. 
^%cvcrthelefs, tii conl'cquL'nco oV rcccixius advice from fimie tcaoluis 
(not the moft cumv cunt) of the iuHthematic&, that I had nut (^ivm il.^ 
i m fv t I *i mttk9J of workmi^ thin lulc, 1 ihalHUti* this nuuh-appioNid 
tide, vcilatiiu, from a ^vJ! lu'wu trciudip, aiul fticw its fall:i. \. 







9j^*%» If 4^. fefftt for ilie mmmmmmM^ \% mm % 
<bjr», h<y«r kmf wiH «M/. Ierf« for 4 fnen ^— i#i!^# f444ifi» 

kwf w^gb* 6 •Meciy Irmr fnsdi wlH a lotf ireigb thtfC 0ilto 
f o|^« irhen the wKcat i> to#^ tke bvHiel ?«^>Ci^# 4* MirMc»# 



i«*-MM^M^il»«Hi 



'' il0^ I. Let ttw ^kKipal cmI» «I Mi or pif»y ifkttfcft or 4e« 

'' i« Lee th«t wbieh i«cokefieih fime, tfMbmeet of place, and eh^*, 
ttfee, fc€ in fhe fecund pbne ; Md tlie remdMiing one ki the third. 

** %. V)»fU die dffwf twd t<Yfm mtdksr (f^etr Ifte ^« rfte (xsp^A6efrt- 

^ 4. irmsMinlifyfbMklw fUe flAfd Mrm» mvlftply tlM IM tud 
'«e«ynd fernH hr t dmf^r, im4 flWjMfier thr«e Aw a ditldenrt v l«> 

'' 5. Tf the blank h\U nnder the Aril M fer^vnA term, rnnffi^ff fhe 
third and ffparth terrm ht » dWifor, «nd the fAh^.r thtt^ ht Oie divi- 
dend i and the t^vM'ient ^>n be rhe artfwer* 

^^ ^4^. If tw» Angle nrfet eff (firee, 

'' tMi$mfi1i I, W f4 hMiet eai ^4 %uA«li» of e«H in 1^ deyi^ ho^ 
many b1]f^ieN will be MIcleiN for i« hnriee fo« 24 day* f 

a#^. #v. h^» Amu 
I* A^ 14 : 56 :; fto ; 80 

^« km. Ja, h/» 
*. A« 16: 80:; »4 : i»0 

14: 16; 56 cftx»^>fi4 ^ 

ao ; *4 :— 14 y 16 

That »h:^ fnJe i< nw fr^iirvled r^ miithi*mii(i<rai prifiei^e* ii r?»d'»ft? 
fr-'/m ififp'-^fion ; for by a <lifff rent ftjif^m-^nr </ fhe 'ioefti^w Vr.^5u<h 
*%%f!Cij A%t*-e.Ti\y\t to the ro!f4; a ^liffrr^nf anfwfff wi'l arife. Th«4, b<wpr 
e«f>ly mi ji;ht the \tBfnef, reared to work fh»4 fnf.^Wm by *)*# Aa^e- 
men% order (be mrfnbefi aa folbywi 1 

HiS^-»* i6 )< 14 X ;4 ^ 

»o : — J 14 i6x»o ^ ' 

Aec/if dmji; if, thift t uew et the anfirer «^H be 5^ boMle; v^befvae 
^he troe anfwer »« iso bn^hela. The ffttkitm H, aevtitJMMs ^tM>4 
n thi« laft cafe af/eeable t* the nilef . 

3 <^- 



itjk 4* If 96 pionccn io ^4 4vf irtft t irench y<> y^inla 
loog« tow nany pioDocrt wiU oift « iMnch 136 yaixh k)«f in 
% day I ?— ufV* *^^S pionctn* 

Ji^ {• If 10 men mow 40 icm ia 8 dayii how mwy 
dayawUl it rtquirt 3 mea io mow ifQ acfti?— .4(1^ too 
diyt* 

Thfe iwlt may be pioTad by two iiigk nile«« 

Tbo fiftUowInf rules in thii cbipier* coMcpt wlgar firip* 
ttant andl tht citradiooa of rooci, art wrougtu «itl)er bf 
(omt of th« r\tUa of propoitioo, delivered in the lour pre* 
wUos teAloMi or by the role of pradicti hereafter to bo 
fpokcn of* 



SKCT. XI. 

Ol' KKLLOWSUll*. 

Vkllowship ii time rule winsrtby nn^rvhiuus and ochtrs^ 
trading in company, and empIoyiui( 4 jtMiit <A|>ttil ItiHl, 
^re enabled to al'ccrtain each |)ArtiK:i'N pitiouUr luU 01 i;Aiiit 
^ccorJinj; to his Ih.uc in the trtinc j >'uu iKk W. 

Thit rule rU'o icrvc* to liivulc a b.inKi iipt** ell »tc among 
Ww creditors; to pay legacies, when ihcie \s a \\t\\\\cwy of 
^hetcft*ior** cffei^s : anil, in Hne, to diviilc the Ums 01 profit 
of any joint concern nmongthe loleri or propiIeuMS. 

The rule ot' fellow ihip i* either iinglc or double, that ii, 
without regard to time, or with time. 

Fri!f^^ifw:f't'0iit /I'vt-, or finale fellow lhij». Is when dif- 
ferent perfons employ their refpccWve ftiK'ks for the fame 



# 



JbiSr* At ctM wMe fioek of M ihe piitoer# ».t» |b« 
wliole giin or loA^ ib b cieb mtn'f ptrcicuitr ftock io kb 
ptrticubr fliare of the g0in or loft* 

i^r#^* Bjf iddiilg citb pehoo^i'gwin or ioft tdgetb«r» 

TlMrefore» fbe wbolo Aaek of oM the pojtfuri U to bo 
Qi3de rhe ffrft nmnber In the rule of cbree^ the whole gm 
or Joft the kcooi aiimber, ind tbo pertieubr floclr of ioy 
one paitoer the third nuoiber $ then the foitrth Dumbeff or 
toArer, it tfaet pertoer't loft or g^iot wboie Cock wai tbo 
thlr4 number* Tb» operitkm bi ^ rule of three muA be 
ftpeated if cbero be more thao two. purt0eri» eod performed 
at often at there are partnert cooeerned* 

Exampli u Three peribot ttiM ioto trade together r A 
put into the trade looA B 170/* and C 300/* i at the making 
up their accompu^ they find they have gained $$o/* profit ; 
what it each peribn't fliare ^ 

A'l iock£,ioo 

B'f fiock 170 

C'% flock ^ 

Whole flock C^ 



IVMt Sunk. 

57''^- 


ili 




i70 
?4» 




a^o 




to 






t 


470 

u 

IIL 




5»o 




57#^;*<'4f<3A''. 



loc/. 



/ 



5<W 



no 

~ B't 



SM 



<:> . . I 



SM 






B*i St0et. 



>$oo 



5^'*)93S<»jo{iH o «4 JIJ 



3*5 

It! 

ao 

57^) 4o»^>(ot. 

•40 

4 



-.1 



390 



55^. 
S7,o;io^oo,o(a19 L c* 4»o 
"Tlo 
340 

iUL 
•70 

a© 

i7><»)54o,o(^ 

ill 

57»o)jJ4/>(|ji 

39© 

4 

jU 
4»o 



300/. 



TAr 



The Proof. 

A'8 OiJire 96 ' 9 9I US 
B'l (hare 164 o 8| |t$ 
C • flitro •S9 » 5,4 f fg 
Whole ftUk /.c<o Ol^o 




1 • 



If there be injr renuMiderH StA fenuitiden in the proof 
noli be acMed together (if they be fraAioni of the fame de* 
BoniHiatioa), and divided by die common divifor of each 
<|iieftion (i. #• the total ftock), and the (|iKitient» which is ttai|p 
o^ the (ame deoomination, added to the particttlar liiaiA t 
ihtia, in tbe foregoing cduinfrfeb I added the three remaindaflt 
3%Of 39O1 and 420* to|^ther» atlld dividing the total bjr {70, 
the common divifor» the quotient u a^ which are farthing*, 
at they arc fraAiont of a farthiDf. . 

S!jf< z. Four pcrfoni place thetr money in the public 
fmida : A put in '^60/. B 480/. C ;oo/. and D 860/. When 
the capital came to lie fold our, the principal and intercft 
amounted to ^abo/. what it f ach man*! fliare of the net pro- 
6c ?— i^iv^tarrv A 270/.B 3f»c/.C$i5/.D 64;/.^ -• 

:!?». ^. A b^nki'ifpt it indebted to four rrediton in the 
following fiimt: to A ; {fA !^i. to D (*o^i, uj. ro C .^c^/. an^i 
to D to8/.i2f. The lunkrvpt*? cfiate it worth o?»iy ;^ ^7;.! ;,. 
how much will larh cictUtor iccch** ' — //«/. A 111/. y/. -yu 
B 111/. 181. ic^.A c: ()!/. 8(. \d. ami D 41;. ai. ;!«/. 

ji^ar. 4. A Hup iKirj; loll value 1 7 ;a/. ; of which A fvitd 
346^'. B ^19/. C* i^niL and D 1 i%L Vn\Ari\* ImtUiing her ; (he 
was inl'urcil to ihc .iirount of 1 jdo/. r-h-it wai each perfon*^ 
hU } — y^fl/uvr, A 74/. B 1 1 1/. C 1481". D 37/. 

In tiic fccond cxanipie, the wliolr {lo<k (iiti placed in the 
funds is to l)c found by adding cAfh perfoii's rtoik together, 
and that made the fit fl number in the rul^ of three; tlie 
whole f^^in it to be the fccond numbrr, the particular Aock 
of any one pcrfon the th(rd number, and the fouith number 
ii hit (hare. 

In 







In tiM thM'eiample» the wholt amottnt of tht banknipt't 
debts if to bt^mide the drtt mi.i>ber ( tht ytlttt of hit efleda 
the fecontf numbers and an j creditor*! real due the tUrd 
number, and the fourth numiber it that creditor*! (hare* 

Fiihv^ip miitk'fim^ up-do«ble If llaw(hip» ii when the difl» 
fcrent ftocki are employed fiir different timet. 

R9$li. Multiply each man*t particular (lock by the timt 
b ia employed for ; then fayi< by the rule of three, as tht 
total of all thefe produAs is to the whole gain or lois, fo ia 
oach man's particular produA to his particular (hare of the 
ilkM|norlo&« 

dttlius the i«le of three muft bie repeated at often u 
ttere are produAs or perfoos conccrned| as in the fingle 
mie. 

Kx^mfh !• A put aoo/ in a certain trade ; B live montha 
after put 300/. 1 at the end of one year they And they htfi 
funed 350/. profit, what is each perfon*s (hare } 



\ 



^« 



Total 

4500 

aoo 
i> months, 

H^A*spfoda£l 

300 
1 
a 100 Vspiodttit 

4500 Total 0f the prodtt^U. 



Wholt 
Uain. 

350 

1400 
140000 

70 



Produ^ 
1400 



A'lAMrr. 



45 

390 

|«0 



300 

270 



•1 



3000 
ae 



•'VouL 



45i0o}6oo.oo(i3'* 
45 
150 

l*oO 

IS 

45,00) i>6,oo(4< 



Bb 



n\ 



. I _ 



1 

f 

■n 

-ft 
■uy 



wf 'fWfwW •vWWI^lP* 




f 



i{ 






ilOtt 



St 




<4< 















e o 



Tba mitbal tf proof In ihi« rul« U tht &«« m In iht 

^. a. A| H| Aiicl rem a |»AAur« In rcMnmoii» At 40A1 
l^r AMfiDm I A putd in it j rurn Im t miuifha In rh« yufi ■ 
yufi In 7 h\r 4 mt^nih«i und i^ p«i(<i in • for Iht wiinit yur 1 
what mtiO Mth p»ri^ pay luwMiiU ih« urn t ^I^amti A 
!»/• «•<• 7|/ H ) S 14A I4i> 0|*f f 2 I v. !•/. !•!« y^i/. f|t 

Mii^mfft %* A| Bi And C miiK« a Aock Idr i* months A 
pill In at AiA yal/. %i it^ rntl (^ • moi)ili« hr put In aoA 
mntf ) B put in at Arft noo/. and at iha cml nf j niimilia lia 
Innk am 1^0/. 1 C pMI In at Arft 40/. anil at ih# tftiii of 6 
mntifhi |i)/. mnra^.au^at ^c an^ of 10 nKMiibi io/« morai 
at th« yaaf *« rn<l tha y Ijnd tbay Uvf |Mm' joo/* I what to 
tacb parlbn*! prgftt ) 



«>^^^WttJlg AiftrtWItTiR tg 

In thefe eumpleti and all others of t\\c like nature^ wKero 
tho different parti of the floci ol^ each perfon are employed 
for a different timei the ilifftrent (Miti of each perfon *s ftock 
•re to be intiMpned 6y tbeif own Separate tinieSi and theft 
produ^ aBded' to^thtr to malie up the produA of each 
i perfen ; amT thkn eich perloo^i produft added together to 
make the total produA. 

ilThua^ In the laft example, I firft multlpYjr the 7a8<^ 
K/|Mt in by A, by a, the number of moothi it it £. 
tliploytd aloMi and Che produift ia •— i4Si 

Ihhin A put in ao/. more, which, added to the 7a8A 
ii 748/. and which multiplied by to monthi, the 
produftia «. .^ •* ^480 

And which two addbd tofetW givt A*t produft *93* 

B put in iooli for { months, which produ£k is -« iom 
At the end of 5 HMtithi hk tb6k ^t i $df. aild then 
there remained only jo/. which multiplied by 7 
Qionthai the ptoduft is .^ -i^. «• 3jO 

The two {MtxhiQa of B added fogethef are hit tnieoa* 13$^ 

C (mim at firft 40/. which continued alone 6 months, 
that produft therefore is — — M^ 

At the end of 6 months he put in 50/. more, which, 
•dded to the former 40/. is 90/. which multiplied 
by4 months, gives — — 36* 

Tbe laft t months he liad 100/. in the ftock, which, 
multiplied by a months, gixts — • -*-* 

Therafere the produA ot C is ~ 

The total fum of Ml the proJuAs 

Tifttt the work is wrought as before, faying, as 1 loM 
(the fum of the ptodudts) is to $oo/. (the total gain) fo ia 
^936/. (thi produft of A) to 403/. os. 7}./ iVAV *^« ^^^ 
tlK6f the ph>ffts ; and repeat the operation tUt'lc^ more, to 
ind the fliarea of B and C. 
^ B b a A^fmir* 




1^6 09 ▼Ut OAE A»IT HIilTIC« 





£- 


/. 


i. 


TbcOunolA 


403 





7l^W 


B 


60 


»7 


9 tV.*.V 


C 


36 


1 


,7i]Vftt 



i 



00 o o 



iv 



8ECT« XIL 



or AIXiaATIOM, MBOIAL AMO AtTMVATSi 



The ritit ^ aUigpckm ftachcth bmr fo mis tfiffmirt fiib* 
ftanct0 together, and to diicoirer the value of any part of fucb 
mixture; or to make a mixture from Itoown fubftanccs of 
«iy value. 

Alligation ii either mtdid or &kemMti. 

AU/xaii^M midial it that which teacheth how to find the 
rate or price of any mixture or compoundi from having the 
rarct or piiceii and tiie quantitlci of the ieveral fub&anctr 
given. 

Ruli. Multiply each quantity by its rata or pricCf and add 
the produf^i together for a dividend ; add the fumi of the 
ievrral c|i)antitiet trigcther for a divifor; and divide the 
fum of the produ£li by the fum of the quantitiea, and tha 
quotient will be the rate or price of the CJttipoufid. 

Examfti I. A mealman mlxei ao buAieli of flourt worA 
|r. per bufliel, with la 4>u(beU worth i^*i^» ptr bdbil| 
What ii one buflicl of tidt mixture worth ¥ 

ffrict 



or VULOAK AElTBMBTtQ. 




Frioe of t buftd 60^. Price of 1 biilhcl 40^^ Qiiiutti 

No. of biiihdi ao No. of kulhtlt la 1 1 

laoo 41^0 •? 

laoQ 34 

i6o Cm the AifvMt 

80 

■gv - = 

la thif eiimple the price of the buflirl if reduced intt 
pence (at it moftly (hould). The aniVver it the price of the 
quantity, which if of the fame denomination with the divilbry 
which here it bulheli. 

Ft99f. Find the value of the whole mixture from tht 
value of any part* and if it be equal to the valur of the 
orif inal fimplet the work it right. 

Thot, to prove the foregoing example, I multiply the 
^rice of one bufliel of the mixture by 4 and 8, or 3ft, the 
number of bufliels in the whole, and the prodiid, I find, la 
)/•( then I find the value of the feveral fimplet, by multi- 
plying the number of bufliels in each by the number of pence 
10 a bufliel (which it already done in, the example )« and the 
produA b68o brought into pounds, givet 7/. at follows: 

The Proof. 



leNttmberofBuftieU 
muUiplicd by the 
P«noe in a Bu(hcl. 


Tlie Price of a Bufliel of (he 
Mixiuic multiplied bftha 
Number of Bulheli. 

4 4f 

»7 6 
8 


te)i68o pence 
e^Q) 14^0 fliiilingt 
y poundt 


I 


^700 



o- 



I9§ *i^ rxHokt Aitrnukrie* 

Q«. t. A {nicer miird ibc (otlowUig km ro^ihcr, t ii» 
t$lbi.ai 8i. per IK tOtbt. ai 71. 44/. per lb. lolbi. «c 6i. M 
per lb. ami t4-bi. at 4/. per lb. whac U one puuiul of cbi» 
mixiure worth }^^Amf9f9r 61. f { /• |f 

:(a.3. A ^iiitner iniact { galkmi of wine at ;/. per 
gatlont with 9 gsllon» «t ft^. 64/. per gallon, and 14I gjlkma '^ 
at $f. lOi/. per gal'ons ^bai it one gallon of thii muturc 
monh \^Ami\oir 6/. to|</. (f 

^•4* A galdCmtih melct 10 1{ ounces of goltf buUioa^ Jk 
of i4rarati* fine, with ijt} nances of i8c4uufinc« botr 
manjr carau fine i» chit mixture •'—WSi^'/r \t\%\ canil 
Ine. 

MigMii$m alierttait ii the meihod of finding what quanthf 
of fimplei, whtiftf ricet or pricei are given^ will form • ttdt* 
lure of a certain given rate or |)ricc. 

^aie I. Wiite the latei or prices of the frreral flmplet 
under each oihrr. a. Connect wiih a curve line the rate or 
price of each funple that is \ch dun the rate «>r price of tht 
miature, with one or mote of tticfc rates or prices that art 
greater than tliat of ilic n.ixuirc ; and each grenter rate wirk 
one or more that air Id) : aiul )>l4ce tl»e rare or jirlce of the 
mixture on the Irft hj:.d of the rates 4»r prices. ;\. Write 
the dilcicncc hctwccn the latt of the mixturri and the rate 
of caih fimpic opttufitc the rute wiih which fuch fiuipic it 
conneAcd or linked. 

Then (hcfe dtflfcirniYS whiih Aantl oppofitr any rate is the 
quantity which chat mce rc4|uires to foim 4 mixture of the 
given r4tc{ but if their 1% iiioie than one dilUiuKeoppoCte 
any fimple, their fum is the 11 ue dillctence. 



* (Milditavnciany mixrd i^iili co|i|>rt ur fonirtithef bjft metal* 
wtiirh i« callrd tlir allay \ aiul tht kuUI i» tOA lu be fii many caraik ftne, 
«• U cttiii4itii |Hiie giikti iliuk, If ail aiiiclr wcifihi 14 tmait, and ruw* 
taint 14 caiats iit gold, and t nC allajri it ii laid i^ b« n caiaia lUw. 
Viku a caiai i» nta) U lccn» |ia|c 1 jj. 



Ot rOtOt^B iMaTMIIBTIC. 



199 




£f.i«|p//f !• A gr<»€( r woiikl mix KM it 41. pirlbt 7'. 
per lb. 94, per lb. and lar. prr lb, in fuch prqpqn'ioil thtlt 
the mature may be worth (^. per (b.; what 4li«iU>ly of Mi^ 
miift be t»ken ? 

The Anftver. 

8lb. nt ^. per lb« 
fib. nt 7/. per lb. 
ilb. at 9^. pf r lb. 
• b. at lOi. per lb. 
I4U). U 6i« per lb« 

' In this eiamplf , I fird (l«te the work at before dire fteii^ 
plKing the prices of the teat iu « column over each otlt^ri 
with 6, the given pi ic|: of t)ie mixture, op tl^ lef^ bandi 

Secondly^ I conneA the prices wuh each other by carve 
lines ; 4 the top figure, being Icfs than the rate of the mix* 
tutCf I conned with 7, 9, and 1O9 becaufe they are all greater 
than 6| the rate of the mixture. 

Thirdly, I find the diflference between 6, the price of the 
mixture, and 4, that of the firfi fimple» which is a ; I there* 
CmIP placp % oppofitc the 7, 9, and 10, as the 4 is linked to 
$W of Hheni* Then I find the difference between the 6 and 
ibe qext figure 7, which is i, I therefoie place 1 oppoGte the 
4b bei(\g the %ure to which the 7 is linked. Then the dif* 
lerence between the 6 and 9 is 3, which I place alfo oppolite 
the 4 (the 9 being linked thereto), and the difference iKtwecii 
(& and lOf yvhicb is 4, 1 alio place oppofite the 4 (as the 10 
is ftiro linked to it). Thefe differences, fo placed, contain 
|he true proportion of each fort of tea at the price oppoGte 
to each, that fl)ould be taken to form a mixture at the 
defir«:d rate. 

B^ opppfitft Ibe 4 there are three differences, vix. x, ^^ 
Untt 4, which are to be added together, as feen in th^ |a(t 
^luipo, Thu^ ther^ muff be 81b. of te^ at 4r. per lb, alb, 
it 7/. per lb. alb. at 91. per lb. and alU at tor. per lb. ; and 
Hit vhple quantity of the mixture is 141b. at 6/. per lb. 

4 Theft 



■M OF vtaoAH Aumtunre. 

' Theft qutAkNis are provrd in tbe (me maiiocr m tliofe m 
^Mgk^nn mediat, vit. by finding the total value of all the 
tw pki hi their (eparate ibtOi and the total value of the onix* 
lure; and If thefe two faluet betqual, the work it right. 



Tie Prwf of the foregoing Example. 

m 

Wh^oftea, atv.pcrlb.it i it o t4JI>- of ^he mlx- 

4 ture at 61. per lb» 

}a ShiUinga §4 <hiUingi» or 

•Ih. at 7^. per Ih. it 0140 4/* 4^* 

2 

14 Shiftingf 

Tlh. at 9t. per lb. b o tB o 



h 



18 shaiiiv 

' . slh. at io». per lb. ia i o o 

12 Total 440 

00 Shillingt ' 

i^. %. A firmer mixed wheat at 4fw the bufheii with 
rye at y* the bufiiel, and barlej at i&/. the bulhel, how 
much mud he mix of c;ich to fell the whole mixture at %%J. 
the bu(hel }^A»/iw^^ 40 bu(helt at 18^ per buQieU 4 bufticla 
at 31. per buflielt and 4 bufliclt at 41. pcrbufhcK 

i^«. 3* A goldlmith hat gold to melt of t4 caratt 9mt^ 
ft I caratt fine, 19 caratt fine, and t6 caratt fine, how much 
of each muft he take to form an article of gold that fhall 
make 17 caratt fine ? — A^fwtr, i of a4, i of a 1, t of t^ 
and. 13 of 16 caratt fine. 

When the whole mixture it limited to a certain quantity, 
after finding the qtuntity of each of the fimplet at belhfe» 
fay (by the rule of three), at the fum of the quantliiet it 10 
the given quantity, (b it the quantity of each fimple to the 
lequifcd quantity of each. 



W VULGAR ARirnitSTte. 



2or 



Exmmfh 4, A vintner is deiiroui to mix j forts of wine 
together; vix, at iii. per gallon, to/, per gallon, 9J« per 
gallon, 7'<per gallon, anil 6r. per gallon, in fuch proportion 
a« to make 40 gallons of wine, worth 8i. per gnllon ; how 
tnuch of each fort mud he take ? 

fir 




% 
I 



3 • 



_5 
1 1 



lo this example, after linking the prices together, as 
^Fort dlreAed, 1 have the quantity of each wine to fenn .1 
'^ijcturt of 8/. per gallon; but the whole quantity of the 
miitture thus found is only 11 gallons, whereas it fliould be 
40 gallons, therefore I fay, 

ft 

GmIL CJU Call, CiiL P'mfu 

Ai II is to 2 fo is 40 the quantity required to 7 2/1- 

40 7 *i'f 

40 3 SiV 



IX 

XI 



a 
I 



u 

21 



40 

40 



The quantity required 40 o 



^t/tlM ;• A grocer has fugar at \od. M. td. and 4i/. 

per lb. of which he would make a mixture to confift of 6olb, 

and worth ^r/. per lb. ; hoM* much of each fort muft he 

'n\ii}^AnfoHr^ ^Ib, at 10^. $lb. at %tt^ 51b. at 6^. and 

451b. at 4^« per lb» 

Sometimes it is required to take a certain quantity of any 

one (imple to mix with the others, and which generally al- 

lert the quantities of the other fimplcs. To find what pro* 

portion of the others is requifitc, I fay (by the rule of 

Vol. I, Co three), 



^M 



W WMA1I AUffffMOTM' 



iht€B)f «4 ttitf ^nt^hiUy ^iHiU Aiftpk ^hok (MriimlM 4^iih^ 

iii mty mtmt 6mp\9 iff fbe ^nnM\iy nt^uu^iU 
Ps^umph ih A Hfffiiff W0U\d Iff j« tMh§ «t 1 1 V« JM/ lb« 

jHt th< ^ h^w m^^h ht tfitib PjH my(i h« iA^f ihM iUe wtufU 



14^ 



9 4 f)> 



1 




% 

i 









% 






CTAumfle $ bill f^i f}rf4 fiMf r\\i^f\\\{m irbkb ftiiNiM Im fnheft 
fii MUU tutif i hy ihy ih$ t^k tft iUfHB), $$ flb# <fiMF iidarf 
iHjf ihef& Unmtij h ffi» U9>bf Obo qtianH()f' ff^ttiftfit I/' b« 
f«1l€h) fe i* ^lb« (tb" ({mttiVy ui i \fi, pef \k) Ui 7»lb« (<U 















WbJfb, wMbih^ 
ni yd, Y^i lb, U 



r* 

*5^ 



9tit0jlt0n ji A muim m\M^§ w\nff *i i«/, f9/« mA 6/« 

tf t t^fflbiNf «(^Hb §ff ^%\hn$ ui 4h p€f f^Wffh | how miteb «l 
M'b ('/r» rriufi b^ «»Vff iff m«li« fh* m)Miir« WM'ib ff«# ftef 

tfffm fb« fitf9f^\ti% •umplH H \§ •vi4«rti ibu (toft am 

fiirflfil WifJrO fft ¥ffftk)lt% M$ rttlf f it4li«tfrdJ»| f« iki IIMtlMNl 



or VUtttAn AIIITMMItTUS aoj 

of ft«tln( tht qutftion \ «• m.\v bt ixtrtly frrn in th« ftttirth 
«nil nxth fXimplcs which, X\\i^Mjf}\ quiie iHRVtcnt qutftioni 
from nch othfTi y«t cohArt of th« wry rum* fi|t«irfs and 
n^y bt Ihittrt in tht f«m« m«nuf r i but arc hrrv ynrlftl for 
Cb« Ihfermition of (hi ItAtncr. ntul A^lmit of Kill grriittr 
nrlfty, if tht itnrnt r mty provt nt hin Iclfui e. 

All tht uution cimt U ntv-rffiir}* iti linking tht niimh<ri 
logcthfr. III th«t of cvc!y twonumbtr* thi«t ntt litilicd togc* 
Ihtri ont ittuft bt grtntcr and ilit other Icfi than thr rttt 
orprlttof tht mixiutc. Therefore, iltt lit ft cMiimpIc iti 
thil rulf» having but one number ttfi than tht rate of the 
mittture, tdmiti of no othtr method of Attlng than tha( 
dcfwribed. 



i. .1L1L« L vsmrnsaMF^^f^mi^ 



8ECT, xm. 

or VULGAR MACTUmil. 

ih9 HiiU nf 7 Artt. 

A rit ACTION ii any part or parti of an integer or unit, 
and ^m vulgar frafUoui) ii tcprffrnted by two nutnbcri 
pUred one abo\'« tht othtri with a line dr^wtt beiwem ihctn* 

I'ht number below the line li called tht m^M/ffifMr, and 
fhttvahow many imrti tht intt^er ii divided intoi tht nuin* 
brf abovt tht lint li called the #rirpffrrr«/#r, and (Itcwi how 
many of Uioft parti tht fraction rtprtftnti. 

ThtM tht A'oAioA to rtprtlent thttt f9rth\fs \n tbtu 
writttn ll^ISlSl^f^ and li properly called thret luurthi of a 
ptnny i^-^t penny being tht tnttgtri or unit, of which tht 
frtAlon tt t pirti 

Cca Vulgar 



i04 O** V»t.C»Ali AniTHMWIfS 

tlmii ih« 4«mm»itittl4if » «• ft }« t(» '('hI iilwffy* rffp»«l«HU 

A Jln^lt tf^t\\m U mity » liH^U c}(pt«(liMn of mty Mft)gn«4 
pri) Itf of iin inlcget f 

HM(1 U ft UfAiWmi or » ^MOiM»i iMfl i\wy 1»mv< (Iio tmrfteto {/ 

Tlmt-if Mir ntio rniAiJil nMitil)«i»y whuli ^tri wholi* MumtKti 

'rt>6 f$mm§n mtrtfHfp ui two or mor« iHtrntMBMi U (iut 
MumlMtr whl^li will AW\A^ rn^hof rlnfm wifliMiii m mm\\\Am\ 
%\\m 4 i4 iIm ^mniitOM intArttrs of it Ami \^. 

A HMOtbtff ibttt eA»i' btf f xnaly ftmftireci byiwoorniM^ 
MMmbvri U «a|1i?4 itifiir f#/«^/#/» wW///// i nfui if ii (ki itm kar^ 

HlillM{»llf I fl»U«| 4$ («M(t Og MMt flic I (miMMIM »MMll))»t« 9 «li U^ttl 

( mid ii iHii fbffir l«Mft ««*mmoo HiOt(i|il« ti i f« 

/" Ihni thti grrtifii/f lemmoM Mt^tt/Utt nf luu or^Otr 
l^irftf^t MimiMMM im^aIhivi Ihu it ilm^ Uh a i«Mi:«Mi»l(?r, tiM 

•llvllgi )» W U ^ivit|«4 iiy ioilt UltMittilt^iy K«u| )f CiMltf Mill 

l*« 



OP VUltOAH AHITHMSTIC. M$ 

wmmmmmmBKBssBessssssssssssxesagssssi 



b% a rcinabMitr» ih« lift divifor ii ilill to bt diftdtd bf cha 
laft rcmiiiHiir till there be no remainder i then the laft di« 
vifor it the grtateft commou meafure* 

But if there be more than two numbers after having feuod 
the greateft coromon meafure of two ot' thenii the oommon 
mcafure of that common meafure and one of the other num* 
bert b to be found in the fame manner i and proceed in 
this manner through all .the numbcri i then the lalt common 
meafure will be the common meafure of each of them. 

JEMN^f 1% What ii the greateft common mcafure ol 
•6a4, 3ia6|and336? 

6a4)3ia6(5 6)336(56 

3iao 30 

6)6*4(104 36 

6 :^6 

•4 

•4 

Thtti 6 h the greater common meafure of 6%^ 31969 and 
a« What it the greateft common meafure of 81 and 6^ ? 

3. What is the greateft common mcalnrc of 7201 3^^* 
mul 1 736 ?— v^«f/^ivr 8. 



rRODLUM II. 

To Jimi tht^ leaji common Mulhpl^vf tivo or mot^f 

Nnmlers. 

J?»/<. Divide the numbers by any number ih;\t will diviJe 
two Of moi-e of ihcm without a remainder, anil fct the quo- 
tient of each number under the liividcnil 10 which it belon^jM 
Isringdown the undivided nunU^rs, or rholc which cannot 
IM dividedi Into the fa<ne line with the quotient. Tlict^ 
I divido 



3o6 or ▼cfLOAii ARtTNifrrrc« 

divide ilie htond luiTt in the bme amnmtt^ bf tuf aonter 
ibat will dWuk two i>r osnrv of chenit nnd hting dovn the 
f|uo*i«n!f Slid undivided nniiilicrf, w htrore. IVo^ed hi 
ihii manner if Inog at tliere ran be found any two numbert 
that can be exa^lj di«ridrd by one number. 

When the oamtert are io far divided that there anr no 
two inmiberB that can be dn tdtd by one, then muliip'y aU 
the dnrilort and the quoucnif continually together, and ilie 
produA ift the leitl con;nu>n multiple* 

KxmifUi. What iitlie kadeommonniultipteof 7,8»4, 
and a ? 



n)7 *• 8 M 4 



•• 



a 
a 



t)7 « 4 t. 2 •. « -♦ 

7 M a ,. I ,, I V^ 

TT *--- aH 

a 



Ile-.e I difii^ tlte nuniljcrf firil by a, at tbst cumUr 
ex:t/tly lucafuitf the 8, 4« anii a, the quocienti 1 pUre node; 
tUir Oi%iiUiidft» 1 ihcii diwic ihc neat line by a, ai that 
n*tr»fum 4 ar.d a ; the r{t:o( cni J place bcloar^ and thr: 7 I 

'I he's us there arr no (mo oihtts uhkh admit of a cominoa 
frcar*uc| 1 nk :((lply (he (!iu»v9ft aiut <].totkcrM continual!/ 
ti»/;c(ner| an J ihc prodj^ 56 i; ihc Icall cimiiM>a moltip*c 
V*. ihciii y.\ 

Ucfofr J::'.t'.'H):iAxan b** H:-.;:g!it by any of the rulet %t\ 
•r'.(i;fi.r:ic. It li nRe(Ta:y (> t.-du.c tlicm I'lom comp^nftd l# 
fttu; !c ucKv, aiul Co t>etttg (!icin lino tcverJ ciclicr forma; for 
wl.rdi pi;f{.ofc there arc c':j;h; U4)» or altcri g tke !orii» ol 
Int^.o. It, V. i:h<v.tf chjtig'thg chcir %a!uc, as fol!uw : 

Ca/.' I. To icducc a n)ixf:d number to an improper frae- 
lion, 

k U* Multiply the integer by the denora'mstor of the 
f.-**iKf^ aod add thereto the numeraiori and the produft 



OF VULGUR AK^THIJETIC. 207 



■ r T- I. ■ 1 1 11 1 1 I 1 1 I , 1— — ■»— p— Ml , J 

uriH form a nomrnitor to a fr«(Sioo» wboi'c dcagnutuuor ir 
the dejuuninator of the former fra£^ion, 
ExMmpk I. Reduce jo| gallons to aa improper fradion. 

10 

40 

~ y the fraftiont required. 

t. Reduee 56^ J to an improper fn^ipn.— -^-fi/^rufr * JJ'. 

Ctf/et. To reduce aii improper fradion to a whole or 
mixed, numbert 

This 18 the reverfe of the former cafe. 

JLuU, Divkk the numerator by the denomiriatori nnd 
the quotieDC will be the whole ninr.t^r, and the remainder 
(if any) will be the numerator to a fraflion, whoie iteAonM* 
nator 11 the divifor. 

Ti)vi» 10 reverfe the^ft example in the former caie» 

ixmnfk !• ReduceSSel fio ill cquiv4lcnt, whoiey-Qr mixe4 

^ number. 

4)43(»^ 
4 
^ i€{ the mixed number. 

i. RedtKe the fccond example in the former cafe "^f ' 
to\x% equivalent, whole, or mixed number, — Anf\Ker 56} {. 

Cafi 3. To reduce a fras^Vion to its lowclt tf:rms. 

Rule. Divide the two terms of a fraction by any number 
that will exadtly divide them without a remainder, and then 
divide the quotients by a number tha(4iwill ex^i^ly divide 
them* and fo on till there can be found no numt>er that will 
eXfiftly diiude the laft qjpotieiUs ; then thcfe quotients will be 
the fraction reduced to its loweit terms. 

Of, adiy, find the greateft common meafureof the nume- 
rator and denominator, as taught in the tirft problem in this 
legion, and divide them thereby ; then the qxiotients wiil be 
the fradioD reduced to its ImA teni>9. 

Fxamfle 



iiumtiri , vi«. n fra/lkifi of n yiird \ aihI Invcrtlnf Iht fltfl Uim 
lliff qticAinti will flmtcl lhti», 

f toA |. /„ --The Jtff^iHr fifV; (tr i #. t f }«/. 

Tbrn mitttiplyuif (be ihrrr tipprnnnfl ff^^urci nf itir fric* 
tt'ini ingritfcr ftir a nttifirminr, mul tlir rlurp tiiidf i moll 
figtiti-t fni Q itcnriminaliir, the anj-^fr jc /,"/., of n (MiutMl, 
wiiultv rulurccl In il<i rcrti viilur, i« w. i ti/a{ nf ■ penny. 

Here it muft tie nbitftrveily iliAt itie fltft nml (hirfl franifni^ 
nitf A be tedtirrrf to the fame liinnmituitifm m in wimlr niiin' 
licMi «« liren In tbr fnrrpiing esMtipU, wbr tn they «re hiMb 
fri^inniinf nyiirflj (iihI (lie font lb fmdliim is uf ihe fame 
flcnniniMli«in with the ftcditil. 

fjt» •. f r I nf ■ ^iillnn nf binnity ( rHi \ of a poiimf, what 
will %%\ rofi It that rate f*^/lnihvrr \y\ nt ;/.oi. flf/. } 

j^ir. V If f*, nf II buk »r I'llNrtt i;«>ft 14/. 141. Whel will 7) 
t«lei roft at that rntr ?».ff/?i<rr i»a/. lei. 

Q«. 4. If ia|lb. Iff fiifir cott f fi.^^i wbet ii the prk« 
Of 4V|lb. f'^Anf^ %L oi. v4i/. A^w 



f^nh, IVrpfifc all ibe fii«nifin« a« Ibr the fnitgoinf f nK 
tlieii (yMiliilci (ai tnnglii in tlir mif iif tlirve in whiilff nuiti- 

lirtA) wlirtltrr tlir iiiirdiim lirlnnirt in thr invnfi^ rti *1if-it 
riiir, Ami it it larlniti^ in itir riilr #il (ht«r invrrff tlii- ihinl 
fia^tuHi !• irtlir iiivrirH, by rranlpfifiitK 'be niirtn^f^lor iinil 
il'imiiiiinifirj nnil fhr wnik i« wt««iiKht 9%%f\\y in tlir fMn« 
nunni!! na in llie ilireH iiilr, by mnlnplying ilte thire npi*! - 
niiifl tf»riii« Iff tliP fm^liiinfi tifgrllier Ifti n huihf latnt, atiil il.« 
iliifVrfttnfl tprm«(il tlm thire rraHinip f..r 4 linioimnai'iri 
<«liil liic fiaHinn tliiM fnrnif il will W tlir nfilwri. 
/>»•«/. A* irfi«rr in whnl» nniiituiii. 
I'.^^mf^if I. II A Irht II 5 nf n,...j/. |,.i J „l rt year, Ir^v 
iini:h iiTiM U Ichil A lf;i ,•.. nl n yrar in ndini ? 

After 




OP VOMMI ARITtlMITItti 

Atier dilpoling of the (iMfttoiu ai iMrfort directed, I run- 
fidrr ilMt ,^ of'ii ycnr brin|( a limber time than f, it will not 
rt^|uire Ci nuuh principnl Ictit, thcrrfiiie the greater of thjr 
fiill iiml ibini nuiiihcn mud 1^ the liivilor (at in whole 
nuiubfr*) ; the third ri.ii*\hiii thereiottfmuft he iiivertedi and 
Uie ipicllion nil! Ihtiul tluii : 

Itfatrtvear 4 of looo/. ^ott^y^wt 

A/^V#r «?f{i^ or ll%li\ rquil to !(£/. I4r. 7^ 

Qjitcflloni lx)th in thia rule and the fornirr are proved by 
back-Aating the qiuflioni ai mxxhole numl)Cr«; thui the 
ferrgiHng example n\.iy lie piovcd by ri\)'ingi if -J^y of 1000/. 
pniuii^l ret]uire ^\ nC w yr.ir, wliat will ] of logo/, leiiuire? 
and the itjv^^vr ii { { ni or I (>f a year. 

.^•r.a. How nuuh fliaJJiMin will it require at | of a y.ird 
wide to line the i^itrmcnt* made with loj ynrdi of cloth at 
1^ y»rd wide?— «Y«f/<iMT V/i ^r V* ^^i"l ^" t4{yardi. 

1^^. j|. If It UKM ran ntuw a4| jrrei in to) diyi| how 
D)any days will 6 men retpiire to do the fame }^^Af^^mt 
91 j d^yi. 

.'^w. 4« If a ho.uii hr j of a fiHit to brradthi how manjr 
iiKheii in length will timkr a (quarc foot }■- At\l\ 16 inchri. 

From whnt ha« hern delivered in thli fvv^^ion conremlng 
mlgar fiAdiot\i| it i» \\a\\\ \\\\\ rvery i>ther rnlf in arith- 
metic may l)e wioii^^ht by vul^inr fr:i£)ion« nti well ai by 
whole numl>ei«, \\t ihr opctation in lv)th crilcB dfprndi npoii 
the lame printiplr; ihiu. in the luir o! three diicft in vulgar 
frrtAionH inv«:itni(i the lii 11 fraction, and mnltiplyin|{ it by 
the loeond and thud, u the (ante ai multiplying; the (inHmd 
And thini frai.Mioo!(toj^rtUcr,»iul dividing by the liiil ; jind in 
the inxerlc rule, invrrtiop, the tUitd fia^inn and nuihiplying 
it by the firi^ ^nd Ici mul, in cqnul to dividing the product of 
the fit ft and ferond fi .\<huiu by the third, ai the learner ni.iy 
piove at hit leihirr. 

Re % •;! CT. 



Cll 



o¥ vuLOAR ARrmifvnc. 



SECT. XIV. 

fir rHACTlCK. 

Pi AC net it ihc moft c«pcdiiioui rule in ariihmeric, and 
it of gfficral ufe among men of biiriricft, at ii readily dif* 
CO vert rhfl value of any number of ioiegisri from having ihe 
viilue of one. 

By thift rule are anfwered all quefliona in the rule of three 
dire A that Iwive nn unii ffir their firft niintbcr. 

A«/(r. Divide ihc giicn niimhcr of ioccgrri by one or more 
aliquot parti of a prnriy, flttllirii^» or pound, or any two or 
Uirce of ibem: iiiid the quoiiciii will be the anfwer. and of 
the fiime driigrninalif>ri of which the divifur ti a part. 

All aliquut |iart of a number i» fiich a part, t^ being 
taken .tny fiiirnbrr of eime«, will cXA^lly mcafure that number 
without a rciraio<ler : thu% a i» an alii|tiot part of 6» for it 
it ront^iiicit raa^lly 3 iimo in 6 { and ^u ii an aliquot pre 
of a jioiind, for it ii conraincd exactly four timca in a pound; 
but jj. %ti, is not nil iiliqtttJi pun, f<>r it i« nor cxaAly ron- 
tJincd .i(iy LUttibcr of tiincii in a pound without leaving 4 
rcnijiiMdci. 

iftfore ihc Irarncr can |icrfoifii thii rule, he niuft prifcAly 
under (land the following tabic* ol aliquot parU| and retain 
tltcni ill hii iiKinory. 



i» 



i half 
j third 
% fourth 
I fuih 
{ ri}'.hth 

,\iwr.ltli 

I'frhi^tcchthJ 
nuit I i 
fuurtli \ •^^ * «^"»'y- 



Tht aliquut Vitri\ 

J. 

o 



huM 




^/ 



I 



OF VVLUAU AHITHMKTIC. ai9 

wmssamBseesesemBgmKmBmmmmmmmamamr 

Ofm f^nwrm ofm Cm. 

half 
quarter 

kvcnih 



Of m Hmmdrtd height. 
aqn, or $6 b•^ / 1 uilf 



aqn, or $6 b•^ / 1 uilf i4b«\ r . half 

I or tfi I ;. J I quarter 7 I :. J 1 quartei 

14 f"^ 5 eVhth 4 r^^^kvcnil 

7 J L.'gfutcenth 3 J J Lj eighth 



Thrfe tables are fo plain as to need no explanation ; their 
vfe is to diCcovei by what nunnber to divide any |;iven nuih* 
ber of infcgert. 

Cmfi I.- When the price it left than a pennVi divide tht 
given nutnber by the aliquot parti of a penny equal to the 
SiTen pneei 'and the q\iotidht gives the anfwer in pence, 
which reduce into fliillings and pounds by divifion | except 
the given price be 3 farthings, then it is brought into duU 
Hngi, and«nfwcred at once by dividing by 16. 

ExmmfU I. What is the annount of 80471b. of old iron, 
at a halfpenny per lb. ? 

Here^liiivide the given number 8047 by a, 1)8047 
as • fiirthingi ia the half of a penny, and the laUoa^t 
quotient 4013 ii the price of the iron In pence, a, o) Uf% .< 
and 1 rennaina^ which is i halfpenny, for ihc »^ «< 

remainder is always of the fame n.ime with " 

tYic dWifbr ; I then reduce the pence into (liillings by dividing 
by la, and the quotient is 33$ fliillings, and 3 remains, 
which is pence; and then reducing the fliillings into pounds, 
the anfwer is 16/. i;;. 3 J//. 

M.xmmpU t. What is the value of $763 yards of trimming, 
at 3 farthings per yard ? 

In this example 1 divide the given number 2«o) 

by les as before dirrftcd, as 3 farthingji is ihe »6) 5703(36,0 
fixteenth part of a fliilling, and the quotient '^ — ^^ 
it 360 fliillings, whicl) reduced into pound* is ^^ 
s^. ot. %\d* for the 3 that remains in the firil '^'Z 
divifion 11 3 fixteenths of a fliilling, or 3 tla\cs =^ 

3 fiirthings, rqual to 3 J//. 

^. 3. What comes 44 q, at \iin }'^M/twr qs, 3 J,/. 

.'5.«» 4. What is the value of 3370, at \J. ? — ^-fit/. 7/. S». 

J Cafi 



ii0/f %, Wh«h III* prk« Ilk mi 4lM)Moi fmn ul h fiiUllhUi 
(IivkW th» givvM httwbiir t>y iiK-h iilu]ii«4 |i<iir< iirtd iti«^ii^. 
lieht U thr Hfilw^r ill niillifigii wbh-h rfktiH lir icUiu^U iftf» 

Ilrri9 lh« tflvrn min)l>rr i«f i>i>tHi(U i« 1)^/0 
divirfKl b^ 1. ii*4^. i» ( of it lliillifiK, %i(>)*i^%% (iM\\s^< 
iiiMt it (piii:* 90} Hiittihgo, wMdi »r«s 14 

M 14/. I v« 

^, 6. ^' hii II rlif: s'Asw r>f ^o?^^** <'^ ullow At 3 A p«r 

»• I mI II fl|llliM|f| aImI Ihf: 4»»hkHf t^ ;/. I4I, }^. 

IT 
per lb. #- ./■/'Mv/ 1 1/. •*/. y. %)%\^ 

h9^mfh (), WUl lb llir viillir of 4)26tb. M $J. p«f lb, /-* 

f-/'4vr 4'* »'• 6) 4II6 

4=1 

^'•{/^ 1. MiMi ib» |»rt(^(jf ibn iMrftci u (MfHv aimI fiit^ 

iblliji*. ilhrt M(.| jiit Nllqitol )>AI| (il M AMllihU. lilMl W|i4l »lll|tM 

|Mrl ol 4 (bilUriK »• tlir iiriifitfl u$ iIh; givdit |iii4!#, aiiU ltd 
Ibnit il, mill ilividis 1I10 given miimiIi^i by Out iili(|itni |miI| 
i«t(i IW thi» rtiiMiiiiiki (Il ibv ^lu^ (.utliaiii ivlmi |*aii ii U of 

ib» 



» 



llMflvcii prioi« ftiiit 4)f%Hk: thr <|uork>nt by Iti and if thtr« 
b« Aili a rrnviimlci- ot tUc ^\yt\\ price, confuicr whut ilkjtfot 
|Mrt xhn k df tbe \h^^ 3nd HWide the luO i|UoC)eii( thereby | 
rtiffi add Ml the qut^tif^iui tof^thtir ftw the anfwrr. 
Stfimfk lo. What U the valuer!' jjcwu o! butter, at BfV. 

(k/. if } of a (hilling a^^i6 equal Hi s|cwt. 

«i/. it 4 of W, ihcre fort di\ i«ltJ by ^Ijofe («|ual to 4JI 

V* i^ i ^ *^* ihtrelbi^ divide by 4)toa ren^ainy a, 01 1 ol'6A 

f < raiiiauu a, or{ ol'aA 

HI 

.^li|/Hvrai/. iji. 6i/. >S 

In thU cxamploi 1 divid(^ the glveti number firft hy a» ai 
6«/. it thm^rcfi aliquot part to the price, and the quotient 
i« 3084. wMeh U the price at 6#/. per )b, 3 1 then divide that 
quotient by 3, (br the other W. in the pricfi and itquoret 
io%4. which it the price of the article at a^. per lb. and a 
reroalna 1 md for the hulfpenny 1 divide the hl> qxiotient hf 
4« w» one halfpenny U the fourth part ot iJ, And the quotient 
u a^J.whkh ii the priir of the butter iit u lulf^)enny fter lh« 
tb« three quutknt^ added toj;rther give the ittitwer. 

E»0a^h II. What is ihe vulue of 137 yuidk of clothe at 
io|«A per yard? 

For the t*L I divide by a) ti7 
For the 3*/. 1 divule by *) 08 lenmini i, or M. 
For the i}«/. 1 divid« by aj 34 5 

'7 «f 

T ■■■■—■ ■ ii fc ma I • 

^n It* What is the value of jaolb. of foap, at 7|</!, per 
lb. >— -irtl^^fr 16/ 51. 

j^w. 1*^. What ia the value of 860 yardi of liaeni at i i^J. 
per y44d }^4ti!/h^>ir 41/. 4;. 2J. 



99t 



^9 YVMAft AHmiMITfOi 



CVf/# 4* Wh«i) f h« prktf it 4Hy tuimbdi* df IbilltnKi nn^ff 

Fiffti If li tM tin «v«n numbtfr of flilitingii, itiultl|ily fl» 
|lvct) iitimbcr by Imlf fh« pMtr, umi «toul»ic' fh*' Did Agttff 
0» fttr ridbi hiiMili wbkh will Iw Atiningiy mu\ M f H* •HtMff 

S'Cfitiftty. If flid iifkft In» Ah odct nurtilHir nf ntl)t)MK«^ 
mulii^ity ihi* qu<itulfy by bull ibr ti<K( lc(« tuimtu'r, wb^tU 
will br iih tfvi^it nonibefi tb«;^ fur ib4 oftti flulbng «4il i^, uf 
dM |lv^ii tumtbitr lo ih« Ufi inodM^)) (»n«l i\w (um of th^fo 
two qimmtf i«4 will b« the tfhfwrr. 

^. 14. WhflMMlM v«bii>gl4;Oytir(UulilMb«i«(4'«P^ 
y»iri! ^ 

Itiffi I ttmlfi|»ly fb* givcH ^^^ 

BumtMt 476 by i|biithhc pf Uff« 
fiiybigi « ilm«i 6 ifi !•» whit^b 
iloiibM H tf 4 « I r«i clown tbc! 4 
fttllbtg*, (tmlcrtrty fbQ 1 |H»utti] 
in be iHld«4 (M »be irM pryduA, r^ylttiff « ffimrf 7 1< 14* und 
1 1 carrtid U i f , $ «Hd €Hfry 1 1 ib<ii « fimo 4 W BtMHl 1 U 
4 I fbett t tiitl t»fl tbr (itrl A|^titr 4 (gr rttilbii|{«i| ditd ibc tell 

^AMfHfU I ^. Whrti i«i flic valtir of 46* yttrd^ til fjlnlb, it 



MS"! 






••«»)4M 
.. Jl 



til ihU r»tim|)|i*, y britig itti 

•ifil numt)cii> t fdko f for cti4 
tiiMicipbur (bc)h^ihp hftll'cif fi 

fttr Mr«f rvrh Mt|iM(M*f) ilh4 
r»i(tbi|ily (i« ill lh« ItiMtt'l r^. 

4nt\i\t*^ tlfiubbn^fbv rtill ruiinbci Imi flntlin^a, 4ti(l ibff pro* 
4ti/t U ijH/. ifti, wbUb U ibit tirirr Mf tba r^lmb tf 61. |Kr 
y»til I ihcfi fcM th(f rjfhft (tiUhh^ 1 i»ka « iw(>tihcih p>irf «f 

iltr irtvcu MtiiHrior, umi tit0 riticitimf Uftt/. fti. wbkh U the 

• ' i 

p.tirnf f <i! ijoib 41 ii.p^rydttti iin4wb)ib| 4d<bi(l ic#th# 



OV rVI.aAR AAITIIMKTIC. 



a»3 



Examples Jor PrtMit'e. 
•to UjI t yufdi wl iji . per yd, tiOJ jMelUM 17 1. per cU, 

it It 16 4 



/••E 



1 --/if/%v<r. /.J 7^ 

99 a. ■ ii 



8 Ati/kvfr% 



tiO( iyo ynrdimt y > per y<l. •|0)i8 8Qy»riltwt iqi . per vd 
i> «9_ HI 



i« 4 ■ 1-^ • 



17 Afi/kvtr. ifi*7Ji^ 



o 



Jt^ir. t6. What ii the value of 5^14 yardii at li. {icrpnl^ 
•--*l^tiYf ayj/. 141. 

j^ir. 17. What U the value of §468 yardi, at $r. per yard t 

.NHt* ^iMp ^1^^ pri^'^ 1^ ^^* <^" >'^ ^'^^ l*^*^ f)\ir(hnny thd 
given nurnHPrnay be divided by 4, ai { in | ol a |x>uiid, 
and thtf quotient !• the nnlwer in pound*. 

And w\ym tb« price is aj. It i« done at fight. l)y doubling 
tht flift figure on the lifjir hand lor fl)illings ai\d ihc otiicr 
Jiguret are pound*, 

RjMm^t I a. What is tlir vrtluc of Rj)6^ fi,illon« ol' vytler 
at *!• per gallon i Kg7. 1 1 «. .i^y Wr. 

I ■ 

By thii method of workinp, hv a». a variety ol' cx.im|de« 
ftMy tm wrought very ek|)cdJtionlly. bv dividing the Rivrii 
price into i^arti of ai. earh, anil linding the value of the 
everplut) if any. 

MM^mfk 19, What U tlie value of 444 gallon! of Hollands 
at ji. ^ per gallon > 

for e#« per gallon, I take 4V> ^'* 

For the other %u per ^Mm 44 *^ 

For the n. half the a«. line a* 4 

For the 6*/. h;ilf the i*. line 1 1 • 

For the yf. half the iut lino _. ^_' !. 

And tHeti add them together for the ./•/ j • • n ^ 



Vol. I« 



Ff 



Irt 



194 or VULGAR AllITlIlfRTIG. 

In thii manner cxamplei in chit rule nnay be wroiight« 
chough the price confift of any number of fl)illingi and penee^ 
and which would fuperfede the neceffity of fome of the fol* 
lowing rulei. I fliall neverthelefs infert thcm« that the werk 
appear not deficient* 

Cufi 5. When the price ia fliillingi and pence, which mate 
an aliquot part of a pound| divide the given quantity by fuck 
aliquot part. 

ExmrnpU ao. What it the value of 8796 dollarii at 31. v't 

per dollv ) ^\*JV^ 

Jh/wtr 466 /. 

Here I divide the given number by 6, ai 3/. ^. it thf 

fixth part of a pound. 
;j^«. ai. What ii the value of 3S7S yarclsi at i/.&Z. per 

yard } — Anfwtr 897/. i8i. 4^. 

J^iv. aft. What it the value of 9478 galloaijiif fpiritii at 
6j. F«/. per gnllon ?— yf/v/ourr 8a6/. 

J!^». Z3. What ia the value (»f 1793 yarda of JineUi at 
•i. tiL per yard ^^AnfiMr 349/. ai, W, 

Caft 6. When the price conlifta of (hillingi and pence, 
or fliillingSj peuiTi ami i'urthii^ga, which do not make an 
aliquot part of a poond, diviile the );iven number I7 the 
gieated utiquot part of a piMuul that the priie coutainii ; and 
for the remainder of the price, if any, conrKJer what aliquot 
part it ia of the former aliquot pait, and divide the quotient 
thereby ; and if there Hill be a lemuindcr of the price, con- 
fider what aliquot part it is of the lull aliquot part^ and 
dividt* the lall quotient iheicby ; and proceed iu thik manner 
as long as there is any remainder of the piicc : then the Ann 
of all the quotientt will be the aiifwer. 

Rx^mfU t4. What ia the value of 3716 yarda of clotb. at 
7i.4l#/. per yard? 3)^7*^ 

10) 114a 

16) ia4 4 o 

7 '.^ 3 






<«M« 



In 



or VVLGAR AJlITHIfXTIC. ^15 



T 



In this example, I divide tlie given number by 31 for 
6r. 8^ ai that it the third part of a pound ; the quotient I 
again divide by 1O9 for the 8«/. remaining« as 81/. is the tenth 
pan of 6i. 8//* i and this quotient 1 again divide by 16, for 
the halfpenny, as that is the fixteenth part of 84/. ; then the 
three quotients added together give the anfwer. 

Or the price may be divided into the aliquot parts of a 
pound| and then the given number mult be divided by each 
of them ; thus, in the foregoing example, the given number 
of yards may be divided by $ for 41. the fifth part of a pound, 
and 6 for the other 31. 4//. the fixth part of a pound» and for 
the halfpenny the given number may be divided by 84, the 
aliquot part of a (hilling, and this laft quotient is fliiilingK ; 
and the three quotients added together is the anfwer. 
s ^. 15. What is the value of 784 gallons, at (u. 9</. per 
gallon?-— 4i;/^r 264/. la/. 

j^. i6« What is the value of 1464 gallons, at xii«7^. 
per gallon ?— ^N/tvrr 9a i/. %s. 

Ca/e 7* When the price is |X>undi, fliillings, pence, and 
futhings, multiply the given number by the number of 
pounds, and the produ^ is pounds ; then for the remainder 
of the price, work according to fome of the former rules, as 
Che cafe may require ; and thefe Aims added together will 
give the anfwer, 

ExamfU 27, What is the value of 416 cwt. of fugar, a^ 
a/. 9/. 3 jtf/. per cwt. ? 

4i6».nA;N 



For the a/, take 


83* 








For 8i, 


— 


166 


8 





For IX. 


_ 


ao 


16 





For 31/. 


— 


S 


4 





For i^. 


— 


I 


6 






.f 



Anjhjir £^io%^ 14 o 

Ff a roi; 



f ff6 C? TVI.nAK AMTUMMTKS 

FiM- the t^. t multiply the given nuinlwr hy <i ^^^ ^^f* 
t%iTKluA B^t ii pdtindu i thru fnr the Hi. I itutltipty the g\Yeli 
itunilier )xf 4, retting the Jhuhle ni the unit ligune Apart for 
IhMlingi, nsdiirAeil in the foiMih <nit \ (or the if. t tiike th« 
eighth |Mrt of the 8#% line { lor the ^^. 1 tiike the fotuth p«rt 
of (he !!• lines And for the | I tiikt the fotiith pnrt of tilt 
5«/. line I and the fuiH of tlietc it the iinCwcr. 

4^««a8« Whttt ii the vaUw of iB^^piecetof linen, •! 
4/. 15ft io|</. per piece ^-^^^^p^inw* f077/. 71. yW* 

Gt/r 8t When the ninnber of hitegieri whniie v»\uc to 
ret)Uirc\l h a wImU nunilwr with rmAMMu annexe J, And tlit 
value f)f' the whole number \yy (ivitie of the foregoing nileH 
to which adit the v^hie o( ttu? {Miti rcprcfcntevl by the fra6« 
lionn. 

h\Y^mf4f 0^. WhAt ii the value of ajScwt. 84IU of foay^ 

at iL i9i.4i/,pcrc\vt. ^ 

B78 |r^i»/> 
Fiv i/. take a;H o o 
For iA«. atft 8 o 

For,v«4<^* 46 6 A 
For ^cwt. o 19 ft 

For Jt'wf. o 9 10 



In thin fx^imptr, arret fintliog ihr value of the #78 rwt. at 
the given piUr, 1 lu\d tiMt 841b. im ) of an c\rt. I thrtrh^rt 
t;tkf •! of the givrn f*iut, vi/. tul 8«/, lor ) titecwt* and fi«r 
the othri' } r\rt. I take } of the prtoe, qi. io«/« 

.^», 10. Whftt in tite v.ilur of ^08{ pieces of cloth, al 
t/. ii^. (v/. per piece «* .f%'iivr 14^^/. oj. ^^iA 

f.W/g. Wlien the i]vian(itv whofe value it fought ii of 
level al den«>minationii, (ulV, lind the value of the gt^aieik 
dcmnuinafion ( and for the othrr denondnaiionni take an 
fvpuvAlenf pArt or paiii ot the given price c ami add tl^ 
lc:\eial t'umn together lt>r the ant'wci. 

Kjt^mpie ^i. What la tho value of locwt* af^ra* a Ub. of 

tobacco^ at 4/. cj. td. per wwt. f 

Fof 



OF VULOAR AHITN 


IMBTIC. 


ti7 


4 5 


6 percwt. 
10 cwt. 




For locwt. take 4s 1 j; 

For tqri. g » 

For 141b. 10 

For 71b. ^ 

Anpwtr ^.4 5 \'\ 



9 





The cwt. bein){ the greatcft denomination, ii found firfl^ 
by ntittltiplying the price of an cwt. by 10, and for the vahie 
of the aqrtt I take half the price of an cwt. then An* the ailb. 
J firft find the vahic of 141b. by taking half the |Hioe of a 
qr. or a fourth part of tqri. and half ttiii price for ttic other 
71b. ; Che(e fuini added togetlier give the anfiver. 

j^a.ja. What ii the value of tBycii. 3{qrf,of fupa-iii« 
Clothi at 301. per yard ?— -yf^uwr 43/. 61. 31/* 



SECT. XV. 

or BARTKR. 

Bartir is that rule whicli inilruAi traders to exchange 
otie commodity tot anuchci ; 16 thai neither party may i'ullaia 
any iofs. 

Rmh^ Find the value of that commodity whofe quantity 11 
fiven, by the rule of three or pradice ; then by the rule of 
ihreei pradice* or divifiont find what quantity of the other 
commodity fliould be given in exchange. 

Example I. How many gallons of brandyi at 6/. per 
gallon* muft be given in barter ibr ;cwt, aqrs. X4Jb. of fugar, 
at •/. xo/. per cwt. ? 

ruf. 



taS OK VULOAK ABITHMIfiTtC* 

7 • 14 

a 

3 lo o 

ICO 



I 



«9 « 3 

to 

i» 

lii- 
aio 

8 

— An/wtr 6j galloni 4} pinti»] 

In th5$ example^ I firft find the value of the given quantity 
of fugar by the rule of prarticr, which 1 reduce uuo \Knce, 
atui it produce! 4575 pence ; ihcfe pence arc then divided by 
71. the \yt\KC in 1 jjallon ot brandy, and it quotes 63 gallons 
and 4} of a pint for the anfwer. 

Thus it appears that queUions that concern only one price 
of each fort, of two different kinds of gwHli, may be 
wrought by prai'^icc and divifum only, as the foregoing; 
but thofe of a more complex nature nmll be rcfolvcd by 
the rule of three. 

^.a. A grocer has laolb. of tea, which coll him 6r. 
per lb. but he intends to barter it at x\\c rate of 8j. \^t lb. 
with a dillillcr, for Hollands that cof! \\u\\ 41. per gallon. At 
what pri.e muft the dilViMer rate lils Ifollands, tlut he may 
fcave as nuich profit as the grocer ; and how many galloni 
Biuft he give for the laolb, of tea ?—../« -iv*, he \\\\\{\ rate 
kis Hollaudi at ^s.^. per gallon, and give iSo gallons foe 
the tea* 

la 



OP VOLOAR ARlTHMItTlC. tt) 

In rcfolving thii queftion* firft find what the Hollandi muft 
be rated at, by the rule of three» faying, if 6/. rrrjuire 8c. 
what will 4/. require ? — Anfwtr 5/. 4V.— Then by practice 
(aa in the fii ft example) find the value of the tea at 8f. per 
lb. which, divided bythe price of i gallon of Hollandai at 
before, quotes the anfwer« 

j^. 3. A vintner barters 196 gallons of wine for i^cwt* 
of fugar worth 6</. per lb. how much wu the wine worth ji 
that rate }'^'Anfwer 4/. per gallon. 

i^. 4. A barters 310 gallons of gin, at ^ 61/. per gallon^ 
with B for 61b. of tea at 51. per lb. and for fugar at %d. per 
lb. ; how much fugar will A receive ?<— ^«^ufr i icwt. iqr« 

J^. 5. A vintner barters 608 gallons of brandy at i\m» 
per gallon, for fugar at 3/. loi. percwt.and iij/. lu. ia 
ca(h ; how much fugar fhould the vintner receive ?— i^i^^Mir 
S^cwt. tqrs. S4lb. 



SECT- XVI. 



OF LOSS AND GAIN. 



Loss and gain is that rule which difcovcrs the loft or gaift 
ifirom buying and felling gooils ; and inftrn^s traders how 
to fix their price, in order to gain or lofe any certain fiim, 

RmU. By the rule of three dire^. Though queftiods in 
this rule may often be anfu ered by praftice, or other ru'es. 

Exampli I. At how much per lb. mud a grocer fell tea 
which coft him 41. 10//. per lb. fo as to gain aj per ccut. 

profit ? 

' At 




or VULOAK A»ITNII»Tie« 

A* toe/, it to li;/. la ii ^i. lo^.lo 

••00)73,66(73 pence 

4 

fi0e)ft,64(t farthings 
t 
"S^ ^-Z- *'• » I'- rVli <*r I? per lb. 

lUriwfi fhc giiff pr loff ii required at any rare per cenf, 
%ih«re itic iiiiercft liai a $ ur a cyplicr on the rigtii li^nd, ae 
k muA cuinnionly lim talri ihc aitlWcr miy be rciiilily foumft 
by fliliiinK *^ or (uUrsi^tutg from ilte |ivri) prtrc fiKb a purl 
a» tl»r iiireicft it of ihe principiil ^ ihiiki if ii br irquirrM 10 
laift 01 \oiv ; |i«rr rritt. (a* ( i» flie iwrndcih pan of an buri* 
drcd) the ttiiUct 16 fiiufid by uilJing Co or fubrra/liii^ fr<«#ri 
fb« i^i^cii priLc one (Htmicih parr ^ 'at\t\ 11 the |;ain fif I'^ft 
be 10 per uritc . ihco it i« otic icnib pan 1 and if 1 $ prr cenu 
it »f ^ ; amt to \ter icnt. ji ^ ; nhJ 3 ; prr icni. ii J, Arc. 

:^i4. 1. A giorcr Uitfgbc N|ctifc. of fngtr, wbich r<*ft 
31/ 1^1. fiV. i bur, it Lciit£ d::rrM2^cd, he it willinf{; ifi ItUt 
t^/. fOi. I'cr i«(ir. 1(1 Uic fair r^f u , it bftw nuith per lb. 
inuft he (rtl It *— //w/fi.i-r 7./. pel lb, 

III fliii cx>ff>(ijr 1 iiibtraM (|ic b.ft |.rf fciii, from ch^ 
piiriciptl^ Miirl rhc frinani'ltr u fhr (••(t.ml ri'imbrf in (hr 
nilr of tbrrf, ibc pniuffi.^) iif fiift niiffit/rr, fbr «holc pncc: 
«fl ihr fugar iftic ibird ritmi>»rr ; -iii<! tUc totmb iitif«>brr «vi J 
\m itir w^Kiio |»rur ai tbe rc'lmrd r-^ir, wiucU di-idcd by iho 
fiU'nticr of p/ju(*(lt« givci 7V. itic pMt« i*l litk. 

4^«')* A wliolefdb. f.t/ror tu bi-l*iiid imdr ttnen, «bMK 
colt hfin ir{V. per yard| ilic rA(ict.(t e,i UtMUuf^n u»lMndufi 
li^. |jci vi ill, II Hrji ji.M III l^titduii ai ii. ',/. p-i y^iil, .finl 
c'lc mail |i'4<lcr Mr«< alb»vvr<l t'l per irnt. piofit^ ^UaI |MOfil 
had fhc wliulci4lr fft/liii ^ — Jhj.l'., ^41'^! «^eut* 



•» vviiOAiiA AxmiM rrm 




ki refolviiig thia quiAioiH L fajv m iii ft^.' theenpenc* of 
rBakiB§.«iNl txpoitiQg.tho linen, U to i»« 9^1 thm ittMl<prlee| 
fa it. looA to i^oA I thut tfacr» ii jo ptfoentv profit, whloh^ 
after deducing a6 per cent, the retail trader's profiti U«vet 
04 por otnu for the fliAop* 

J^««4« A mtrohant bouglH 100 gtllont'of bnuidyj at bn 
per gaUoDi. of which quantity 4o«ga]loiit wore lolb; aiiwhat 
prica pergaUod muft- he Ml the^reaaaindari that ht' may 
gain 10 per cent, profit upon the money it cot^ him ?^ 
Jbifium^ 1 Ut {mr gilloo* 



flaaMHaaBBBnBHBBffOBBiai 



SECT. XVH* 
o» BauAi\toN* or PAirafBNTs. 

EqITATio!! of payments is that rule whereby it difoovefad 
the time tOipay at>one paynicnt feveral fums due at different 
lioieH fo that neither party may fufhiin any loft« 

Rmii* Multiply^ each debt by the time at which it is due, 
and add all tho produ<^ together ; divide tho fum of tlie pro* 
duAt-by. the fum of all the debts, and the quotient will be 
the anfwer, or the equated tiow to pay the whole, 

Exmmpie x. A is indebted to B in the fum of aoo/. to be 
paid ai follows : 60/. in 4 months, 40/. in 6 months, and looi. 
in zo months ; what is the equated time to pay the whole i 



Debts. Months. 


Produas. 


6o/. In ' 4 


a 40 


40 6 


a40 


100 10 


1000 


aoo a>oo^ 


i4j8o 


Mfi'^tr i\ months. 


^1' >i 
80 


• L Gg 


•«»« 



v^i^ 



ajS Of VUtOAR AEITIIIISTIO. 

4^. •• A ow«f iooo/> of which | U to be paid in 6 
inonihif f in 8 monlhii and the remainder In i o nnonehv | 
what U ehe tqualed fimt to pay the whole }-^Jtifiu'fr 7ff 
nionthi. 

Ill this example, \ of rooo/. mulclplUd by 6 monrbi pro* 
ducfi ti and \ miiUipliad by 8, prodiicri jf, a^d |^ (the 
rtfmainder of the looo/.) multiplied by to, prodiirei %\^\ 
and i}Bmh three prodiifti added together givei 7 [ } niontbi 
for thtf anfwer. 

And| n0i0^ when the fums or timei of payment are given 
in fraAii)ni| the Aim ol the protlu(^U Is not to be divided by 
the Aim of the debti^ ai it is in whole numberi. 

J^. 3. A tradtAnan owet hli creditor 144/. ; 447. he paya 
in ready money, 60/. ii to be paid at the expiration of 6 
monthi, and the remaining 40/. at tlie explrafiun of II 
months 1 but thp tradefman deflring to have more time for 
the paymenr of the laft 40/. pAyu his creditor the 6o/« due 6 
monthi afcer. In ready money 1 how long may he defer 
paying the laA 40/. to make him amends for this prompt 
payment f-^Jn/wer 17 months. 

In this example, the 44/. to be paid in ready money fd 
iifgle^cdi but inr the 60/. paid 6 months before due, I flnrf 
by the rule of three what intrifd it would gain at any rate 
per rent, in that time, and then how long the 40/. may br 
lent for that interell at the (kine lutr, which I find is 9 
munlhii, and which added to K months, its time of paynient^ 
gives 17 months for the aniWer *. 



"* Ttiii rult:« ilimigli giiaily iiUtl liy nun ot liuruicttt. U out mniU*- 
iiutii'iilly nunn. 'I'lic rMitui nt iliu n\\c t^ivtu hy niuKy wiiitfriii if, iluii 
tur the iltfliiiir jMyiMtf a tiini bt^foit: itm iinio it ii iluui «iii t'i|iiiit lam 
lYiuulil bo foiburH, lor M lung a innt: tfui ii ib (Inc \ hui iliib i« a niiAaksi 
rur by ibtt dttbinr imyieg montiy belinre it u diu , Uc luv iba dilooafii 
tmly \ but kc«|jin)s ihv numny aliai ii u ilui^j Uu gaiiu clis iiiisifAi 

whi^h i» j^imnt ilmit thftlu^uuiu. 

SECT. 



OF VUtQAR AHITRMSTIC. ^33 



SECT. XVIII. 

QW THS RULK OP FALSK, mNQLR AKD DOUBLBf 
(OBNSAALLY CALLSO POSilTlOH.) 

Thii rule teacheth to anfwer fuch queftioni ai cannot bt 
rciblved by any d\n€t rule In vulgar arithmettci and muft 
bi performed by falfe or feign«d numbers. 
Poiicion ii cither (ingle or double. 
8\ngle pofirion ii when the quefiion can be refolded by 
one falfe pofition or fet of feigned numberi* and one ope« 
ration in the rule of three direct. . 

itt$U. Take imy number, and proceeil exaAly the fame 
ta if it were the true number through all the proportiona 
mentioned in the queilion. 

Then lay (by ihe rule of three) ai the rtfult of tliU MA 
operation it to any of iti pai ti, fo ii the true refult in the 
queflion to the correfponding part required. 

ibAviM//# 1. A fou alking hisi father hit age, the father 
anfwcred, 1 am double the age of your eldtll brother John« 
and he it three xlmtn the age of your youngtft brother Henry» 
and the fum of all our agei ii 8o yean i what ii each peribn*! 
age? 

F^l/i Sitf/^//i0». Tkf Truth. 

^uppofe Henrv*« age ii 6 Henrv'i age 8 

Then Jolm*« ugc will be i8 ]^^^^ *4 

And the taihtr'n age 36 The father'a 48 

The fum of the agei 60 The fum 80 ; 

Here I fuppofc Henry *• age to be 6| at \vhich fuppofitioQ 
John'i age mul\ be iB, the futher'i 36, and the fum of tbefe 
three ii 60, whercai it (hould be 80: then I fay, at 60 the 
fum of the lulie (uppoiiti^n, it to 8q the Aim of the true one^ 

Og a fo 



>34 or i wMUM AawMBTKu 

ib U 6 the fuppofcd age ot Henry to 8 his uue a^ ; there* 
fere John*! age u a4t and the father's 48, as io the example. 

J^. %. A aiked B how much moocy he haJ in his pocket; 
B anfwered, if you gine me 4 guineas of the money in yo«r 
pocket, I fliall have j times as much as you will then have ; 
but if, iflAondof <hatt 1 iiouid give you o gwwotof ihe 
money in o^fotkMU ]rois sill iken >ham e«ioe as much aa 
I ffliall then have: how much oiooey had each ? — Amjnmr 
4 guinaaa, 

9m*%^ A|NifiBolurtd^lMife#Qr^ia)ra|OiiehefdHo«iog 
tennat for ihefirlLg dapa hft««a tDpqr4 ^^^ hbaCnr 
the next 3 days, and foriHtik jflf iko M3 daya m fluiehaa 
Ihr kiaoforthf lirft6digpsi^wkob4raaa^i«.{ wlvivaa 
it fftr4hy ^^Jkf^mr^ u^fUtitfAciHt jdayaiy.fMrdaf 
the next 3daya,and lai.perdiptheslaft d^i«. 

AtoMr fiffm, or the dmdU wmk tf fi^fh ii vhaa tare 
ttUe pofiiiiKia jfc flaqpiite to gpfCflA anTvcr Id iha^oeft^ 

Kmli I • Take m^i two con venieiia «HBhn», nad mmk wUk 
oflDkoflboBiooeirdingaoikcquoAioii, aa in <ngte poiiioni 
#• Find Ae diffiraoce l»tiiDaco4he rafidtof caoh of aliafr 
faUe pofitions and the nfiik ^ tlioqnBlaoni ihefiidiCBr* 
focaa are oaUoi the orron. 3. Mukipiy each emr hy ihc 
IXMHrary pofttioo* that if, the £rft emor ky ike feoaod poir 
p(^ and the (ccond orror hy tke iiik pofitioo ; then fad 
Ibe fu# iMid drfbence of the produAa. 4. if ike crroM 
are both alike, that is, if the rcfult of the two pofitiom ka 
both greater or both lefs than the icfuU of tli» queflioo, 
divide the difference of the produds by the diflarfoct of ike 
errori, and the ^uodent will he (ke anlwcr. {• But if the 
errors be uid4e, that \%, vi the refult of one pofitioo ke 
greater and the other lets than the truth, then clie fum of 
Ihe produQs mufi be divided by the fum of the eiron, and 
tke quotient wdi be the aalwer. 

EMmmfki. Tkaae perions. A, B, C, but t a ho^, wkUk 
00a 500/. of wb4k B paid kalf Of mock again as A, and C 
ptidaa«MicbaaAMdBlo|Mkari wkat did cock pay ^ 



o» roLQAm AHfTHMwic* ags 

iMBK99B=asaaaBBSi!sssass9B9iii^ssss5ai 

Suppoie A paid /90 Suppofc A paid ^96 

Then B niuft have paid 13$ Then B luuil have paid 144 

And C mufi; have paid aic And C have paid 140 

Refuh 4C0 Kefuh 480 

Firft error (o Second error so 

Second pofition 96 Fiiftpofition 90 

300 Second produft 1800 

Firft product 4800 
Second produ ft i8oo 

BiftmMofimm 3,0)^^ differenee of the produAa. 

Xioo for AU (hare, wherefore 
B muAhav« paid j jo being half ai much again ai A, 
and D muft have paid a $0 being ai much at both A and Bt 

ftoh added ngttto ^ives £ 50Q the original Aun. 



Ffom thia oxample may be feen the method of working 
thii nriey whidi li always the fame, except when the erron 
•m unlike, then the fumiof rhe produAi ii to be the dividend^ 
and ilie torn of the orron the divifer w above dire6h:d. 

i^««. A falefman bought a nomber of oxen, (heepi an4 
Iambi, for which he paid 1 1 $/. s for the oxen he paid loli 
each, for thelheep ao/. each, and for the Inmbs lei. cacht 
flow many of each fort did he buy ?-*-j4W/bivr 10 of each. 

^•3. Tlwte pcrfont. A, B,C, have eqiiol incomeif A 
fnvet ^ of hie income every year ; B f|)endi 10/. per annum 
more than A, and C fpends 10/. per annum more than B. 
At the expiration of five years, C finds himfelf in debt 50/. 
w^at It each perfon's income, and what has each faved or 
fpent ?«-ifi/twr, the income of each is 100/. per annum ; A 
bat fiivcd $0/. .- B has faved nothing ; and C has fpent jo/, 
more than his income. 

J^. 4* A labourer was hired for 4p days ; for eveiy tuf 
lit wiought he was to receive ai. and for e\'ery day he wa| 
Mit he was to forfeit u. ; at the end of the time he kid eo 
veoeive 44^, ; how many days did he work, and how many 
was he idle }^^Jnfwer^ he wrought' aB days and «rae idk la 




or VVLOAR ARITIIMme. 



SECT. xrx. 



or liXCHAMGlU 



KxeNA VCK if that rule whklt tcMclictfi to find what Asm 
i>f the money of one country i« e*iu'A to i i^ivcn imn oi the 
tnoiity of enothrr country, t\ie courfe of exctmiij^e being 
known. 

The r^ur/f »f ixthaitgt \% that {\»m of the money of one 
cottAtf y which it |>ro|)orcd to Im given for a cercain conAvnt 
{um ot that of another country; thiift when we fay ibe 
courfe tpf exdiange between England afid Holland ii 341. 
Flemith per pound fterling» it fiKnifiet tl»at i pound tferling 
i$ equal to the value of 341. in Vknutii money* Ttm couiie 
ot eschange variet on tlie part of tlie foreign eoioaf according 
to the Aatc of public aflfairi. 

The ^sr #/ iMcluingi u thflt quantity of tlie coin of one 
country which \% intrinfically c<jiial to a certain quantify oi 
the coin of aootlier couniry^ according to tlie value of the 
metal. 

Moft foreign countiici h;ive two fo%\\ of coiof» calletl 
eurrtni fudmy and hanf m^nty \ the fiiit \% tlijil in genet 4I ule 
thrtnighout tlie country ; the latter if that kept in the Uii*k» 
of thofe placet, and \% (hier than the 4>thei ; the ditfcreiicc 
between any funi a» it is valued in current n»ofM;yi and bancM 
irtonry, i« called tlie agi0. 

The nw>nry ufed in exchange i» generally imagin«iry, aod 
dil'errnt fioni tliai in which tlie acuimpti are kept in moft 
flace% t the immey ufed in exchange alio diffcr« fiocn curieoi 
moeey in \h value* 

3 lk(«m 



t^ VUtOAll ARITHliASTtt^. 13^ 



: JL ill I i» I a 



BefeiH! the learner can refolve any qiieftions in this rule, it 
is necfffkry that he know how the country with which the 
exchange is to be made keep their accounts. 



Holland f Flanders, and Gtrmany^ 

In tbefe countries accompts are kept in gilders, ftivers, 
and penningSi fimilar to the Englith pounds* flullings, and 
pence. 

fiut the different denominations of their money are con- 
tained in the following table s 

8 pennings ^ ^ erote or penny 

• srotes I I (liver 

6 Rivers l^«i,. ^^^J fchilling 
to (livers f "'"^^ °"^^ florin or gilder 
•^florins I I rix-dollar 

6llorins ^^ ^ pound Flemiih 

• 

N9##. The money of Holland and Flanders is called 
Flemifli iDoney, and tht y exchange by the jxmhuI ilcrling. 

The courie of exchange wich thefe countriis Ins molHy 
been (except during the tnjublcs on the Continent) from 
33#.4i/. to 36^.6^/. Flemilh per pound fterling; and the 
ngio from 3 to 6 per cent. 

As tlie exchange with all countries is fuppofeii to be made 
in banco money, the current money mull be turned \i\\% 
banco befoi^ the exchange 'cnn be made. 

Jhtli* By the rule of three, or practice. 

PrP4/. By reverfing the iiucllion. 

To change current money into banco, and banco money 
into current. 

Say, by the rule (»f three, as 100/. with the agio aJded to 
k, is to 100/. fo is the given fum current money to irs Milue 

in banco. 

Anil, 



Atidl» M tooJL it 10 t^oL with iht agto uddtd to Ui fe It 
iW glvtn film binca to ir» v*lut io tutrenl itioiiey. 

E^Mmfik f% tn tio/* tOf»W»lbflmg» hor many floriuit 
ftivtn, «nd petice curmnti the cmirfr of CKcluingf being M 
)$f« 7|^ Pitmilh ptr pound IWriing, AgK\ 4/. per cent. ^ 

V^il^tikc /ti^ to (^ 
FnrtOf«t4ke %% ^ ^ 
For ck 07 It }i 

For iH . ^ li M:^L 

^ uj6^7 _SM^ 

Then to find the vdue of thti Aim in cnntot monejTi I 
iiyi u 100/. is to 104/1 ^^ '* W^* <7'» sl^* ^ ^^4^* 141* it i/* 

o 

^'^ivr TfttE flor% 9 dW. 6 pence* ■ ATtT;Jr r =z 

Bjr the rule of pradice^ I (ir(^ rcdnce t ro/. tOf» <Wi fteriin|t» 
into FlemiAi moneyi And it prnduort 196/* t7#. 5i^»|* 
The« by the rule of ihvoe^ m befbto 4irtAd^ I brtug ihi» 
money into current money, ;ind it produces t^% 141* ti</* 
omitting the trAif)ion of n fiirthing) und thit multi|^ie4 tff f\ 
rtie numt>er of florins in 11 pomid Flcmitt^ praduttt itot 
Aorins 9 (livers pencts for tltc Anf«^*er, 

J^. t. in 9tt/. t(vf. ilcrling« how mMif rik^ollirt €\mn 
rtntt ftglo 4j^ \wt cenr« eicchiinge ^ tfi f-^^ J ig ^r 4141 
rixMiv>llArs* 

J^*.). In T 8 ;6 florins 7 Alvert 1 giolfi curfeot^ 0|io 
^ } per cent* how m«ny pounds fttrllugi cichioge at 3 jk iiJL P 
^-^An^fjtr 165/. tt*^. 

In Itamlmrgk 

AtcxMtkp^ are loq^ in markt tmd foh lob^ but theeacbitmt 
ts by the pound fterlingi as in Holland* 

odenitie 



OF VULOAll ABITHMSTIC. 

^mmmtmrnmrnagSssgammaeBm 



^39 



% denien gros^ ^fol lub 

6 foh iub I I fol groi 

i6 foJs iub l^.v. ^„^J mark 
d marki p*** ®°*1 drittic, or Hamburgh dollar 

3 marki I I rix-dollar 

7^ marks ^ ^ livre gtoi» or pound FIcmifli 

The exchange with this place hai moflly been from 31 to 
3Jj. Flemtfl) per pound Iterlingt and agio fiom 18 to ao per 
cent. 

Exmmpk 4* In 886 marks 19 fols lub banco, how many 

pounds ftcriingi exchange 36 fols gros i denicrs per pound 

.ftcriing? 

36 fols gros ft den. 886 marks 1% fols lub 

ift 16 

*" w 

14188 fols lub 

a 

^«/Svfr 65/. 7i. 7|A ^34)a8376(6s/. 

at7o I 

in6 

40 



434\^3*o{7'« 
3Q3S 

a 8a 
la 



Here the marks and fols are 
reduced into denicrs, ns arc alio 
thofe in the courfe of exchange ; 
then the courfe of exchange I 
make the divifor, and the fo- 
reign coin the dividend, and 
the quotient is 65/. *js. 7i</. for 
the anfwer. 

^. $• ^" 1072/. fteiling, how many marks, the exchange 
H 36j, 4</. FlcmiQi per p( und ftciling ?-.-^«/. 14606 marks. 

4Ji<. 6, In it^tl.%s. ^\d.{itv\mg* how many rix-dollars 
•Dd fols lub current, exchange at 33 fols gws qJ dcniers, 
1^0 18J per cent, i^^n/wer 8434 rix-dollars a3tfols lub. 

VpuI, Hh /«< 



434)33^4 C?^'* 
3038 

4 

434)i3M3/* 
130a 

nia 



§46 tif TtyiOAH A»tTMM>TIC« 

A<campt»ar« kept ialivrci» f»ltt nn^dcnicm; and the 
exchange it by the ecu» <ir cfown tourneit. 

The ttidhngjs k«i moflly been from $oJ. f« jsiA (briing 

per ecu *• 

xt demerit rfM 

so foil I I livre 

} livret Vmake one^ orown tournotii or ecu 
10 livrei I 1 t>iflotc 

fl4 llvrct J (.Louii d*of» or gtrinea 

EjtsmfU 7* In a46; livrci la foil 9 denicri, how imnijr 
pounJi Aerlingi exchatigc 3 1 {«/• per ecu ? 

Here ihc livrei, foil, and de- ijy, ^1. den. 

nten are brought into crowni ^) ^4(*^ »• 9 

touruoiii by dividing by 3, and 3®^* 8) 8ai t; 7 

that quotient divided by the «*'• ^^) ««» >4 wl 
aliquot parri of the courfe of - S * — Jk 

exchange glvei the anfwer. /wrr a^^^^^^^^ 

J^*. $• In 1543/. 15.1. ftciiing^ how nwny French piftolci, 
exchange 30 J«/. per ecu f-^An/wtr^doo. 

Jn Spain 

Accomptiare kept in pia flics, rinK and mnrvndici ; ami 
the conrfc of cxchaiiKc i» l>y tlic piartrr, and ii generally 
from 38 CO 4x^/. (fcrling p(*r pi^llrc. 

4 mrtrvrtilici v«!lon,or > ") f 

a J inarv.iJir« ot plurc f '!"'"*'* 



make 
one 



rial vcUon 

rial of pintc, or dollar 
pifo» piaftrr, or piece of 



9 1 (pMrtnif or 1 

U m;uv;idiei vclloa } 
16 i]uart.i», er "^ 

34 n).irva()i«M of plate / 

M iiuU of plate 

U'^X^l^^ Sp.M.iihpiUole ' [eitth 

•P»^>»«« J [doublocm ^ 

*• Th« coqKW uf »it«HAN«f m«iiii<mf<l in every ^irt of Hiii itMnv/i 
metni (he f lohmigt «» it |ttteMl)y Aood b«iure the Itie uiiliii|>py 
un the C()Atmeac. 

5. . Aav 




OF VULGAR ARITHMBTIC. 2^1 

Example i^ In 8746 riali of platti how manypouadt Her* 
ling, oxchangt «t 4 if/, per plaftre or pifo ? 

rials. 

Here the riali arc brought ») >746 o o 
into piaftrci or pifot, by divi- '^ ^* ^> '^n S o 
ding by 8, as the exchange is J^; ^J ^Jj '*J ,♦ » 
by that piece, and the remain* * a < 6i 
der of the work is wrought as Jw/mfer jf iSg o~| 
the 7th exantple. • 

^. lO. In 178/. $^ 1 1</. fterVtng how many rints of plate^ 
&c. exchange at 4o|</. per piadre ?— ifft/wrr 845a rial^ 
plat^ 8 quartas. 

In Portiigml 

Accompts are kept in reas and milreas ; and the exchange 
Uby the m\trea» and generally from 60 to 67^. per mllrea. 

400 reas ^ rcrufado 

1000 reas, or "» >ma1te one< -t^^^ 
ti crufadoes / J l'"'*'** 

Example 1 1. In 1864 mitreas xoS reat| how many pounds 
^crling, exchange at 5^. 9*/. per milrca ? 

For 5/. 4) 1864 o o 

For 6^. 10^ 466 o o 
For3</. a) 46 la o 

Here the milreas are For io8 reastnke o o ^i 
brought into pounds and At^pwrr /53 s 18 7^ 

ft^WUngi by praOice. 

«^. la. In 1 509/, 17^ how many crufadoes, the exchange 
*^ m^. per milrca ?— /f*/wrr 14045 crufadoc*. 

In Veniit and Leghorn 

The accompts are kept in dollnrs, ioldt, and dcnari. The 
excbangjc is by the ducat and piafti e, and from ^tJ, to 541/. 
p«r ducat, and from 4$^ to 54c/. per piaftrei aad the agio 
to per cent. 

H h a 12 



94^ OV VVLOAR ARITHMITIC. 




It dc*n«rK rfoldi 

ao folfli ( ^.1^ ^. J lira, or pUftrc of Leghorn 

SJfoldi >'«*'^ ^«S groflc ^ • 

§4 grofliJ Lducac 

EjiMmfk I3« In 846 piiftret 10 rnMi 8 dcniri, how numy 

pounds AcrUiig9 exchange 4.^^. per piaftre f 

plft. fdt. dan. 

For 4o</. 6) 846 IP 8 

Fur 8//. 0141 I 9( 
For^i/. i6j ftS 4 4 

W Anfi»tr £ I 

j^». 14. In 83 lA 141. 8^. Acrling, how many ducati, 8cc. 
curicnr, exchange at $34/. per ducafi agio ao percent. ^•— 
Anfuif 4S 19 ducatt 14 groirc* 

The foregoing eaamptei will be found fiifRcient to inAruA 
tho Irainer in the nteihod of performing ihU rule) I Aull 
therefore iiircii rite reuuiin<ler of the tablet of foreign cotn^ 
and a few i|ueAiiinf with their anfweri» omittiag the opera* 
tion for the pruAke of the learner. 

In lltiffia 

Acrompts nrr kept in rubles aiul roperi ; and ihc* exchange 

\% by the luhlr ; und whrii inndc immeihatcly wi(h London, 

ii ffnti) 41. to |;i. |>er ruLIc ; but when made by tlie way ut 

Hamburgh or Ainlleidam U from 4K u\ ^o lUvert per ruble. 

3 foprri ^ - altinc 

10 <oj)i (t I I |;nvrna 

*J^T'f- imakeonci P**iH"'" 
a |)i)l|)oliiiut r"**^ wi\\ |Militm 

a |M)litins I I luble 

!^p, I J. In $337 rublri 73 copcci, hou* tnnny |)Oiindi 
ftrrlinjj; rxrhao^T, by way t»f Amftri<l.»m» at laa r«iprci 
jirr lix diOl.ir of ^0 ftivcri j and exthanj»c between Holland 
and I'.UKland nt 341. ;«/. FIcmifli per pound flcrltngf— 



0? TULOAm AniTHinnic* 




j^M. 16. For 94.1/* i4i. 81/. paid in London, how man^ 
rwblf • wuft be received at P^tcriburgfi, exchange by way of 
Holfand it 34^. 9^. Klemifli per pound flerling. and exchaoge 
from Holland to Peteriburgh at 50 ftiven per ruble?— 
AnJvHT 7870 nibks 36 eopeci. 



In Poland and Pruffia 

Accompti are kept in florins, groii and penins. Thf 
exchange ii by the way of Hollaod| and from 140 to a^ 



grot per pound Fieinidu 

18 penini 

18 gros 

30 gros 
3 florins 
• rix*dolIars 



[groi 
ooft 
florin, or PolUh gilder 
rtx-dollar 
gold ducat 

i^. 17. Tn 437/. 17/. 4^. fterling, how many rix-dolhra 
Poli(b| exchange 190 gros per pound Flemifli, and 341* 4A 
Flemtfli per pound flerling ?—ifif/wff 1411 rix*dolltn 4 
pos 13 penins. 

In Sweden 

Accompts are kept in copper dollars, and oorts or filvet 
dollars. The exchange is by the copper dollar, and moflly 
from 46 to JO cop|)cr dollars per pound (lerling. 

B penins 

.J runftychent 

10 ftivcrs and % runftychens, or") 
3* ninftychcris J 

5 copper dollars and 3a (livers, or 

9& runrtycheni, or 
4 narcs 

•4 natrcs J I copper rix-doK 

^. t8. In {838 filver dollars 9 runOychens 3^ penins, 
bow many pounds (Icriin^, exchange at 49 copper dollars per 
pound flerling }^^jiHjkx3tr 357/. 8/. S^//, 



■} 



make 
one 



^runflycheM 
(liver 
marc 

copper dolial^ 
filver dollar 



«\. 



't«-w»_*«s£ 









'^«...«»-^"'"' ,„ „„ll...., •" , " Mo,. «"'« 

,„,v.fc ot »*■•»•';»• ;,;.;„,M\ -^iv*""*'.'"- ^„ „t.t»,d w 



et vuioAR ARttmitm #41 

Ai a40^. Loodoti it to 34.1. 6*/. AmiUrcltm, fo is 331^. Pirii t» 

11 

4>4 



•4,0)1 366,* (sW 

UP 

x66 
144^ 

4 T 

•4,o75y;^(3/ 

:=s for Pai ii« 

Here I fajTf m a40^* the penct in « pound flcrUiif of 
K-^^Midoii, U to 34r. 6«/. tht Flemifli exchange, fo k 3^. Hic 
^SKchangt for «n ecu, or crown tournoit of Ihiric^ to s6JL 
S^V fiurtbiogi the Flen)i(h exclunge for an ecui aoi m ^hm 
Q^^ vrfe of eicWange between Piiris and Amftcrdmn. 

Thit example will be fufiicicnt, a^ the rule oe\*tr vanei|« 

t.'K^iUgh the courlc of exchange between fcvrral (tHiiuriei b* 

%Vvtu 10 fiml a piopoitH)tiRt courflt between any two| in 

^'^hich cafe tlicy nnay be lefoWcd into at many qnethonc as is 

c^^ceflarf in the rule o( three, nnd all the firA niunbcrs mtii** 

^tplicd together for a dlvifor, and the tccoml and thud iHrnv 

I^^Qrs in each queilion multiplied together for a dividcodi tlica 

th^ quotient will be ihc aiifwtT. 

:^«* aa. A niercham in London is drawn upon by his cor- 
l^fpondeitt in KuHia for mont y to thenmouatof la joor«ibl«t) 
^exchange between I' upland and Ruifia being at jo^pcr 
niblft; between Rtillia and llollnnd 90^/. jkt ruble; $XiA 
between. England and liollnnd 36 a. 41/. per poutid fleriing; 
which 18 rhc nu^il :Kiv.\ntageo\)s nu thod for the London mer- 
chant to p;iy by ; direi^Uy to Kullia m* by way of Holland, and 
what is the advantngc ? — j-in^'er^ the London merchant will 
gain ^3^. 171. lo^^*/. by making payu^eat by way of Holland. 



Mi 



ot 



t«*»** 







i 






VROft^' 



... I . '- • I 

■ ■ * 

PROBLEM I. 

The firft and laft termai, artd number of terms tcing given. 
to find the fum of nil the temis, and the commott'difrcrcncd. 
Rule. To find tbe fum of ail tbc tcriBi| qoulti^ly the ftim 
of che extremes by the number of termif a^d^hall^Lbe p/^d^ft 
^111 be the anfwer; and tt) find the coouDoa^ifferciUfeof tt)f 
ternii, divide the difference of the extrcmea by. jhe uuml^ 
of terms made lefs by.i, and thp quotient will be the aii(w4yw4 
Jixumfk iV What js the fum of theicriqs^ and.the cocat 
nn ^n difference of that progrcffion, whofe firil term is 3, laft 
tOLTcn 67, land number of reiriiHr]|3'?l 

lafltcrm 67 laft term 67 33 

' . iirftterrt f-*' firft term 3 ' 1 

■' ■ ■ t\ f '70 difference 64 3» 

I - .', f^mhcr o( terma jn • "^c ^ 

• iQ 3>)64 • 

ajfo ^ cbpvpop diffej;en98 

; 1 1; q Anfyjcr^ fum. of the feri^. -^ 

In the firft operation, 70, the Him of the es^tremeji^ is 
inulHjUied by 33 the niViSlber of terms, and ^alf the 1)rbdlnSfc 
144511 tlie fum of the lerics, or fuiii of'^itf thti nuipbcrs,' 3: 

$» 7f 9i "» M» »S» ^7> >9. *'» *3. ?5» »?».*9» V\\^'^ 35> 

S^39f' 4^ 43» 45» 47i 49> S'. S3» 5S» S^i9» t*»^3» ^St 
6), added together. 

In the fecond operation the difference of the two extremes 

6)f and 3, or 64, is' divided by 3a, which is one lefs than the 

AWabqf 9f tcnxtf 9 and the quotient a is the common diflbr* 

CQce. 

» PROBLEM II. 

HaTuig the two extremes and the oommon difbrence,* ta 

iad the mimher of terms. f 

RuU. Divide the difforenoe of the cxtrenset 1^ the conw 



\ t. 



IT*- 



»n& * 



Ai^ 



t» 



tY»»«^»'' 



fiteo^ 



wA^^ 



lYvc 






oi i^^ ^ 



«c»tf 



*(• 



61 "V «»"«'*** 


















•r^ »*»'^* 



V - 



%i^^ 



*0«^«^ 



,n every •^^!: of ^^y'-"* 






tetv«» 



ivco 







t?- 5- ^ ,.„-r i»** * . \otttney »^ ,,e,y «•'*-„« 



tn«e»*"\:;:»^>/'«*'* 



iA»y^ 






1 PrOJir*/'*'"' , v-tke**" 






■cd\i'& 






noin 



OP VULO^R AMtTHIIRIG. UQ 



Tbiiii la geometrical progrcfliofi, tht numlitn mm io« 
creaM Iqr multiplication, and dccreafcd by divifion i vhereai 
in arithmetical progreflion they are locrcafed by adid^l^D and 
decreafisd by flibtr&Aion. 

The number in geometrical progreiBon by which the 
leriei are multiplied or divided, it called the r4ti0 1 whereat 
^n arithmetical pnogreffion t|ie number by which the iarlet 
are incrcafed or diminUhed ii called the oMtavMi MJmwm* 

In goometrictl progreffioo, at in arithaoetical progrefioo, 
liaving any three of.tlie following lecmi, the other two OHgr 
l)e readily' fbiind. 

., the firft term! j^^^^^^ 

a, the lad term J 

5« the number of termi. 

4, tlic ratio. 

J) the i'um of all the termt. 

• . ■■ 

PROBLEM t. 

Having the firft and laft term and the ratio, to find the 
luro of tlie tcrws. 

R«/r. Multiply the laft term by tl)e ittiq, and from the 
produft fubtniA the iirft tormi and the remainder divided by 
one left than the ratio will quote the fum of the feriet. 

S*^9^ I. What itt the fum of the feriet of a geometrical 
praydEkm whofe extremes are x aiui 6$ $36, and the ratio 4? 

laft term 6$ $36 
rati o 4 

a6ai44 
firft ter m ^ 

one lefs than the ratio 3)»6»i4} 

the fum ^f the feriet 87^81 

Hera the laft term i^ multiplied by the ratio 4, the firft 
term 1 fnbtraAed from the product, and the remaiodei 
'^iMed by 3, which it i left than the ratiO| and the quotient 
^7ilt b the fum of ihevferlcf* 

ii a 4|r. 



7p or virtaAn A%trnutTte. 

^M. t. Whac u tlitf Aim of « fori^i of numbtfiHy in (pofn«- 
fdrtl |Mti^r(Mon« wrtiofv eitrrin^ <ir« 1014 ind {9049, «n4 
ihc rafio ^ ^—-.^^^umt iBo6i. 

rRODLI^M II. 

Hiiving «tt« fii4 c^nn and fhc laciui to find tiiy other rrrii. 
fcipilred* 

Xkh, Wrife down a few o( ilie leading lermi ot the leric«, 
■lid pVaccr ih<ir indioei ofer ctwnii f^iuiiing wMi » cy|)lirr». 

Tlitfii add any of ttiufc imiiccrb iO|(etbei, whidi will malK 
411 iftd^^ an mtH |(4» tlian Itie iiiiuibef whkh cApi&lic* di^ 

iildLc; »( V.tt In in |cr(|uitcd. 

Multiply (h« friiiu af ihe rpiici fngfther l>cloii|fiiig co ihote 
indiLC), iiiid (he |M-«)diKt vwitl iit a divittirnd, la be divided tiy 
ilitf piiHlu^l ui ihc; lirft fri'm, fiuitci|)ticrd by a niititlKr dfi unit 
UU iluii chr nufiihcr ui icnti) iuijlci|flicd ; and iltr (|(iciiicruc 
will be ihc «ii(wer. 

i»dmfy )i Wbi( il Uk Ull tcrrni «)t ilMt (||onKt«if«| feiie. 
nrliulc 111 A term U )| tdiiu a, diid nunibrr gf teniis 10 r 

Indlift* o, I, *, ^, 4, ^, ri, 

/ radi/i|^ friiiii ^, 6, ji, 94, 4H, ,^6, li^*, 

4« 4 

y s 

«^ll i| inJcii lu tU loch CriiN. 



I u- w . ( , ^, ;. fciJi; a. . .,•! ,.-. i t i.a*,., *: ..,.i. , ..r (.i.ii.r.af* , ||..., 

• Hi. i...u* ..( iit(. i„.i ,t,i,. i^ ^^ iimf .1 lUf (c ! icim I, tn« ir. it 

I-/ liir »>.'...i, l|..- ii..!Mfa ji.»j|| i.,^,.. ^,i|, ^„ .^j^i,^ ^,.,j ,,j^ |#|.>4vX| • / 
it.i UIDla «klll i.c «.. •l.J^i,^ Vs.ll«M*»l dlv,Jlil^ hf ttU |»ll|«u4 «r tf-« 
fifll UrfHi »« 4iir/Uil MU.ti 

la 



/ 



Ot TtfUtM • AHmiMCTitk C5 1 

mmammmmmmmmmmmmmmmmmmmmmn 
Inthif «ii»inpir» the Indkvt 4 and 5 mU«d lofiihtr are f|b 
«Mch it I M% than the number «f the tcroi lonitkl 1 then 
the term belonging 10 tlirfe iinlicct* 48 and 961 «r« inuMplictl 
toffiher for a divMcnil. th« iiiil tcnn 5 mulnpliet) by 1 i«*)'i 
than the numbirr of ttmi«, whk'h arc niuliifiied t«fiiUiai| 
n the divifor ; and the <)uoticnt 1^36 b the anfwtr, 

Mi#« The Dumber of terim muUiplM lu(cihcr inlhit 
^lample are a ; therelbre 3 the firft term moluplMd bf c 
Ml than %^ or i of\^\ produoet 3*. 

Em m ^ h 4* Whit it the 1 5th term of a ftriet whofe StA 
Urm fa 5, and rittio 3 ? 

f, a, 3, 4,' 5, 6, Indlcef 

3, 9» a7« li. a43, j%^ Loadluftermi 

a9i6 1 c index to the 1 jth tenu 

«77«47 

«77M7 

i434tigo7 the 1 5th term, or Ai^^tr. 



Here« a« the fnft term ti eqnM to the rativ), the Micm 
nuift begin with i» io Dead of o; and ui many indices mutl 
l»e taken aa will nuke the entire index to the term to\ti>h% 
vii. 1^^ and the produA of the termt niuft lua l>r divided, 
at in the fom^er cafe. 

^*i* What it the laft term of that geometrical fi^rlet 
ihci« the firl\ teim it i, ratio 2, and number of tera)a a j f 
•-^^•/r 4 1^4304. 

J(«. 6, A peii'oo having an elegant houfe to difj^oie o^ 

^effred h to Tale on the foUowintr teimi : for tHe firft \vim)o\v 

tlie purchaftr wat to pay 1 farthing, for the fecond w)ndt)W a 

&rthing«, fer the third window 4 farthlngif ^nd (b'o»i'd<iu- 

bling 



13^ ^^ YvtiHAii AniTuiirricw 

ll»#<UviiiHs ihM I tmk hdwolitn ilit divUbr4S it eon- 
tiiiUKl in 4|4» MvU th^ inrwor^a I pUo^ both to xh» quolWiM 
MiU dlvtfor M before mmI muliipb' tHt cMvilor »lia ihtMtbji^ 
^4Um |irtdw^ 1441% i^ficfd Dudtr tknti Aib(r»£t«fl from the 
^[f&WtKHl itert rawiioi tQi. i« which hriogkiji duwu th# 1»A 
purio^ ^ I hiiv» §^9 (ior ih« l<(ft vi4iplvi>iH)i nod iho dpuUU 
oC H9 ^ i^^ ^ ^ (Uvil'or « ihi» hift (^ooiioot U 6. whkh \ 
ylwt m ^hf qMgliooi «od dt^ibr* nod m\»Uiply tho divHW 
ihcurtbyi.ikni ih« prodMCi U w^wA to the Uft v^iolv^nd i ib^« 
•436 it the anfwvr, 
^^•^ W httt i» lh« IquMt rool of 1 ^ij^^t i ^^<^i|/%^'' 

4t*' 3- What is 4beiil|itMf root of . 1*07 1304 >— .Aj/^wr 
4698, f 

I'd 0xtrQfi ih^ C/aJ# Boo/. 

l(«/r I. DIvUie the given nuAtbej* jnto perl(Hh of thrire 
Ivi^urea tach, by placing a point gvf^ ^^yeiy third flg\ue» 
beginning with the uuit Hgure^ \ . 

a. Find the gi^atel^ cubtt id the flrft poiMi 0l4 placo iti 

cuh«? roi»i un the ^i^hl hand of the given nunU>er, 

3. ,6uUi4et the cni»g figm. the iiiid penind «od t^ the 
4ri«ainvlcr biin/^ dQWiuhe iK^ni fciiodi^ which iac^Uod tho 
rciolvcod, . , ' 

4* IM44K tluqv tmw4.ihe loat Miukf tho refoivtnd, aad i^ib 
ilntf iiiu<« the ^ui4ic u( tl\e rgm» th«^ Uit^ boii^ rMKiv«4 
(U^« l^fice (v> tlw IvMi i theie {\m addtit luni-thfr iiMrm a 4i« 
viior, 

^, Seek huw ut(tn thia di\ iioi i^ ctMUJ^intd m tho rtiolv* 
end, cxclutive ul ihe |ilac.^ of uniu, andp)av« oaoM ihou 
the 4ufNver in the i|autien(« 

6. Umloi the diviim pl<)co the mUe ut* the Uft qupiitttt 
h^iiir^ i\\c t4iuic ui it multiplied by three tinvea thf roA of 
tho ipiPiient, 4nd thre4 tintea the luot multiplieil by Ite 
fqnare uf the ijuutieut ; vaelv td' tlie two Utiov lUMiibon bting 
removed one placf (At ther towarOi tho lolt hatiei flum tbt 
4 <«>f«tdiig» 



or yuLOAit AaiTiiM«TK. «57 

for«gotngi and the funi of thcfe three numben ii ciUcd the 
Jmhmhfmdt 

7, Then Aibtra^ this fubtrahcnd from the refolvcnd, and 
to the remainder bring do\^n,the 4)cxt period fur a new 
refoUendi with which proceed ai before, and fo on till the 
work be finiQ^d. 

Em^»^^ What ii the cube \opx p£ {64^6(^(1 ? 
% • • 

16456659* (1548 ^ ^ ^ 

laq cube of the nrft pcnod 

765) .^c)^^^6 fji'ft r^jrolvcnd 

1 5 three limci the root 5 
7 q tlure timoi ihc fi|uarc uf 5 

76 q fiirtdivifor 

,64 cube «vf 4 . . . - ; . 

•46 iijunrc of 4 muUiplied by 3 tSmci j 
1^00 three tiiues 4 multiplied by the U\\mt of j 

31464' fuUralwnd • • A. 

96744 )jriQicga fecood rcfol vend , . ,4 

16ft three timet 54 ^ 

$74$ three lime* the fcjuare 54 

H7642 fccoiui divifor 

qi2 cube* i>f 8 
10368 fqiiarc of )S multiplied by 3 timet 54 
^984 tlKee timet 8 multiplkd by tlie fqua'ro of J4 

yioa^Qt fecund fubtrahcnd * 



■v**' 



^Hpiw 548 the culx? root required. 

^K. 5. What is the cube root of 380017 } -^f4fi/i\)fr 73. 

!^.t. What is the cube root of 405 1%*^ ?— ^/jAvfr 7|. 

There arc many other mcthodt of extrafling the cube 
n)Ot given by different inathcmHticiana j b\u ncMic of whicli 
1 "have feen arc fo fimplc and eafy 10 be remembered at the 
method here laid down. 

After what has been faid, it need hardly be mentioned, 
that the cxtraftion of the fcjunre root it proved by muUlply- 
thgthe root into itfelf ; and the extraftion of the cube rool, 
by roultiplying the root three ttmct into itfelf. 
- Kk. CHAP. 



25! M PaCIMAt AHITHMCTtC 



CHAP. IV. 



Or DECIMAL ARITHMETIC. 



SECT. /. 

HIDVCTIOK 0? XITCXMAI^ fllACTIOirf. 

A DECIMAL /rtAion ii that ffiflloii wbofa dMomlnitor 
1|A9 an unit in tbeiIrA ptice on the left bandf with m mmny 
cyplieri •nnexed iineccfliiiyt tbiit |^, -f^ -f||^ riilvf 
lee. ire decimil fraflkmi. But thcJfie fm^Hpoi »• ubmlly 
cxpreiTed in writing without a denominator, by writing the 
numerator, and prefixing ai many pointi or cyphers before 
it on the left han<l, «• there are more pbicei of figurei in the 
denominator than in the numerator. Thuf the foregoing 
fraAioni are writtcti .5, .» j, .048, .0572, and tnpreikd five 
tenths, twenty«flve hundrcdthi, forty-eight tbooftndtbf, 4rc# 

Cypher! placed on the right band of decicnal fra£ttotM 
malce no alteration in their value : thui, if a cypher be 
annexed to the foregoing fra(ftion .j, it will be then .jO 
fifty liundredtbf , or half »n integer, as before ; if two cyphen 
.foo it will be five hundred thoufandthf, or {, and the fame 
of the others. 

3ut cyphers placed on the left hand of a decimal fraAioo 
ftecreaie their valtir, every cypher decreaftng ic in a tenfold 
proportion! thus .5, .05, .00;, are five tenths, five bun* 
dredths, five thouCiudths parts rifpeftively. 

Tbe 



or DXriMAL AKITRMVI'IC. 



359 



The nliw of every figure in a decimnl fnAion Incmlie* 
in « renfold proponiun from tlie fiili |>lice on tba right 
hand, ■( in whole nunnbcn. 

The figure* in the lirft pincc of « decimxl fraAion on the 
lel% hind are railed frimts, ihnfe in the fecoiid piece ^mmI^ 
thoTc Ja (be third place tbirJt, &c. 



DECIMAL TABLES 



Oant Wtightf and Meafurt, 



TABLE I. 

tl. and II. itwln- 

Dtt.Sh Dt*- 
■ti 



luiittilh Co 
Lonic M«r. I foot 
lluy Winhl tor. 



• V^ 








'.' 




.JK 




,7 




M 








.JJ 





TAIiLE III. 






ifiirPMi-niiit 





.<"*! 1 


s 


.ct-Hiftl 






} 


.oo«ij 






TABI.R IV. 


^tirJwf. tti. 


1 1 »lb. th» IflMfT' 


Qrt. 


littimtl, 


,1 


.75 

•5 


;■«../. 


U...m^.. 


,J 


;i,io„ 










in 


.pii)ii« 




,C*nt<7 


II 


.<^Ti4>a 


J 


lO"*'; 


5 


.0+4''4J 




tOJUTU 




.f.i>ljS* 




,pt?K,«T 




■iv^liK 



i6o 



Ol' MtCIMAl- AHlJIWMIiDi. 



— >- ■ p t- 



M 

b 
/ 

4 

4 
I 

A 

\ 



ilttHl.i'* 


1 );*•»» 


. "•♦/'•♦ 


# 


, .» ; i> n 


# 


.'^•'-\U4« 


ft 


,.»«■'*•>■« 


*; 


I^i^ll 


4 


,.i.nf.y^ 


{ 


.i^,«i 1 if» 


« 

n 


,i>,i.><<;M 


1 


■ .-.-. ■ . 





t.UtltH.tt\ 

,11.-. I '.y.j 



TAHLK V. 



M 

7 
4 

fi 

4 

a 
t 



li ■ w • - ■»■ ••■» « 









TAIU.K VI. 
I. i tin hi Sfft{lnrf 
I Tun il\i« lui.^f^i. 



4 
I 






4 



pa kai : • ■ ' 



1.1 M ' 



TAni.K VII. 

,i-i»l«iK.j J.hftfiJ. />•!■ 

l-^BrJ>.r-.irt . ... ^ ,f, 14 

I I 

1 ■ I II ^ ».».*.'• J 

I lltif^dirriil \\\e 



4'» 

«i 
N 



I A ',' V V V 



s 
5 

4 

\ 
% 

\ 



i 

"■■'•■'•'• ll A 

..pri|.».» 1' ' ^ 



■ ■ ■ ■»»» 
,1' : I 4 



I 

I 
I 



t t\ W- n. • li V ;. 



t 






t 



(.»,'?• t. 'rcMriliiiT rt Villain li.ii'iinn i«» a tl#vinml onr oi 
(he Itttiir V:ili)c. 

A?!//**. Pi\ ulc the immnatoi Iw «lio vlfJiomiiniDr, .lud tll^ 

• juotirnt will \k thr iK^muiI li.uMi<u\ ir«|iiiirj. 

It' the lUiinrrnttM' tir ir»o iiUiOI to l>cr iliMitrtl hy th(» ttrih^- 

Miii^Uni*, add <»»^i- 'M njiur i vplU'iN fhcirti), in whivh f«tr m 

ti»invpl.i(T» innll l»f icjiu/.trtl tu^m ihr i|Monri\i ^'o^■d^■ln^.O^ 

.tn t)K OitlVirnir* \\\ \\w luimlw I oi pKuvNoT tltviii^di ii) ili«* 

divMirnd nnd tbr duiloi^ .md ilu* uiiMiniii}; li^juir* in lUr 

• iO\»iiriiM (it .'inv^ •^'«' intr*j»rM«. 

r»it ll jlir nundiri (if |.l.»irn in ilu- ipwMimi l)r Irft iMn 
jIn ir.|iiin'<l ivuihl'M «»l d. I'imal phui :», .ti nuiny I'Vphf r» 
nuill l>t |u. u\.i| nn \W Uli !».nul ilirrrnl m?. ;»ic* nm llhry. 

irxri'/^h I. VVIwu \t* tUr daiiUid It'u'iivMi i»t ;i pnund v«\n;il 






llnr 



Here t\«u cyphers cnud be mldc(i (o t()e nttri)c« 4)700 
rator, which divided by 4 quotes 75, which I .75 

xhArk foffflMimEitsi: as there are two decimali 
added to the dividend^ imd the quotient is the feventy-five 
hundredth' {fart of a iihund, or |, equal to I'jr. 

Example 2. What ts the dccSfxial frn^ion ut' a pnund equal 
to Qi/. ? — Atifiwer .03 7 5. 

As there arc but thi ec places of figures a4,o59o^o(.03 7 J* 
in .the quoticnti I place n ryplier on the 

« 

left thereof, for there fliould be io^t figures pointed off for 
decimals, being fo many cyphers Rhntxed 10 9; thus the 

quotioiseiitoo^? ^^ ^ P^i^^* 

'Exampli 3. What is the decimal fraftion of a pound for 3 
farthings ?—-^/»Al^'>'. 00;^ 12 5. 

' Herft the vnlgar fra£^ion for 3 96,0) 300000,0 (.063 12^ 
farthings it ^|:j- ; I therefore phcc 

a» irfanjf (fi}'jjhers as are'necHrary to the rtumrrator 3, f\'hich 
in thif Mfc H 6 cypher^, and the quotient is irafj, Init there 
muft be 6 decimals in the quotient, as there arc 6 in the 
<fivkieid' ahd ndnc in the dK rfor j I therefore prefix two 
cyphert l& the fcFt hand thei*eof tts heforc dirc.^eti. 

• ExtnHpie\, What Is the decimal fraiftion of n year tx 
73 days ^'^Anjh'cr .2, equal to V\. ^'^S ^SoC-* 

€afc%* To find rho vahic of a decimal fiM^ion iu niont-y, 
wei^rht, or mcafnrc. 

' Rtth* • Mulriph- the dK-imal i'mftion by the numht-r of 
parts of the next inferior denomination, nnd from the pro- 
tkift cut off as many figures from rhc ritjht liatul lido as 
tliere arc decimal ph\ccs in the ftiu'lion. 

Then mnlttply ihel'e figures (b iqmrntod un the n<;!it hand 
by the number of parts of ihc nrxt infuior denomin:iti('n, 
and from the produd cut off as many figures as this laft 
0)ulfip]icand has decimal places, as before. 

Proceed in the fame manner through all the dcnomins- 
tiont, then the fcparatird figures on the left hand (idc will be 
the anfwer. 

ExiimfU 



i6a or oiciMAL AinniifBTic. 

Mxamfku Wbatitlbcvalurof .564orapouiidfttriitt|f 

to Ihillinft ia a pouad 
Here I mubipl/ the j^iten [77g^ 

dccfacal by to, ibc number ci la pence io a Ibiiimg 

prti of the ncxc lets dcnomi« 3.360 

»ii«>fS TO, ftiillingf. aiul iiom * larthinjs in a penny 

ihe produd 1 fcparatc the ihrce >*-*40 
truref on the rifthc hand, aSo. ^, .. .ij ..^.r • 
as there arc three places of fcnhing. 

dccintala in the given nuniScr. 

I then muliiplj ihcfe fcparaied figuret sBo by ttt and 
from the pro()iiA 3360 1 fepante tl^ three fit A figofc* jtet 
at before* to be muhiplicd by the parts ol' the next denociM- 
nation, via* 4 s then the 6gures ftaiiding on tl^c kut hand of 
tbrfc feparated figuiet «UI be the an(wer«— 1 \u 3}^ 

The fame rule iervcs 10 difeover the value of any otlwr 
intrgera, having rrgonl to the number of pam c wmfcwd m 
each inferior denomiiution. 

Thot tu find the value of a decimal fraAion of a pound 
tror» 1 fuft mu)n|>ly ihe fission by 1 a to find the ounces 
tbcn the I'rparaicd li|>tircs by sd tu timi the pennyweights, 
juJ bllty by 14 to tlifirovcr ihf giaini. 

j^ji. 2. NVLa( is i^c \ Ji!c oi .6715 of a c\\i. ?— «l0urp 
ttjrf. i^lb. ;o2. 

j^v. 3. What l» ihc value 01' .61 of a \m\ of wine .^-» 

Am/ivtr 9hhtU. S7|(jlU. ti\M. ipC* 

C.*jt y To fiuil (he value u: x dcvlm«il uf A pound Aeiimg» 
by iii!pprtH>n. 

k*'e. UuuUlc the lliH fi/,urc of the ilciiuud on the kiC 
h.sn«! iW niiliiu|;9; ami it Ihc nrxt Jii{ure be {» o« jdmee {» 
add t Otil tni; ntuie u> ii : \\u\\ cuil ilie figuics ia the Iccood 
aiul ;!iiul pl.ioc»fanhm<» (y\c\ dcduckini; \ tiom i^c kcooi 
Cj^uic II i)ct(iLr% ), ami il (he nuiubcr ot laithings be above 
is abjTc I. aiii) u abjvc 37 abiitc a. The other figures ui 
the fracUon, ii' moiC| iiic uc|;Ieclcd« 



:_ -.Qf PtoMAL A»ITHMgriC> >*> J^J 



ExMmpk u Find the value of .564 of a pound by infpcc- 
tion. 

Here I take the douWe of l"^ ^^ 5.^« . ^^ 'O'- 
. ^ A* c luii- For the cm the 6 take I 

5, the iirft figure, focihiUmgi, jp^r the 14 remamiog o 

which U 10, Ab I (hiHin| - ~ 

more for the c contained in ^^ 

Ike 6b and the remaining 14 (viz. 1 in the 6| and 4) I con- 
fidervt iartUngh abating i becaufe they are above it, which 
make 3|i/.: t^ui the decinud.564 of a pound it ix/.3|JL 
at may be ften in Cafe 4. 
^. %. Find the vaJue of .7880 of a pound by infpcAion. 

J^3* Fmd the value of •X47t9 of a pound by lafpeAIoiu 

Cmfi 4» To Am! the decimal fradion of a pound equal to 
afty given numbel* of fliillings and pence. 

Ruk^ y/fv$ii half the greateft even number of' dulli^gs 
for the firfi figure in the decimal, and the number of far* 
^ thing! in the pence and fiarthings for the fecond and third 
figlnfef, Obferving to add 5 more to the fecond figure, if 
the nuiAber of ffiiHingk be odd ; alfo add x more to ihe 
third figurci if the firthihgt exceed U| and add 1 if they' 

cseeed 37* 

Emw^ u Find the decimal fradion of a pound equAd t6 
1 1/. 3|y. 

Here for the Hi. I take 4 of J®'' ^*'' ' V?.^p -5 

. . ^ ' For the odd fliiUmg .oc 

the next greateft even number, F<>|.the3j ,014 

which it 5, for the firil figure Tcbl 

•f the decimal, and for the odd "~~"~ 

idllins^ ptee 5 to be added to the fecond figure; then for 

the 3|^. I take 14 to be added to the fecond and third num* 

bers, at there are 13 fiirthingt in ^^i. and i is added, as the 

fcrthingi tie ACifVt it ;. thu^ the d^dhial is .564 of a pbund. 

^. •• Fi6d tbtf decimal equal to iBi. j^\d.'^An/^Mr .9x9. 

■ ^•S* Find the decimal equal to X 7/* ^«t-*^^i^ii.^ .878. 



i*4 



ftf fiRCfMAf/ kntrnuvftc. 



ftfcCT- II- 



or AMynwp ow MnimAVM. 



ftflmv nf the It^Mrurt^ 
iir«//« Fl*f« f be h%me§ ttnS^)y un^f eneh nDrntf «c<s»f4' 

(if ntiy) (frf'l«r tmh t fiber, nn in pfMvtfiit fff Wbufa Ml 
im4 the ftiMifm$ are uiftp Mr he pf«ced tff«of4iNj| to 
ir«}tie«9 irfx« |yriifM!(k tftt«l^r |yt1mf«9 lez-zuMlft fimtor fii M wfa»tWi 

Thevi flft4 their ft^m «• )rt wh^ ttmilhefif uhd fMviM *tf 
•9 wntiy pUtfn fm detmitU n* Mfn §fpmt to ffte grettdl- 
fHimher ftt (\n^tm^ f>l«r^ in ntty ftf Am fjj^ti tto^fibert* 

t.Miimf4f i, Wh«t 19 the ffirnf^f •t^f^o^i f^^jf I49ft^<^f| 

Ij' ff 'li^ fi'iff,?>firs ^r» »';'l':/| •///jftfhff like 
wh/fk Mirfr)>'.rs j'j'l Oi€ fi:»^hV,f (j>f pl«tei 
jfiifi'/'fj '#fr /or '1/ • jf/i-'I; ar*- r, *'i'i;»J ♦/# ft>jr 
Kie^tcH u\\\u\tii of flM riMl );l4<^4 in ffny (/f 




•'Ff. 44^31 



A/'/rt l\:fampU%. 



f.llff 


71.f'/f 


•4/«»oft 


.'-/»;; 


•'•> 


.j','yi 


7< f^o* 


4?.%2;fl 


t'>fi.l'f,7. 


f tx '.'.* 



'7; ZJ4f 



yft4^fO 

111 or 



9P/,T 



"1 



OP-BMHIAii-^AI'PIIMlVM.-* §6$ 



SECT. III. 

OV CUITIUKTUHI OV DICIMALI* 

DiciMAL fra^ions are fubtra^l in the fame manner at 
whole numben^ hue the numlKis are placed ami the dec't- 
inalt pointed off accu ding to the rule given u» the foregoing 

ftftioiu 

ExmmpU u What ii the difference of a^y.o;!!; and 

Hei-e the appcrmon nnmlwr conftRs of 6 W4<>-oo?7i» 

placet of deeimalii whercfoi-c the rciuaindcr jr- 

fought mull have at many decinial placet; in ' - -"7»rl £i 
Vvery other refpeA it it wrought like fubtraAion of whoU 
nunibcrt* 

Fsxamplrs. 

•aot9» 9a8«iaog4 3*7o:)t 

14.1 #973% 400 ooa * ,ooii^97 

J .889468 518.11804 3. 700-0 ^ 

gM [ii.ji,..J4i iiimai 



SECT. IV, 

■ 

or Mui.Tiri.icATroN of ductmal^. 

RvLK. Multiply the given numbers one by the other, at 
ID whole numbem. 

Then point off as many figures fi>r dpcimali at there art 
decimal placet in botli the nuiuhctsi but it' there be not To 
many placet in the produ(!i>, a^ many rypheri.mull be pre* 
fixed OD the left hand thet-ruC at will ^uko up the number 
jaf decimal placet cequiied^ *- 

Jixamfk I. Multiply a. 03171 by .0056. 

1.1a 1" 



or DMIMAt AMTnMsne. 




*"ltnii1i rxtmple the numtyr of dccim I t.oji 

placei in both tht mulcipltfr tod n^ultiplipuMl '^ 

b 9 1 but tbi produ* cont^ ^ .oaly 8 ^^»{^9< 

flgureif therefore I mtift preAy one cypher J 

on the le<k bfUfA iteffo/f wMch jnakcl the g^^cJLii 
trueprodttft. 

»7'0»943 ^•»PM4 

^ 4'3<PO*& '43^70 

91016*900 108J900 

108117 71 6013191^ 



Thill It eppearf th«t ijpi multipllri^tlon of decinml frtAI 
there U no neceflity for placinK tliofc fignrci of the fi^ ^i 
under each ^thcri ai in tbf two fjtirf goip^ rulcf(*« 



■OBBBiEnBma 



SECT. V. 

Of mviaiOff OF DBClMAt^. 

Turn rule ii alfo pcrf^rmeij ^ aivifion of whole nymh 
but from the quoti^mt point off ai many figures for decir 
at the <leciftia( placet i|> the dividend eiceed tbo<f in 
•livlfor. But if the placet in the quotient be not fo man; 
liould be pointed ot for declfnali, at many ryphf rt iBoi 
placed on the left hand 1^1 npccOary, 



M*M«ta 



'* There l« ^ conrn/M mr^hod of woihing both ihit af)4 
M'owlmc niJi f«vfn I7 tntnjr wriicri on arlthmeflc. They ari, \ 
•Vfi, mil very flBipk, and myycry Well Im fo|»erfedH, hyofoHi 
fomr of ihc (Ircimali In both nutnbcrt| a«4 lyarkifif •ee<ifdlM to 

griicral fi)tf« 



If il M17 time th«re be a rcipaimlcri and If k b^ required 
fo hivt an anfwcr to a |rcater degree of eaaAncfii ai man/ 
fTpken may bt aiKxed to tb^ right hand of the dtvMfiid at 
{e thovght proper. 

MMimfkt^ Piride lllj6.8p30S by aj.ij. 

a3.i5)i836.8839s(79*34| 
i6ao ^ 

a 16 38 
ao8jj 
In thii example there are gg^^ 

thite more decimal placei 694'i 

\n the diirid^nd than in the , 1 o8to 

diTiibri there niuft tberefore , ^*^- 

be three defimali in the* J^^{ 

JSj(pfffip/«r« 

a 3 

».46)W-C!oa4(.i^9 aoay)oa,ooop(4S9S 

146 tl2JL 

Oi ao 

98JQ 

^•43 




6070 



In the fecond example there ai'e 4 decimal placet in th? 
dMdendy and none in the divifori therefore there niuft be 
f piaeei of decimali in the quotient. 

And in the third exnmple at tlie number of decimal placet 
ia the dlvifor and dividend nre equal, being 4 in etch, there 
^nft be no decimaU v\ tiic quotient. 

(very other rule in arithmetic may be performed by deci* 
iml fraAioni as well at by whole numbeiJi, at the fame rule 
fcnret for lH)th ; thnn in the rule of three dirp^t in decimalt^ 
th|e ffcond anJ third nnn^hcrt nre mu^iplied together for a 
dividend, and the firft tuur.ber is tl)e di\ilbr at in whole 
|Mi|abert; and the like may be oblerved ol every other rule. 

CHAP. 



CHAP. V. 
Of STOCK-HOLDINO. 



THB nArvM or THi ruibie ITOTM. 

The {mMic ffockt n( Gnu Riiulit ii in IdTCntiM Is tm(< 
Uiion of Ihi ft«« »r Phtrnrc, wMvfi,' in ihl ]rHr-i)44. 

oatiAK (w.oooL lAd bcinji uu*Vt lo pay the |>rttwi|Ml, coo- 
wnrd the dtbi inia K (lubltc flock, iraaattnW> /loni oiw 
Mitlitual u» MiMhtr, <i>i<li inlercft ai ; |Nr,ociU.i llwle 
pnlilii flivlii «frr ■s|1..) . A,,™1 ,,. i.,../. in<l llic priici 
viried iccording t» the (l.ite i>f |iiih|lc affaJn, 

In imiiarwn or iliii, Umn aticr the rcvfttuiion in Greit 
Rntam, the tnpenk* of Irllllng ilie new elhbliftiinetil, cir- 
rying on Inng wiiri on the CnnlincMl f'lr reducing ibc Fm^b 
mmitrchy, fectin'ng (he Dutch tiNiricr, leltlini^ the Spanidf 
fiK-reirmn, kc. incredf;:!] t'< fiirh t t\tgttt, (hi: it w»i lh»u){ht 
■dvifiiMe (n Anw upon {Kiflerii}', riuhcr ihan teduce ibt (ite 
by an immediit* paymenl. 

It wni thcrcFiirr (hr |H)licy or miniflcr* of ilut day lo ■»!<; 
■ piihlic flock Willi triiii>fci;itilc Itinrrt, thiii converting the 
deht into a lie* fpccics of jiroptny, for the fecurity pf whkt) 
rirhiimfiir pledged ihcir fiiithi and (hii «x.iinple tiai bccK 
(Wcly f(il|invi.(l ever finte. 

' Thi< ryltrm Uid the foundation of what ii c«1t«l ijl* 
Kitloiial dcl't, (» which evriy Qock-holder ii H ct«d)for> ^ 



or STOCK'ROtDtMOt 

-ii fi 




Thui'tbe property in the KlD^om in idea hai been great!/ 
thcreafed, compred to that of former timet i but if we in- 
quire into the nature of thii propertyi we fliall find it eaifti 
only in name^ in paper, and' 'public Faith i but that it fuffi- 
dent f9r the public creditor to rely upon^ for the pledge i» 
nothing lefs thab the 1nnd« the trade,- and perfonal indufiry 
of the fubjcA, from which fourcei the money muft arlfe to 
pay the intereft; in thefci therefore, the property of the 
public creditors does really exift, confequcntly the value of 
the land, the trade, and induftry of the fubjcA, are dimi* 
oilhed in proportion ai the debt increafet. 

To demon llr.ite this, if a debtor owti too/, the creditor 
has a demand upon him to that amount, and though he 
may not call u|x)n Mm for tlie prindpal; ytt fo much of 
the debtor's edate is ahvayi transferable to the creditor; and 
the iamc principle holds good with regard to the public 
creditor. 

Therefore the property of every ftockholder confifts in a 
certain portion of the natioual debt* , 

To pay the intcrcH, and, if required, the principal of this 
debt, certain taxes are appropriated : thcfe taxes weu» ori- 
|\nally fcparatc and diilind funds, and each of thtxn was a 
ftcurity for a certain Turn advanced; they were attcrwarda 
united togetluT in three capital funds, which are the princii)al 
funds of any acov)\int, called the gentr^fund^ the Hji^rcgau 
fund^ and South Sen fund \ and the funds thus united tpgetber 
ire become nuitual I'ccuritics for each other, Jtnd the wboU 
produce of them li.iblc to pay the intereft charged upon each. 
The furpluiles of thcfc three funds, over and aboye th« 
intereft clrar^^cd u^ion tbcm, are directed to be at thedif- 
poial of the railianicnr. and are ufually calcd x\\t Jit king- 
fund becaiifc oiijrlnally cU fijjmd fo reduce the national debt: 
to this have late y been added fevcral other duties granted 
id later yi ars. 

Tl is finking fund, with the o her duties added thereto, la 
the lait icfort.oi ihe uatiofli on which piuft depend all our* 

ho^}ea 



iJO 



Off iTciek-iioLi»tiiii. 



hnpt% of (lirchnrgliil mf IncHmbniHCfi. But hy n fitiiuti 
pnflril ill the i^h yeiif of Ooo. Itik PnrllmttftK vefted one . 
MtliUott ntiiitf«il]y Irt ecmimtMlmi«ri fof tltt rtduAltih of ihi 
lirlx ; in wlikh i»A f«v«nil pmViAoiii ifi' itmdn (r) |>f cvcnl thli 
httid* frorli l)f Ing flpph)|ii ititiiil w Mtjr 0thf f puriKifn <tt Hnx 
t\]\\m f Imf . Irt confeittHsnas of thli i& Byio^^ocig/. hnd br«it 
ttilcemcd h) Fcbi'iiary i;^!. 

stitei whirh ^riml Impcifti havt been (i|>pU«d (o the f«m« 
inirputtii |)Htil( uliirly th« ndimpttoii of the Uod'tnk i Rml 
kvcrid new \^mn tmvi bMft Dpvmid on different condlitotiii 



BtCT. ir. 



etMrt.tt AND COM¥OVifD IMtlCllkir. 



HiMfr.K <fif<i'cft U thf ttllowflnfe med^ by thr t)om>wer iif 
«iny r«r« of nionry to the If iidri*, kcc onlin^ fo m trnniti mte 
l*^ iifhti pfr nnnuAs which H niriif(<d l»y Ikw to 5 p«r rent. 
I^'r unmihs ihfff in, j/. h»r thf uk of too/, for imio yr^r, end 
t«9/. f«r (ht «ft «f ii for two yertri, or 10/. for the ufe of eoo/. 
foe ime ychf. 

Printitptti U f htf ftmi of nifmey Irne. 

/^/#n(^ 01 MHf Ift the foifi figrfed u|Kin for (he ufe uf the 

/^MfffAr/ i» the {It lh(^l|mt eml InterefV ndded togfthcr*^. 



^ l»» »n^ V .utin (tf Uw int«rffl ftn- ittitncy Iftit u ««itfipute4 ftir ftttftt 
^»Mfr*N «r yran, h,h| Utt^lii dnyi,, Hut liif iHt liii«ri>A fm |»ttl)lit boMi 
W-lntiftliiK (u ihf Muufit Mm •»!•( Imt)« Ctimpiintts wiil ihc fffiet lilci W 
ihf NnaIi gr fciiilmiit^ it)ii iim« h nefit mtly vom^i«4 In Mt»riHA» rt 
hhU dn/ii eit4 mi feiMlMitiiei but! !■ <|tien«rf er • ytei iM 4«tf. 



OF STOCK-BOLDXVG. 2^1 



Simple Mere/L 

Rmk* Qgefiioni that conoem iotereft cit rcfolved by tbe 
rule o( three; thus— 

Molttply the priocipal bj tbe rate of iotereft, .mod divide 
the produd by loo, and the quotieot will be the ioterefi for 
ooe year. 

Theti multiply tbe intereft for one year by the number of 
years given^ and tbe produd is tbe intereft for that time* 

But when paru of a year are given, then find what aliquot 
part or parts of a year fuch part is, and take an equtvakBt 
part of the iotereil for one year; or find the intereft for fiich 
pan by the niJe of three dired. 

Example i. What is the intereft of 245/. loi. for a years 
4 oaooths and 50 days, at 3I per cent* per annum ? 

a4$ 10 If 365 gain 8 11 10, what will 50 gain P 
3J percent, £ 

736 10 4» 19 a 

isa 15 10 



J,oo)8,(;9 s(8^- 3^S)4*9 »» 8(1/. 

ao 64 



la 12S1 

f^oo)io,ao(io/. *^ 



ao 
80 



la 

36jja36o(W. 
aivo 



170 

£. u i. 1 

S ti to I year's intereft 36$)08o(f/. 

^ J J^ 

17 3 8 a years intereft '^i^ 

a 17 3I 4 OKKJtbs intereft 

1 3 6| 50 days intereft 



Vov-L Mm !-» 



tff or iTorK-fiotinio. ■*• 

lit tl fffU I IliM uitfllt|>l|' ihi •4f;, io<. bj (hi tM* 

f>f Ifltl. il ••••I rh* |IIO<lua dtVt'M by lOO <)MIM 

■/. ( tl, fJ. Ur (Im Inuntf of mm frar. Tlicii by ilw ttdt 
«f ikro OiiWI 1 Awl tim iNiifvJ) lot fo d«fi, wbkfe It 

Attf 17 it» nrf« of prwno* t IM ili« IntaMU IW t pmt 
tf/i )/. M •nil •ll'> iltr l(>i*i(ll Im 4 iiwHiilM.or onvrltlnf of 
rtw )wr, «f. I p. ^. Wkkh (tm* •44ad unfair, flu Am 
It •)/. 4*. ^ 1m am ntmt, 

0|«AI*m wiNWTimn \mtrH iKi tn rfU4ni hj ilw 
AmU« rvU Af f^rw 1 iInh (to frrii^nc tSifniih imjr Bi 
witwflir, fiifl«i:i if l«ul. |«lfi )/. io<. tJ«r<«nt. In I ym, 
■tMt w4l mV* i'^' W*" ''> ■ X**" 4 ■nn'Ai ami M ittyw f 
■ ' %p.t. WImi Ii rtw thffrcB if <6t/. ft* 1 yt»r, ni 4 i^r 

^m, ■rniin. ' - ^■/»*r tkl.^i.'.y. 

->.',. VVl'ji i» ilir nii>i>iit>i lit 34}/. Iur;|fr>r<, it 4I 

I" "'.I. If "^ VV"''* v*''''i',(W. 

■"..4. Wl.^r 1* 1I.C 1..1.1.1I .i( ^ii/,(o». fo. -) ifufiiilii, 

-r m^, .M.I. |„. ttm,.,,..?- -.-;«/■,."' 4/. H.iI7. 

<),.^, W1,4M« iliir Hiti'i..ui .,1 J4>^- foi •lr**'*t ■< 4i 

I* '-r- """"■' ' ■ /"/■'•'■' «'V- '"V- 

.T'jii. ''. U'1.4i I) ilif ujii'iiinl ',( 400 ifuliieii) foe 4 y»i« J 
" '■• ■""' »wl"/'. ■'<l4l"i Tui. jnf «iii,«iif— >p(w^ 

«.*. ■!■ Wl rli. ii.ir,. II aiir ii,«m an KulM^twr bUI 

i/f ./H-A jt ,1 |i<i tria. |i.i ..1.11.1.11, (W •! ji«n and 67 



-or aroEK-BatDntc. 



A TA£X£ 



The ShmS/fir if limis fntm tim liai' t^ am Kmiii tu 
■Hx Jamu Dat! of another jBoitlii. 




Tift tic «f ;: :! raiiie », t« ia& 'aov masif «aji «re txm- 
t£b«c i.'o=: lij t;i '.i ctic uKur:': to -ftic iasoe tiEn -.rf" any 

Xiica: :jK.- -uaet 1 £:^ i :( for d^ t:i:B-t:r. 






•M 



or •TiKi'BOf.rrtiro. 



«i . .,r^ Uu)«<, itx kM<<(t at M Mtfe> te 

■ ,..!, aimI dwif (iJm tiuoMMi • omv ||IM> 

f^- ■ i-.^a li<tU NfMH lltW (I •4ll«l ■ ■i(|l^|W < 

M iMfHMMi wf NMif A, l^r ilw (wU Iff lMif4« WM**. TkM 
Ah •Mk'MWf «lil U "X prtm ipal fat ilw taMll ptfmmtl . 

M MfpHUNi («>*••«• (iitfid ifdMnfMJ, ■arf () M d 
y^FiMiM* i« tiM Ut, tlwajri tMtMmtmf Uw Ul|j 

l^riMtftl lot ttM Am IRUrf*. 

Jmh)^ t, WIm( h r]w aiiwMM 0/ (44/. iwi I 
fli ||« caM, ^ Miiiwi« WM^nind tatonft f 

(I'itiul yMr"* piJWrlMl 

U...,H ,«.('. w.u/.i 
iliiirl f t^r'* |)riuiiMJ 

(IumI /cai'i uuaitk 
tiMiih ytaf't fdiuJfM 

(i-Ullh ^e*!** IfiUMft 

lir(<i yeat-'t pnntipti 
nf'li xt.A iiiuraA 
(lie A»puii*, 




hit, ifi 



^ 



Afur fi'idinij Ilia fltS ytar'* InUrtft i»y itw fbrc^dg 
ruU »t futn)fK uiitiett, I ii'U ]i III (ha prliu'iMl j ibw 1 tiava 
^bji. C'. 6'/. iiir ills fEiJiitJ ycaii j>iiiKipal, the Hiurcfi of 
wItK K !• aD/. ;j. 6}./, mid wlii^-li addad tu iti piinripal ffia 
jiyj/. 1 a.. ..(./, Jul I lie iliiid ye.i'» piiii<:)fMl, f) wfakb Walfo 
■dJed lib imeivft ei/ ii^j. lojrf. and iJw lum ««(/, i|j, it/ 
f«i rnt a priix ifMl t>ir itu fnnnli yaar, wliicli u alto wMt^ u 
iu iiMtuA .v/' {' «!'/. aiid lit* (UHI 6{6/, Jly«,7^, » Ac 
^liiKiiiJ f„r i),e fifth jraMr, whkh a4d«4 U (tw lit IflWrid 
IJirct 68^/, (6(, fj, tof ill* anfwar r*<|ttir«4. 







Sunarff: .in iMesmtL ifmfium:. 
M^Ui.- 16uilyiu tcft prrucipOf. tut stUo. >2£a. tsif tinr 



4 



«^ 5f ^i 

1,44 ^^ 

i:7 ' ^ 

irf — -«7$ 

"f - 



"J! 



Tiuuf, ^^%i t ^xatC » Dint >i0c&afc <i a ;p«n)ikd ftr «« 



1 



t^ft ■» •TOCR-MOLDINO. 

|»i«tR lit any piKu-iptt (ar «M yui, u iptr WM. ■■ ,o| 
ftnt of ihc prMKifMl. 

M 4 per (CM. pci aiMwn, Junpis inurtA f . | 



}Un fw llf !{'• >n Iht 

IbAliMi .;(, H tiiigtii In Ctft 
^.4 «l icduOkm o( de>.iiii«l 
mAi-MM 1 ihrn mtittip';t{i| 
tkc ptiBct|M] b|r ll»r tiiio, inij 
lh( (Mixliifl If/ titt uumticf uf I 
Tnr*, 1 hMrt loi.bmof. for 




Number oT fm% 
I'ounib 



ruthiD|i 



Then I find thevtiHe of tlw declrrwl Ato9 bi Ibillingi 
and prncc, by ihr rn(c in Cafe ■, of rtJaAIwi uf dtclm^ 
WhI il p((Hlk)cti ■■f.fl|<^. i ihuiiliT anfwtrii toil. it<. a|X 

;^K. >. Whit ll Uw fimpl« inlrrrfl nf ■{i/. iTi> ('<'• f<>r { 

yeaii, *[ 4 prr < rni, (,ei ;u)iiiiii) >- -A»f-wtr c,'jI. ly. 'k/- 
fy. J. Wli:n ri ilic fj.ii|.lc micrtit <.l 1 760/. fot i{ ywri, 

■I ,1 |«r'rni. |,ri.im,umr — ^«/-'y"■'SV■ 
(■.,.■,|,.,Nl,.l i„..rr(l i. ;.ir.. w.o,i,;l,l l.y,lccim:il (nA.oni. 

the (livtii raip pir renr. Tlicii 

|K>wcr Ht it (.xjmfftil liyihc 

till! |>()wrr \iy ilic |)ririi IjmI ^,i 

tlie uinminr, lci>iH wliii h if llic jiriiici)i4l ii txuiilzA lh« 

icmnimlcr will ht llif inlcicft. 

Mmtmfit \, Wbalitlltr compound intcrcft af s>o/.fof4 
7«n, at 4 per ccnr. per uinum i . 



11 (tf j/, f..r I ycir.it 
aifc tlic ■iijriitnt 10 fuch I 
umber of year*. Miiltipljr 
'!>, aixl tlie (irmliK^t will be 



) 



or yrocK-HOLDiMC- 



O*' 



1#04 




4 It' 






tiie feooQcI powcx c\ a.o^ 


4^2 <^x 
1 o&iO 




I.I2^4b<>X 

X.04 

4 499- S^ 
1 1* 4.bU 


tii^ Utifu iiWMu of i«04 


z.iC 98;^^ 56 


tiK: fourth (lOwer of i«04 



i 33 97 J" JAC 
Ovc-';; 2045 i&C tut WUOi^ ilfUOUU^. 



Jr. th : cxj-mpk J ifeii*: ti«': amount o*^ 1/ Jo' • vtiir, 1*^4, 
to '.lit j'jurr: i^o-a*:', ifTir !ijul:i;/ viiij-; tlju ^j^'zt hp- tuc 

^«. £. Vua* h tiic amo'Jzr of 4:0. io ; y^urt, »' 4. j^jr 

Mor v"*::':'i 01. '.ornpioujir* hiXkikI' jjiv , '.jr^.j-. :c <iii(A»ver 
at oiict •.!.t *.'jmyoiiU<!. inl*zreir </ any iun. fo" fc :v oi.i um 
t:rTj»;, at t.;fi'::«j-. lai*:', ytt t-rii:. : j fiii;.; tij»r!eio:o, ^:Vt obC ' 
to fu^v. tilt luauit*:: u: vurAi ioty a;*, '.oiiluu-li'-t!. 



A TAl^UE 



r 



*■< 



■Ctmpomd hUr^, at 3) prr OiU. pr j 
/or Twmnty Ytar*. • 









••nr 










in u,%tt ftfftiit 



)M»j7JTi 



'*ll 



iita..: 






J 



The fbre^m^ tat^c ibem% dte xiraimc cif -J^ 
j^ per ceotk peraBframv eooipoinRC imero^ yir siv 
of years aoc ez'.*eed20g lo : riia% tb fina Gie juumiL ir 3i» 
fur X 5 years, I ieek in the ohk iir cte xnl line oc tiB & 
teeoth year, anJ dte lo^vcr » /g,675j^i» Ac ofni tB 
z/. 13/. 6^. 

Though the tabie be fbrmed oaiT for zJL priocfpri^ m^ 
queftioas chac ^. ^ii c ei a 10^ loo^ voooL «r waj iBoftipiK «f 
xOy may be readily sxfwered by ity by only rooBCviiiig lis 
decimal potat as maay places further cowards the hfbc hand 
as the povcdh principat coBOncfpisn 
amoont of io£ ^ *S yeic^at 5} per 
reft, I place the (kcimai pome one place futher towardi dK 
rn^hr hand; and tiie asfwer k ^^i^^js^, Ik. or 16^ i$s.o|^ 
and for loo/. the aofvrer is X^^7*S34S» lfe*«r 167/. zqc«8i^ 
by iafpcMoOyte. 



n^ Cbm/bw(tim Qfthe T^dk. 

Tbc foregoing tables and all others of the lame 
are fbrmcd by neiripiyhif the principal by the Fatio^ aid ^ 
prodiiif^ ^rvcs the ftoBpic iarcreft for oneyeary wkkk added to 
the principat, the fu:i>is the anoant or pnadpaft for theoeiC 
year; which is to be again moltipiied bythen^ and the 
produd a^Q added to Uie iaf^ pincipal fora aew pr incipa l 
&c.: thus^ hi the toregonig :ibU:^ I mtutiply the prindpal il 
hf ^55, the mtio n 5I percent, and the prodixft ts joj^ 
for the iniereft lnr one year, which added to its prindpal cl. 
is 1.03$ for the fecund yeaPs principal, which is agioti 
matciphed by the ratio, and the produA is .0362a j, whkh 
is again added M i^^ principil 1-035, ^^ ^^ ^"^ ia .0^1225 
for ti^e principal for tiK :hird year, &c. 

hi fonninji t;ibl«» of coirpi>und iiirerefl*, it is fulficient, in 
general, if there be t-mW tbrc:;* places of decimais, which will 
the anfwer Go a fjrtnif>g« 

V<jL.L Na SECT. 



ato or tvocii*NOLDiNat 



SECT. III. 



Ulf UlKCOUhT tin 1li:Vli|llilU|l« 



Diic»UNT b that allowMictt which ii iiMuk fur iIk py* 
niciit of any Aim btloie it in du^ Aocordiqg ro a caiuin ract 
per crni. 

Dilcount may bt wmugbK ckh«r by whub numbcri « 
d^imal f ra^ioni, * 

Tha picCcnt woilh of any Aim which ii diia fooM liiM 
krnre t« that turn which if put Co iiicerrft for that cinMi aC 
the ffimtf rile \vtr ceixu will uiiiuuaK Ko the fum or dcbc Khrn 
c|uC| whether the incaicA be fimpla or conipovad. Difcouai 
ii wroi||hc hy the rule of three, 

/?ai^. Ai the anmiint tif lool. at tlia given rsta ami 
time ii to iiK>A fo ii the fum given to tha |>releiu wortb. 
Then fiibini^t the pitfriu worth fnuii the givaii iuni, aud 
Ihe leiiuiiider it the diltoiint required. 

Or, ai the amouui of too/, at the |{tveu rate and time, 19 
10 the interett of 100/. lor that liiiie^ fo U the given luin c«^ 
cite dilronnt ici|uiied» 

EAdffipff I. What it the difcouni of 1^7^/. igi, due j year* 
heukc« ac 4 j per cent. \Kt aunuuii (impU iittcrvft } 



4A io«< 



9P n'«)QIC>ll6l.t>1I(«. 



ftSi 






4 «o 



13 lO 

to 



£• *• 

$73 «S 
■o 



•7P 



»»47S 
• 70 

803150 



••Q^o so) 
••7»o)3og8i 50(1^64 

ba8 
681 



i36t 



• k 



110 



i 



»97 

ft7)t354(io 



94 

4 

•*7)37M« 
•>7 

JnJK\}ir 68/. 41. i oj//. i^? 

In thii cxnmple, the amount of 100/. for 3 }'ears, ;|t 4} 
per cent, ii made the iirfl nun^bcr in tlic rule of three dire^. 
the iateieft for the xoo/. for that tirne» at that rate per cent. 
la the fccond nun^ber ; and the given fum, wbofe difcount ii 
required, ii the third number \ and the fourth number ii the 
anfivcr.—- 6H/. 4i. \o\tL 

Dijcount by DBcimak. 

Knif. Ai the amount of 1/. for the given time, at t1)r 
gWen rate, \% to 1/. \o ii the intert^ gf the debt for the fame 
ti.cne to the d\fcount required. 

Example i. What it il\|^ difcoun^ of (73A1 x j|« due 3 y(fia(> 
^pcp, hX Af{ per CjBOt. per anoum i 

Nna ?.i3$ 



•St 



Of IfOMrilOWlNib. 

I.I5J if 10 I fail 77*4S^*!( 

•76* 



49* S 

6l*t4)i i^il to 60A 4/f io|^. lb« Mjiwtn 

In thii eMmpl«| I fliid rhe ampunt of lA lor ihe gir#n 
cifYMi tc ih« |riv«ii rate percmic. which ii 1 •!.)(• "^^^ <bo 
iiu«r«ft of the (Mm for ihit giwn lime, at tha givrn rata par 
cant, ii 77.4{6a$. 1 tharrfora divido thii intaraft of ifct datrt 
by tha anioiinr (at it ii tba (rrmid iiunibar of iba rulc)» mm! 
th« qiKiiionr ii 68,«4), or 61/. 41. io|//. 

j(«. •. What U th« dilruiint of 1401/. lai. for 10 moiithi, 
•t i\ |iar ciiit. par annum P — Anfiwer 44/. 16/. 1 \J, 

i^w. 3. What u ihc ^\ck\\i worth ol 71/. due i{ monihi 
hencr, HI ^ pel cant. |)ar aiinuini (iiiiple imaratt i-^^mfruer 
70/. f I ». ^//. 

j{/i. 4. What is the prrrc>nt wot th of 1 ao/. ; $0/. payable at 
3 monihi heiicr, joA at j monilis und the icft at H monilii| 
difcouiit at 6 pfi cent. |)er annum f-^.iti/. 117/. ji. 5/* 



ber.intci dwfl, ftnit u iMimkit u|)uii ihitt lM|i|M»tfui>.ii, tt.4i ilic 4c.l.it.f 
pH> Uib a rum «| MiMlcy Muir il j« auc UiU* |ti#ni>li»»lt wtutltl lltr 
MUiiiity ivwiilU i.|l,i.fivi|i ijitiii liiHi li.ifii tttc iiiiif: 1.1 )i4yiii|i II 111! n >l 
due, siitl MMi(ei,tici.f(/ lUr ilrpl||tir |i4k lliiil iiiU«iiu^c j iUi:iUufc i| i»\ 
|i'iiiit, ih'4i iha UcMtAi ri(.iii ttiluhaigiiiK iHtf detii luttirc ii ii ijiii:, by n 
^f«rsii| |MiyMi«H|, lAuul^ lie lilt f4me iik cin|ilityiiiK ih« what* tum «i 
iRuicft liU il tHti-iiiiic:* diir i fur il Iha diAaifNi ba |iui pm w biiarall Ah 

Ike 



OF trocK-nouiiim. 



«»•$ 



Ex^mpk I. Wlut \% the i^un^ie ut aato^t iOi» U«fik 
ilocki aC 105I per cent. ? 

III 06 

>34» la 6} Jh,fikf€r^ 



i'Q 



■••— ■••« 



■^•1 






I 1 1 1 



Uie (iv«n tinw> iu Hnumui will b« th« au(f itA •! ih« whuk ^Ih ft»r idv 
AuM time* 

In th« method of difcuunting hiUa bankvn commit « (real rmui for 
they reckon the inierrfl of ihc (Vim drtiwn ^u from t|i« tmic the hill it 
4K^fi«Ml tUl it becomes due^ including Ihr Uiyk uf t^nii^ \ ihui Ihcy 
t«lit lli« )nt«if n inftcad of th« difcouiU, and m«kc it more ihan it 
ftiould hr. 

To make thlt more plain : — A had a bond «f 1000/ du« 1 yrar hrnce. 

which ha oi^rt to B 10 difcouni fof him at 5 par cent- \ tt, iu imitaiiita 

of the euAom «f haokaik, afkad A 50/ to dilMmni the bilh hut, tay^ A, 

$oi. ia thelntfreft of loooA ^ 1 year, at 5 per v't'ni. thvrvua« ^hu 

ii to have the intcrell of the j^oi you or i ? If )ou will leiurn me (ht 

biereft (or the «icJL which Im i/> loi. 1 will a^u-e \\\ your in mi. A 

addi'd fAithi-r» U you ^tU ^ive me un mu^'h nu>nry for my t»aiid ai 

with thf Intercft will n^ake up luodA at the yiat'ti t-ml, I will deal with 

you^otherwife not \ to which R aarecd, and A calculated ilic intcuit 

ihuH : aa 4.0^ U W iL fi» i« loocv/, to 47'Oly 01 47/. lii- 4|«/. which ia 

the difoountt and which fuhtfaAed from 1000/. leave:. 95 a/. 7^- 1^- the 

pielbitt worih« — Thot B got all the money he ought 10 have i toi if B 

Wnda out the difcouni at $ pei eent. it wi]l hrinit him jutt aA 71 7)^. 

Hnd the amount will be juA 50/- at thv ycai*s rnd. and fuppitliag A 

put OMI the 951/. It' 7i^ ei ^ pet eem. U will juft hiing iu 47/- i4<-4i4<. 

th« money paid in hand 10 Ba and he would have hia loooV. entiiv at 

the year'i end- 

Bm ihr goods bought or fold, when payment U made in ready money, 
without any rvgard to tlmej one year*a Inic reft of the luin ih gvuvrally 
eilcemed the diicouni. 

Heie it w^^Sk be noiedi thai In eoAfMmd innreB, if the InieieB he 
paid haU yearly, it inefeafe« the amount 10 fomewhat moie than when 
paid annually \ and alto if the difpount he Aibiial^ed every half year« H 
m*kes the reverilen fomewhat lefi thjin when computed annually. 

Q;i«iiiBM 



a84 ^T MBMnAvn AecoviiTf. 

Q^ieftioni of thii nature are rrfolved bjr the ruk of fir^c- 
ticc: thuff in the foregoing examplr, T take the principal 
ftiiii of ettoA lOf. for the prire of the Banl^ ftoclc, at lOo/. 
per cent, and for (he other $ per cent, in the price of th< 
ftucliii I talie a twentieth part pfthe abmc fum 1 1 1/. o/. M 
and for the remaining ^ per ccnt« 1 take a tenth part of the 
{/•line* wbici) ia ii/. •/. oji^; and thefe three h net added 
together !a the anfwer. 

j(af- e. ^'hat ia the purchafe of 197 jl* tOf. India ftockt >' 
1 13^ per cent* i^^Anfwir •149/. iti* 

Hf^y What ia the ptirchaie of 1633/. 41. Bank annvitiaq 
•t 89} per cent. }^^A^fi»tr t4S9^. ly* %\J* 

j^ar.4. What ii the parchafe of 4109/. lai* Wi ihcjpM 
cent, confblidaied Bank annuiticii at 5$} per cctit i^^Aitfim 
ea65/. 8/« j^i/. 



SaiESSS? 



CHAP. VI. 



Of merchants ACCOUNTS, 



SECT. I. 

eP BOOR-KEBPINO TMK ITALIAN WAY; OK, 

DUUnLB ENTftr. 

1 HERE arc fcveral Imoki iifcri by mercantile • 
which the principal are thfc wtijfnhok, the jomrinti^ 
MtgfT* Thefe booki arc generally ufcd by all 

I 



or MlRCIIAW Tl ACCOU WTi> sSj 






bttlineri \ I fliill therefore give an cxAtnple of the ufc of ttch 
of tiieiii* 

Of (he nqftc^Dook. 

ThU bnok| by fome called the titj-h^k, it ufetl to note 
4own wliatf ver iKcun iu the way of trailei ni buying, lUlinifi 
payings receivingi delivering, itc. 5rc. without omitting any 
one thing, 

Thii book hai one marginal line on th^ left hnnd, and 
Airct Hnei for poundsi fltillingfi and pence, on the right 
hand ; the day of the month and the date of the year are 
hlened io the middle of the page. 



Of the JoiirnaL 

Evtry thing which ii written in the wafte*book mull lio 
tranfcribed into the journat in the proper mctvanrilc tcnnt» 
and in a fairer \\m\k\ ; »nil every article it to \k (et down 
KCttrding to the order of time, without any intcrmitfton, to 
make the book of ni>)rc validity in cai'e of any rontrovrri'y or 
viifpute. 

In this book every article bought or lold it (lirtin^;uiflieil 
by the name of debtor or creditor, and to thia l)ook iccourfe 
muft be h«d for the {urtlculird nf any account. 

In the journal, the day of the month is alio placed in the 
middle of the p»K^; it i« ruled with three Unci, for pound*, 
(hiUingUi and |Knce, an the wii\e*book is, and one, and <omc- 
thnct two marginal lines on the lelt-hand, to r«fcr to the 
ledger. 

C^' the /^rc/rfcr. 

Fvf ry aricle ii poftcd ituo thi< b(H)k from the journafi 
but in (hort, in vwr line j every lefihand pr\gc of thii book 
ii called the debtor p;<gc, and each r\ght*haad page the 

i creditor. 



iM 



or MKR«HA!tfX Acvouxra. 



fftnlii«(. \y\ity iWhiiW |Mj|« HDtA i»Vf » rmtitw |M|tK »i 

an * tU|t« ui itt* Ikine nnmhtr wttti lh>>iv callcJ ihv iiv- 

r.tluntn n» titv Wit h<iHil i <ki it)« uyf oi r»-h |vi^c i« ||t« 

Km))*) l>iil it tAviA Aitl tw t4H<i«c<)t iltoi In ilw Malh^tMtA 
«> fiy Hntrk l« witiit-H <l<tWH in ^itttiwrj \<-'»\n U»i<n*^^, mwI 
riu^riHi] ihi) tMMitiiktrt lm»ih« )>HtitMl u iftiUtttft Rwn 
th^ii ttik! Hiiiitu ihrtn •li»\n in (h« ni.'it<titi<lr ttlittiii-, ttii1tit< 
iniflt'Dit toch yttu>t\ or miiilo by ilw ttaoir »| >|.-lMni tM 

h-n>Hl. 

AH thlHgi wtirtJ, «r <h« iv.-rtwr, mv <ilr^l«tA Kl <U» 
Avlivtirtl, iir iIm) tlrttv«m. 



r*rtt«fi/i<. ■/ **i^ t/>^'fh<- It.f4^ lUI. 



.Vil»,l. IK.'). 



' I " 



. I.I... J,w.. *.. 



k , 



It, JTt IOmI, I.' Iw »4I>1 lit ft .ll.lint» 

H.»Klii.>l U',l)i..,i. \\,li;„n*. .,..,. 

lil'iifiki, nr I '. tS. |>.i ,Mi 
IK > II It III ..I liil.ii lidHaiJi, ctoi:. (il 

Ij ti 



A|>iil),l. itl.>|. * 

iJU.in ltrt.-ii .I.U(. I f« tkniV NlliKl., ••;. la., 

tOWtiHlK Itl 4.,(U.tt#t V*lJ. IM h« t<«Hl tt) 1 
|W It. ■- .. ,1 

f Irtl... !;'»« «lrt. PI- i« h»„.i .KhU |.,i t^ j.«U*, 
«i il*,j..i >dMl. |p)t)iv ln^ munihi 



*•• 


- 


1* 


• 


» 


^> 


1 


tl 



ov MSftCHAirrs Aoeomm. 



287 



I Liibon fagar debtor to Williain WiUianai for 
icwt. at 1/. 18/. per cwt. — — 

Green tea debtor to Joha Awards for 6olib. 
at«$#«perlb« -r- — — 



i|x8 

'SI ^ o 



Jo the firft of thefe examples I make Iriih linen the debtor, 
as that Is the article received, and Henry Snrith creditor, as 
he is the deliverer. 

In the fecond example John Jooes is the debtor, as he is 
the receiver, and broad cloth die creditor. The fame nay 
be obicrved in all the other examples which foUow. 

Thus an experienced perfim may keep a journal without 
a wafle-book, as they both, import the bmc thing. 

I ifaally however, give a few more examples of each : and 
Mt& the form of an inventory, as that is always taken down* 



London, January ift, 1803* 

An inventory of all the taoocy^ goods, and debts, belong- 
ing to me, A. B. of London^ merchant : viz* 



fncaih — — 

fn Canary wine — 

In French brandy — 

In Florence oil — > 

In 1000 ells of Iriih linen at 2/. 4J. 

per ell — — 

Doe from John Smith, by note of 

hand — — 



1124 9 10 

5*^ '3 3 
224. o Oj 



116 13 4 



$0 



6292 



5 



January 20, 1803. 

Received from Benjamin Hughes, in Jamaica, 50 
puncheons of rum, at 18/. per puncheon, to 
pay in 6 months — — — 

Vol. L O o 



900 
January 



0» MERCHANTS AOCOUNT). 



January .,0, iBoj- 
lioii^M of H<nry Jotu'i, lo yardi of 

biii.irt doth, «t 171. ft-/.|K:i- yard ^17 10 
Uauxht ao ynrdi nt Trrp^ at ;^i. b-f. 

I'fr vartl, to p»j In 6 ninnihi t id 


ai 


a 


A. 




February J, .B03. 

Sold to Henry Brown to gallons uf rum, at 8<. 

per gnllno, Iti ^ monthi — — 


8 







February 4, 1B03. 
Kecnved of George Jouei too/, loj. Hub upon 


too 

60 







. 


MBrch4. "B03. 

Pfliil 10 Thomw WillUinfon ^al. due by note or 

my hnnJ — — ~ 

March j, 1803. 

Bought of Jiilin Eilvr.irdt 1 pipci of MailciM, at 

30/. iK-r pi(w, to |Kiy in 1 nnm[lis — 





SolH to Henrv Willwms +0 ijailon. of brandy, ■■ 
1 a., per u.iUoiii t" pav iii 6 livmihi — 


•4 






H,>i.C.I-i ,.f |>-hn ■ninmiv t. [inr.'Tf^n. of Tlnl 
I'li"'^- ■"" IS-I"-! I'ui-duvit. 1 . !■<■ i^iid in g 


iflo 







tlo'U;lit J jiii'i-ci i.'t imilliii, (It V- pi'r [liccc, fi'i 


8 





• 



OF MRnCRANTS ACOOVNTI* 



9S 



ft89 



JonrnaL 
Inventory, Sec, London, January i, 1803. 



•^ I Sundry accounts Dr. to (lock 

Cafli — — 

Canary wine — 

Flench brai>dy — 

Florence oil — — 

1000 ell!) of Itifli Jiocn, at li. 44/. 

per <:ll — — 

Note of hand of John Smith 



t 



£b2i)i I <; 



4150 (; o 

1194 9 10 

526 13 1 

a24 o o 

116 13 4 

JO o c 



(anu.iiy ao, 1H03. 
Rnm Dr. to Bcnjainni Hu^hcs», in Jamaica, for 
$0 punchcotH, at 18/. per pU'icheon^to pay in 
6 monthi — — — 



£' 



ii. 



6i<)i 



5 



laruKvry 30, ifi")3. 

4?|^um1rie« Dr. to llonry jt^nes, viz. 

^Broadcloth, Kir 20 yards, at 171.6//. 

per yard — — 

Serge, for ao yards, at 31. 6/-/. j^er 

yard| to pay m 6 months — 



900 



3 »o 



j Fc!>:*n.iry 3, 1803. 

UHenry Hrown Dr. to rurti, for 20 gallons, at 8; 
I per gidlon, to pay in 3 months 

Fchnia ry 4, 1H03. 
Cadi Dr. to Oorgc J(mrs, tor 100/. ioj. ilue 
upon bonds — — 



— 80 



1*3 



100 tc 



H 



« 



Thomas Williamlbn Dr. to caQi, ft)r ^0/. due by 
note o f hand — — — 

March ^, i8o^ 



Madeira Dr. to John Irdwards, fpr 1 pipes, at 
30/. per pipe, to pay in 3 months — 

"\ " ' M.irch 6. 1803 "^ ' 

Henry Williams Dr. to brandy, for 40 gallons 
at 12.C. per u-^ ''"^n, to psv in 6 months 



it 



u 



Mairh o 1H03. 
Hollands Dr. to John Thomas, for ta puncheon?, 
to pay in 9 months — 



• j March 6, 1803. 

f {JMuflin Dr. to caHii for 2 pieces, at 4/. per piece 



180 
. 8 



Oo ft 



l.etif^€r% 



) 



or MBacHAirrs Kccovnrt. 



1 



■4^1 ill m \U 



Hi 






B|3 
II, 

111 



llll 



I 14 JIJI 



T s--i->i i °"; 
"^ -■ -•'■ I - II — '^ 






•lllll' 



o i 



111 






Of MBHONANTS ACOOVNTi* 



1191 



o 



UL 






1*1 I Wi 






rm 



o o 



•r* 1 



T 



3. 




n 




e_ 






^ 



14 



J( 



) 



iVT> ACCMnrfK 






nroiir 






< iiiHi 


''111 
I 


1 


1 


'i'i'i' 
illilil 


11^ 


1 


1 


li 


f 


' a f * 


*t* 


f 


« 



iii^ 




dl 1 


1 1 


M' •• 


I'll 


• u o 


I'll '1 •( 


"r" 


I'll 

r.i' 


'-;.- 


'1, ■' n 



i - 1 ! ' c 



op MKRCtUNTfi ACCnUNTI. 



:55_^; 



Is 1 1 



:^i ^Di 

4 i^A a, t. 



c3 g.t 



I ri 



II 



.1 



< r 
la 



I.S 



'(■'■ I: 



^^5' 


««4 


_. 1" 




r 




1 


"^"l 


■i.!> 


^'l 




2 






1 


•* 
, 3, 




hi 







•94 Of M UMiuttti Aegmmn* 

Ihoft p«rtHh(i or thingn tt) whk*h ihr oth<»r |m« ()* k foul hi 1^ 
ilfbtnr urt «iu<?fiKl un th» flvhtt^r Ati^i t)i li>f> l^nti |Mit«, with 
lh« w«^rt( 7)i) And thofi^ (trt^rtinft or (hln^A hrlon^lnil i«> th# 
KifiHi acv'tnmti to whk^h ih« orttipr |Mrty U (klkl to bt 
ennNtori ii« tnh»»t't( on the rlght^htinH fhii^i or oii^i^littMr 
piigts with th« word J(v^ am i»Hy li« («t^o io ih« AM«^t\|; 
tXHo«plei« 

Th« Anom lo th« oirrow t^nlttmo lo th« IrJi^vr Ali«r th<ft 
dny of th« moothi Uith lo th« debtor nod oi^dltoi Adr^ C\niw 
whAt |i«)t«i lo tb» Jout haI (hip «n(i ir>A )iri» inkto iVoo^ i imi 
thv l«tt«r R In tb«tip coluomi fl|nlAi»« (h« t^iitnindcr on rht 
talMH^ of that |)«rtkuUr ^t^'tumt. Thoic flgMr^i to lh% 
mrrow ^lumo oo ihis debtor tld«| brfori^ ih(» otoneyi (li«w 
III wbM |M|t« of the l«d^r thtit «o(ry iUod» oo tht isrtditw 
lldi» I And tb« Af;\«r«i In th« Uke rolomn on th« t iihIUot Atbi 
Ibrw wlmt |M|{« of th« trdg«r lint «iuiy AAOd* in on ibf 
dcluiu lidc. 

K«f h dthtor jwgt of th^» Iwljjcr mnft bf ntimbtrttt thi^ 
fi^me »H thAt \m\ of thv l«d)^cr whcvT tht tmtiton iti th« 

*rh«' U\\(\\\ ll|{\iirrt (^1 (hr hc|^ititno^ n( rm h itunnMl rnliy 

\)|tprt ll^\iir iUtw'n (hr «)rh(oi litio, (\\u\ \\\p \x\\\n A^\UV th« 
firdMur, 

*rhrip thit^r liOf^K^ rtic ot nmy hr ulrJ l»y rxriy o^dtt 
id lmlini-l0| in t^nv line N\h^(«\ri, cmwilt ^tn hy lbi>' o^vi^* 

*rhri<» .M<» (rvrirtl i\\\u\ JHJokii ttlr*! hy nuMvhtinlRi •• 

Mill, thr r/f A/ A^**^ ihwIthhU rninc^il iho di«y \vbipinM\ 
mII (uin* Ikihimc due, Nvhrihri Co In ywA \\\ lo U0 iinrtvvdi 
l\v l»llU «»l mrlMnj^r, iioira, luMub. »\i. ih.if l\v rom|wir(o( 
mvlpurtud prtymciu* to^^Mhcii |MH»>iiion nirtv l^i* nm«W bi 

SfiiWdi 



or MnnoHANTt AocovNTt. a9$ 

Stcond, the r^A#»^, which ii rultci imd puRfd Uk« the 
MgtTi whtniin nil vttrccipti of monex Aie cnccr«d on tin 
left*hand ft>lio, ntui all paymenti on the rightf with tht dagr 
of the month (the year \Kh\f^ fet on the top of the p«ge)| 
for whofc Mcronnt the m^ney wa« receivevi or paid ; and tht 
loliil debit or credit on each fide it yfually c)nce a month 
pofted into the ledger to the account of cafli therein^ with 
references in the cnfli-Utok to the Icvnal foliox in the ledger. 

Tbirdi the invptit^^ok^ or book ot fii^\t>rie8, wherein are 
copied all invoicen of gooda (hipped, atui alio of gooda re* 
oeWed from abroad, which ntult always he entered f>n the 
lei^hind fidei leaving the riglu-hand tide blank ( and on the 
advice of the fale of goods which arc i^m abroad, and Alio 
on the fale of goods received from abiond ; wiiuh ure to be 
entered o^ the blank or right fulc. I'hc u(c of this book 
iai to fave the journal from any eraftu'es. which would be 
\iii;Etvoidable id taking invoices of cho fcver«ii goods icccirtdi 
fciir, or Ibid. 

Fonrtbi the r^Y^/^A/»*»l, wherein are given receipts f»>r 
money paid I tl^c receipt lo be j^ivt n by the rca ivrn lor 
whole account or ulc, or for what it is icieucd , und the da/ 
of the month, and d,ur ot \\\c year. 

Fifth, the l#»»i a/ *7»*fr^#i 0/ mo'*iLt»,tt/'fy whoreiu are 
entered all the chnrj^c*; and cxpcniru ot any j;oo»U bought, 
ibld» received, or Ihipprd ; Inch as portcit*^r» wharfiJ^jc, 
warehoufc-^room, &c. ^iC ; the whole account ir omc a 
month trnnKfvMrt^d mto the cm Ih book, on the » n Jnoi lulc, 
tvith rcfeicnccs to the book of cl>ar){c^ ; and (Ive lunut in the 
debtor tide on the l.uuc a^cotuu ni the Icc^^cr, 

Sixth, the h^k •/' l^wfA^U fxf^^mts, therein are cntei-ed 
the charges of what in expended in honlrkccpin^, Inch at 
appareli houlc-rcnt, Irrvants wa^^et*, povkct cxponf'k, viC'» 
tualii jkc. &o. : this is once a uumih tuouucd up, ami carried 

to the ca(li«lHM)k. 

Seventh, the irttfrhok^ which contains copies of all letters 
lent or received from abroad, and alio inland letters. 

Vol. I. Pp Laftly. 



196 or MWCHAWTtl ACCOPWTi, 

l^iiUy, ibe «#/# of mtm^randum S^k, wherein are iniertrd 
■ftiiit f thm occiirt for the help of memoryi and of gieti uii^ 
uhei'e there ii a muUipliciry of bufincfi. 

Gtirwral Rulen. 

The prltfcipAl rule hi book-keepifiiir ha* nhtnAj been 
detivefed, in the (je|{infiin;i( of fhi« fr;^lon, vi/. To make all 
thingi received or ihe rerdvcr deWror to the dcliv<>rrd or ihe 
deliveiert. But I iliaU add a few more ruin, whkVt niiijr 
fci ve to eMmpUfy the foiegoing rule more fully. 

I^iril, ftit-'k it dfbtor t0 profit and hfl fw a)! inotiey received 
and nothing given for it 1 ai rht profit of t^ytry eonrimodiiy in 
the trade, legacief lefr, money leeeived wirli an apprentice, 

P9f contra eredifor^ hy profit and hji, tor all money ptiid 
and nothing received for it; ai the difcoune of money received 
before due, jufi of goodit uninrured, lo(« \yy aecidentf, abate* 
mcnr liy (ompo^iiiun, lionfciioUl rxjirufci, gifu, kcUc, 

hec()ndlyf iur money rei'eivtd make caflt debtor 10 the 
party that p;iid it, and the party 1 rediror by cafli. 

Thirdly, lor luonry paid tiiaki: tlic receiver debtor tocafli, 
atui (.,i(li r.jc'lifor l)y the parey, 

I'ourllily, Viiv [[(HuU hnii^Jit for ready money make ttwr 
g<Xi(U iWAtUii to ciiflt, ,\\u\ v.a{\\ rrr/litot* hy thr ytujiU, 

Filihly, h»r y^oocU (oM /or ic.idy inonry make <.;tfli dciiMr 
to fli»: \fjuti\%^ and j;o' (h c jrdiior hy r .iHi. 

Mxthiy, f'/»od« honfjlit on < rrdit, in«kc the good* dch'oj 
to fh<f itiirr, mihI t'nc lellnr ciedil'ir by thr fntt<U, 

fiCVciiiMy, fjoiwU ioM uj/Oji (rrdtc jufl the ronffaty ; that 
ie, ihr pr»ioii who hnyjj thi-rii muft be dt'htor to thef/x>«l., 
tuA thr goiith (ffdiloi hy tin: pairy. 

J'.i^'hfhly, h»r ^OixU houglii jiaii /or r^.1dy \ymyr.y tif\d tlir 
K'll on I (e(hf \ hid ifiakr th0 goo'i* (h-htor to tin: pNiry Un 
iIm wh/j|c{ Icrorully, make thr p^iriy d* hior to raHi \ur ilie 
thotiry i^aid hi(|} 11} p4i't of llide f/iodn, atul cdfli cicdiU/r hy 
♦.he jMiiy. 

Niialily, 



OP M£BCHAirT3 ACOOVVn^ S^f 



Ninthly, for goods fold part for ready mocey- anit rhc 
reft on credit ; fir ft make the party debtor to the goods SiC 
ihc whole, and the goods creditor ; fcrondly, make cafti 
debtor to the party for the money received of him m part of 
thefe good5, and the party creditor. 

Tcothly, when difcount i» allowed for money paid before 
it :$ due, make the party who receives the money debtor to 
£a(h for fo much as is paid him, and ftock debtor to profit 
and lofs for the difcount. 



To remove an Account full ivritten to another "Folio. 

Firft, if the debtdr Vidt be more than the creditor, make 
the o!d account creditor by the new ; but if the creditor (ide 
be more than the debtor, make the old account debtor t6 
the new, and the new account creditor by tb6 old for the 
fema?ning fum. 

Secondly^ in an account of company^ whefein there is 
(>laced more feceived of another thian his ftock amounts to» 
as much muft be added to the debtor fide as there is phced 
od the creditor tide, in order that in the new iaccount there 
may be as much debit as was put in, and as much Credit as 
was received. 

Thirdly, in all accounts of mcrchandife, the gain or lofs 
muft be entered before the old account is made creditor by 
the new, and the new debtor to the old. 



To balance or clear an Account when full written, 

m 

Find ihc fum of the debtor and creditor fide, and the 
diferer.ce place to its oppofite: thus, if the creditor fide 
exceed the debtor, then the line is to be written in the old 
account to balance on the debtor fide, to anfwer the line on 
ibe creditor fide in the cew acccuot. 

Pp* H»^ 



i^S or uncHASiTt aooodntc. 



How to Ubma ike JcctmtU ai the Year's Endj and 
ikerel'y to know the Siaie ofylffairs. 

Firftt^ven the iccouyt of ca(h and bear (h< nctt rfmainder 
to Ulanoe debtor. 

Secondly^ find the value of all goods bought and fold ; an<L 
for goods bought which remain unfold^ vaUie them at pnmc 
cofti and bear the nett reinainder to balance debtor. 

Thirdlyi find what all the goodt coA which are bougbc^ 
and alfo how much thcv were fold (6r^ and bear the oect 
gain or loft to the account of profit and lofi. 

Fourthljf^ even all peifonal accounti with )'our debtoci 
•nd crcdilora in the order in which they are wrote dowa* 
and bear the nett remainder to balancci &c« 

Fifthly, even all voyjigri and k^on accountt wbcftin 
Chere ai either gain or lufsi and bear the nctt gain or lo6 to 
the tcoouot of profit and lofS| and the goods unfold to 
balance. 

Sixthly, even the account of piofit and lof;, and l^ear the 
nett rcm^iiuicr to Aovk. 

Sevcnihly, even the fto^k, :in(l Wn ihc nctt remainder to 
balance creditor, 

LaOIyi find the fvim of both {\\c. <*chtor and creditor fides 
of the balnncr, and if thry Ik Uxh alike the at count has 
been kept truly, oihcnviir not. 

If the debtor and trcdiroi fi.lrs < f the Im'aucc be not both 
alike there \% an crior,\\!nvh \m\i\ l>c li^und by prit^kiiii; o%*rr 
the \yQQk% ajj.iin, 40 tec whether every lUbtor and ncv^itor is 
entered in the ledger*. 



With the r««ic in ihe 1fHl|(vr, tiiU marking it ihu« ! . uml «m thr t^coii4 
%iaminiUion thu» \f Ace. 






or MBlOHAWTt ▲ccouiatk 



«9f 



The fhrm of om hvfHce. 

March 69 1803. 

Invoice of looqn. of mhmt in facki« flipped on botrd Cht 
gpod (bip Neptune, William Brown mafteti end coiiiigiie4 
CO Henry Jones of Jamaica, for the account and ri(k of John 
Dalton and l'hom%ii Kdwurilt of London, merchantii marked 
nnd numbered a% per margin : 



locori. of wheat, at xai. per quarter 
toolacki, at is. each — - 

Meterage — — 

Porterage, at 1/. 6i/. per quarter 
Cartage — — 

Lighterage — •— 

Fitighti at ti. per quarter 

W^ 4 
Tbtcomojffion on 98/. 8/. 4^. at 1 per cent. ^19 o 

£99 "7 4 



ADW 

BO 

No.x 
to xoo 



60 








10 








a 








7 


10 





S 


t8 


4 


3 








10 









The Fbryji of a Bill of iMcVntg. 

Shipped by the grace of God, in good order and well con* 

ditionedi by Henry Williams of Kotuion, nuTchant, in and 

\ipon the giKxi fljip called the Mercury of London, whereof 

it mafter under God for this present voyn^c John Di( kfon 

of London, mariner, and now riding nt anchor in the port 

of London, and by God*g grace boxind for Antigua j to fay, 

One bale of Irilh linen, utul one bale of men*t 

A D flioe^, and five hundred pair of filk lltKkingt, 

No.3, 4, 7. contents, *Vc. as per invoice, being marked aiul 

numbered us per margin, and arc to be delivered 

in the like good order at the aforcfaid pKire (Antiy;na), the 

danger of the fca only exctpteil, unto Mr. Ftbvard Drown, 

merchant there, or to his alligns, he or they pnying freight 

for the faid goodi, three pieces of eight per rwt. with primage 

and average accuftomcd. la witncfi wlicreof, the mailer or 

purfcr 



3 06 fl> MWCHAWTI ACCOWNTiii 

|niilrr 91' (he fittil fhip hith iiffirin«<t m ilirte billi uf \»i\ng, 
•II ol' iliii irhi'iir ihd iLilc, Bite of wliltfh iltrrv UHU Mii| 
wceiDiiHOiftI lh« urlitr iwo (u fliind void ] imil fu (luA Iml 
ih« |1>mhI ail|i 10 hvr iUflrtd porl In fjifFiy. Afli«n. 

IXittd in UmdofS ih* 6[li nf Maich iHoi, inflite taA 
CMMitlf unkiMWii (• jM-x iih\^at 



An Aettmt <^a Salt, 

l/iitdeii, Mnrth 6ih, iGoi. 
Aeminl of ii h\* a( two ihAur<ind I'uor Itiindffd ]nin)« 
of mullln, iwff iliiiiirDiid rwn liuitdi«l y-iiU of dlmit/, iwo 
bD^flifMl* «r rum, llv« fwl. ol' %ari a»d rive hundred pair 
of cMirm (tiwkmits rnclvcd I'roiti u» \h>aiA the fltip MniM. 
CipMln Thctiiuk }iific< «(itiuititiid*ri tur Kutiuntef Rdwitrd 
Will* u(}Mm», iiinchiiiil, ii dcblbf 



T«|«.ilrri.j!«..J»lltr(. 

To ctiinn)iilii>ii tit Itlr* -^ 



To ihc nni piAilu/i, Uil dcbli 




-jiFd, Lcndjn, Ailt M^rcli il)»i, 



OF MXnOHANTi ACCOUNTIt 3OI 

Muft writcu cm inrrchaiui nccounti give a viiltty of 
c)i«inpl«i aod lulti to inform the learner how to &att Xh$ 
|(pveril aiticlea avcoi cling to ilchtor and crc<Jiiori but iht 
foregoing examplcii and a ftiiA Attention to the gAeial roki 
\^(wt delivered, will be faOicicnt for any ordinal capadtjFt 



Conr9rnh9g M<r Expariifig and Importing of Chpit^ 

Ooodt to be ex|H)itcd inuft have a bill of entrji in thi 
following form t^ 

Ia the Marjai Captain Thomai Jonei| for Jamaiciit 

Two thoufand four hundred yards of mufliii. 

Two thauf4nd two hundred yardi of dimity. 

Two hogfl)tf,idi of rum* 

Fivecwt.of iugar. 

Five hundred pair of cotton ftockingi. 

There muft be frvcn of thefc bilti, one of which mnft tiO 
jn wordi at length, the other* m.iy be in flguit*» t thofr billa 
•1^ entc*re<( Into booki by the clerki of the Cutlom Houfe* 
When ionic gooda pay tuftom and others do not, there 
mnft be two entile* made, onr for thofc which pay cuflom| 
and the otl\cr fur thofc which do not pay. 

importing Guo(U\ 

When goodti are to bo Ittndcd from any fliip orrived, th4 
ontry-book of the Cutlom Hpufc ntnft be fearchcd, to And 
tlic namci of the flnp nntl the cuptAiii, as ulfo the waitera 
;hat arc to attend tlvc landing of tlic guod«| &c. 

TIkf I'hnn of a Dill </ Kfi^ry inuanis. 
In the Maria, Captain Tbomni Jones, from Jamiica. 

Fifty hogfl)ea<l» of fugar. 

']Pwenty bags of cotton. 
1 Forty 



O// 4- Wliot ihifc u ia aJtovtiKe iiiidc for Urc, tint, 

X*it. After ibe tire Rui) uifi ire dcduOcd m bcfan^ 
(bridt iht mnainder or ImkIc bj' i69. >nd ibc quotient t* 
tbecM I ifacn (uKraa iIk [lolT (mm (be fitttle, ud tbt 
fdHlodtf It thr fiMi w(t|t»r. 

Msfm^ A. Wh» it the ncit *c^b( of tybhdi. of u4iK0a« 
wti|libi| nocwu ttpu toib, ffKiU, tut i4lb.pcf cwt. tfctt 
mimiant 

Cm. ^/. tf> 

For i4lb.pKrpn*Utc,iliviikb]r 8)140 • M graft ^^^ 

tj » q urc ^^n 

■6)i>] o ir ^^H 

4 t ■ ; trett ^^™ 

i69)T7ft I 14 fnttle ^' 

H7 ■ »o mtlnctglit. 



) 



^•. ;. What ii the nine of {Bhhdi. of fitfar, each Ud. 
wri(htn)[ 6twt. icir. giofi, ir t [;ulnn uiilaluir perewr. 
urtBlti. jiriiwt.ireiiunc) ctuff «i ufu.1l ^—A/.joji. 141.7!'/. 



Commiffiunf Brokerage, and Infurance. 

C*mmfi»it )* an allowance of a ccrtiiin fum per cent, to an 
•fern atirond, tor bityinji or ttlling gooda for hii pnncipil' 

Brtktr«g* ii an allitwance to a broker for affidin); a perAm 
h procuring or ditpitliiig of gniKia, at auAxinecn, OocL- 
brohert, lie. And the allowance il gcocndlf at a tcruiB 
rale per cent. 

h/uranci ti a premium at fo much per ccnr. given to 
cenaiii oflice* or in<iiviiluali who engage tn m^ke good ibe 
lofi of any (Itip or meichandile, which raty baf>pcD from 
ftormi, hrc, &c.bc, 

RuU. Qiicflion^ concerning thefe rulci arc refolved in the 

funt manoer ai lUote in Ample iniereft, \\t, by muIiiplyiDg 

5 Ibt 



OF MSMBAvn MsBoammu 90$ 






the priacipal fuoi bf tbe nste per otnt. and dhrkkR^ tiie 

produ^ by lOQ. 

Exampu I. Havanicb b^ooaEuiuifiaoaf 5402. 1AS.WL 

at 4| per ceDt. ? 

£. s. /. 

f40 IS 6 p r i n cip al 
4i fate per 



Sl6s JO o 

•70 6 3 
i,oo)»4,3S 16 3 



1100)6.56 
\% 

XfOo)6,75 

4 

ifQo)jtOa Jmfmer 14! 6f. 6|<^ 

i^. s. What it the oommiffioo of 1059/!. i6i. io/> at sj 
per ceDt* } '^Jmfmer %'jfm \ht. iii. 

j^.j. What if tbe brokerage oTgoodifiiki to the aaaaopt 
of loi 7/. $/• 8Jl at 1} per cent* }'^Aufwer i^^^JL 

^•4. What is the iafurance of a fliip and her cargo, valued 
9^17863^ i8i.9^. at J 7f percent.?— w^^MT 3193/. 3ff.6|^ 



SECT. XXL 

rKECEDEMTS OP KECEIPTS, PROMISSORT KOTESy 
BILL6 OP EXCHAVOB, BILLS OP OiEBT, BILLS OT 
1.ADIRG, BILLS OP PARCELS, &C. WITH THE tAWS 
OeKCSRlfUIG TBBM. 

£i/2f of Parcels. 

It is nfoal in ibme caies for (hopkeepert to ddircr to tfaetr 
caflomers a bill of the articlet fold them, with the total value 
^aft op at the bottom; thefe arecaUedUUtafparDek* 

Qj) a A Limen-^ 



SL 



o» MtmcffAUTi Aetnvtin, 



Citfie 4. Whin 4b«l-« ii in iilkrwim:« itiMie for tare, tiett, 
unci tl(iir« 

Jf«i>. Afk«r (he fure imd trttt «re deduOfd at beforeri 
<1)v)(1f th« rpftittlhdcr fif ftittte hy i60| ikmI the (jtiotlcht li 
the clof I (heti ftiiitra^ ttt0 rloff from the fiitde, iinH the 
rirftwittdef li the ftett weight. 

KnifinfU tit Whit )» the nett we)ght of t^hhdft. fif \h\mtn^ 

weighing i4€K:Wt.ftqr».Bolb.grc/li| tare I4lh«|iercwt. trMt 

«• before f 

CMtf« ijfh tit 
Vor 1 4lbi |Nrr ewt« tdfei divide by (I) f 40 % %o grofe 

• 7 » fj terfl 

e6;iej o n 

4 i e { trctt 

168) fti f 14 fiittf^ 
e ft* 



*!«■•«■*- 




M fiettwet|bf< 



4t^f ;• Whet If (be v«ltie trf" jUhhdtfi rtf fbgiir, ejith hhd« 
Iriflghiflg 6t:Wt« ti|f. griWi, «t e gttltipii »itid e b«tf per t¥fU 
Htit fib. |ier twt. ired end ditff e» tiAt aI ^'»- /^iv/ $o{/. 1 41.7 }//. 



iUimmiffimi^ Ihoheragef ami /rifutftrirp. 

V9mm{fi§H Id Art ftllowfttire of a rrrtMifi ftitn |^r ( rrtt. t<> en 
•geht iibriindi lor buying or fellhig good^ for hln |fnnr f|Ml. 

tlr§kfrt$^0 M en »)l«iWeftte to • broker for nfDOlo)/ e |irrfon 
In firiN^ifrirtg or 4lUfiolJrig of g^NHki •• eiiAloneertf il#Ak« 
l»rolieri« lie;. And tlie fillowem e )i gettemlly et 11 rcrln^n 
riite tM*r cent. 

infur^Mrf In fl |irfnthfm nt fo miirh fjer rrnf. giv^'fi t*> 
certflin ofticed or indiiriduall who ctigfl^^e to tntitto p^tu\ fli^ 
lofi of Any fli)p or iT}fichand)le» which niay hii|vprn frofu 
flormn, f)re, Hir. jkc^ 

/f*/^. fiifc/lkm^toticef fling thefe ride« «rf r^f^lvrd In the 
ieme meitiicr a» titoie In Ami^le IntereAi vli« by ttinliiptytng 

J till 



or MxncHAirrt AGOMiiTt. 305 

the prlnclpdl fum by the rate per cent, and <IWMln| the 

prodii^ hy too. 

K^ff^ t* How much li the commlflion of {40/* tii% M 

At 4| per cent, f 

£* u / 
540 ti 6 princlptlftim 

4J rate per cetttt oommUBoa 

ei6e 10 
170 6 ^ 

t|Oo)a4,^ to 3 
eo 

t|0o)0,j6 
t|<»)V7S 

i^%t% What 11 the commtffion of 10 $9/. t6i. to/, at i| 
per centt f—s«if^^W^r ay, i6f. 1 1</. 

j(fr. J. What U the brokerage of gnoda foki to the amount 
of 1017/% %u M at 1 1 per cent, ^— ^^ff/nurr t$/. ji. e/% 

J^% 4. What It the inAtmnce of a (hip and her cargtt. vaUied 
•U7863A tBi.y/. at ly^pcr cent»?^if<|/^rjt93/«3#.6|«/« 



SECT. XXI. 
^i^RCiDRNTa or RwrKti^ra, rnoMinsonr NOTiiep 

niXAM or KXCHAB9UK, fitt.t.S Or IMtltTi AtLLS Of 

uotNo, ntt.t.a OP r4uciaS| &c. with tum law* 

Bilk of Ptttcelu 

Ir ii nfual In fomc calei for nifipkeepem to deliver to their 
CUftotneri a bill \)( the ai ticlct fold thetiH with the totdl value 
(Aft up at the bottom 1 thefe are called bklli of parceia. 

Qj^ a A LiniH^ 



3o6 0F wnxMKiKTi JMCWfm* 



A Lbm^draptr^s Bitt. 


s 


Mr.Franciti Mairh lo, 1803. 




Bought of John Green. 




/. J. 


/• '• 


A 


t J yards of dowlalii at i 6 


per yd. 1 17 


6 


30 yarril of diapar •- i 6 


do. a 5 





ao yards of Holland — 56 


do. s 10 





40 jrards of Irifli cloth — i 6 


do. $ 





to yards of muflin — 70 


do. 3 to 





{ yards of cambric — la 


do. 3 





to yards of printed cotton a 6 


do. a to 







jf»3 >• 


6 


jI f^9oUm^draper*f BUI. 




Mr. Wm* Smith, March ta, 1803. 




Bought of Henry Jones. 




/. d. 


/• /. 


Jl 


tyyOTdfofintferge at 40 


peryd. j • 





18 yards of drugget — 80 


do. 7 4 





f J yards of fuptrftne fcartet i 6 


do. t ft 


6 


ff6 yards of fuper black cloth t8 


do. 14 8 





a { yards of (halloon — a 


do. a 10 





1 7 yards uf drab — 180 


do. IS ^ 







U^^ 


6 


A Ho/hr's Bill. 






Mr. HolmeSi 


March 14, 1803. 


» 


Bouglu of James Richards. 




i. </• 


if*«- 


/■ 


16 pair of worfted (lockings at 6 6 


per pair j 4 




16 pair of do. — ^ g 


do. a 10 




6 pair of bUck fillc do. ..» 14 q 


do. 4 4 


• 


la pair or black worlled do. «^ 6 


do. 3 la 




8 pair of cotton do. — 80 


do. 3 4 


4 


4 yards uf hne flannel — i 8 


per yd. 6 


1 




^19 t 


4 



Received of Mr.Wiiliam Moqpiri. Uiis ^. of 
X S03, fix pounds, for one quartef V rent, due si 
laHy for my mafler, Roben Kerr. Per 

2^6 o^ Maci^arJ Htmih 



Received, Fei>nttr>* loth, 1B03, of Mr. batuuel VVil 
twenty-nine pottnds fix fliiliio^, in part of a bi!I of fijuy 
pounds, due the 3d of May next, to M;. Joun Leu ii;. Fer 
-^^j;^ g ^ Nicholas Mamfis/. 

A Receipt on the Back of a Bill of Loiciuuige. 

March ifl, 1803. Received <he fuiJ cooceou €»£ Uie wiibin 
aieotioned, beifig 500 pieces of cigf:it. Ftr 

500 pieces i 7^^^ ^ ilfim* 

PROMISSORY NOTES. 

I promife to paty to Mr. £dward Brovrn, or order, tbe fum 
of fijciy puunds on the «9tb of this infant March* Witods 
B3/ band'this 6th day of March iSo^» 

^60 o o" Edwarii jf^ms^ 

March loth, iSoj- 
I promjfc to pay to the Honourable the liafl laciia Com- 
pany, or bearer, upon demand, two hxLixdi^d pouiacii, i</r 
JBdward Williams. 

£%r^o o o //<'/»C>' ^^^^^'^ 

March i«th, iS<>3- 
I promife to pay to Mr. Jofcph fixx>wa, or ordcij live Oioutto 
r date, ten pounds ten fliiliin^s, for value rcc«iv4xf. 
^10 10 o H^illiaM JUl^** 

March 14^^^ '^^'' 
I promife to pay to Mcffrs. John Edwa/db .'H*<i ^ '"• ^ 
rer, the fum of twcnt>- poimdj ten fijiihn^i, ^t- cJerji:«ii<i- 
£*o 10 o je<;^^/ / AUrf^"' 



Jiff or M%Mtl^nf§ A«anfivti»# 







pm^nAti Mfi (billm^ff for Mt Mi4 fiftfifh^nyi Var 



I*. MiMi^y, M^lifrrh \f*mh'U, Mu\ nfl/Hvr/l Ih^m f,^ UhA-inn 
I Uy it^^U^\ Ihi flt^ Mr^ ^r IhoifiM < :«i«i Jt<i|, hy vlrltMi *rf 



f<«^«(v«4 




1lfci^tv«dof Mr.WilHiim Mtn^Ani ihiifth of Ptbrunry 
i%oj« (In pouR(i«« for ()nf qunrttrN vtn% Am it Chrtftnu 
I4A1 ft^mf m^Aert Roh«rt Kttir« Wr 

K««t^iv<H^ F«bm(kry ipth, iHoj, uf Mr. Sumvirl Wilkliitoni 
tw^ty«n)nf poumii (ix ihiUlni^t, in |>«ii of m bill of (ix(y 
|HHind^ tluo the 3(1 of Ma/ ncxti lo Mi .John \xwW r<r 



A Rnwpi i^h ihp Gavk ^/'<t UiU ^' J^jriAiu^. 

Mirth tft| iSov Re\^ivrd ihc foil conrtiiU of th« wIthUi 
iR«nYion«»d« Iveing {oo pi«c«» ol' t\ghu IVr 

PR0MIS80RY NOTBSU 

I pr<mtife to (My to Mr. Kdwnrd RrowiH or orttffi th« Aim 
«f fixfy poimds on thr it)th of thU tnftint Mmh. Witntft 
my luind^hU 6th d^y of Mitvh i8oj. 

^og o o KA^Mfr*/ 7«*'^'' 

M^ivh luth, iKoj. 
I |)romif<i> to (Viy to the Hono\iti^bl» t\w Knit lotlU Com* 
|^i>yi or Wiiitr, upt^t iltiDnnii, two huiitltril ih>uiuIs loc 
JWward W«lumt. 

I promife to pny to Mr. JoA^ph Omwni or onki, tivc u^oiub* 
^'Wr ihxt^ trn iHiuhiin (cii lhU)tt^«> ioi' VAlue »rc«iv^U 

;^So IQ O WV//MI4V iiW^i^ 

I promtfo to piy to MHtV*. John Kvlwni^U mi\ (X or 
^tfr, tN turn of twruty [n>\\\\iU t«o flulDngii on tlr n^nnd. 

.1 \#># 



yto or mwcj uwi icotmwn* 

A Noi§ from two to 0910. 
We or tUher of ut promifo to pay 10 Mr. Robt ri ScoImi or 
hit oid«r» on demand, rwclvc pouiidi ua (blllifigit for v«lit« 
rccirivrd, Wiinrli our tuiiidft 



tm^fm 



/ tt fO o 

BILU OF EXCH/INOE. 

^ J3i// payo(»b 0/ Sight. 

LotuUttu March (fhi i8o3« 
At fight hereof pay Mr. Robert Windi, or hU order, the 
Aim of cwenry»fire puundi, for value rceeived of Edward 
Millft, end place it to account^ ai per advice from 

To Mr. John Willu, Youi humble iervaot# 

Merchant, High btrett, UriOol. 7#/w MiiUr. 

Dovtr, March 13, ito^. 
Ten d«y« afrer fight lirrenf pjiy to Mr. ThoiiMi TruA, or 
bif order, fifty poundi ten fliillingii iiiid place it to accouiK, 
at per advice from 

To Mr. John Francii, Your bumbU iervani. 

Linen -drjijicr, ChcA\tfidc, Umdou, iiiwy HtiL 

torti^n Bills oJlUihungv, 

i^ndon, Martt}6, 1804, for 544* crown:, 
Mi ^*^\ti» llftrling \Ki i^nmiu 
At \\(m\cc* \iAy (liib my fiill lull of rKcltaii|{« (my Iccond 4 
mul thiitl fiot U-ih^ ytx [tM) unto MvAUuvy Ur«>wn, or a 
ortjrr, five Ituntlitfd mul lony nowiik, aX (^{«/. |>ct ciowm^ . 
for the value rirccivrd here ol Mr. Muurd Wllli| and piaLi^ 
it to account, as prr advice fi oni 
Ti» Mr. John luiwardu, Your humble fcrv^u' 

Men liHiit in Andicidttni. yjjn '/t$mtt» 



* tifrtfirr liitiwt^ii IliigUml aiiil Kuniu , m I.ii^UikI mtil |{i*IUt*W, 

n»«4iilli«i briWMcn HheUi..! 4im1 luly, il.i'. lU'ii.Oit: ^ »ii«l ^»c=«m 
Kl»|^ii|(4 mul 'luikey, toui llliilii|»», Ait . 



br MBiottAiiTi JMonftn. 311 



Nupleti March it| 18031 for 6401% loi. 
At tbnt uikneea pay ttiia my flrft bill of exchaii|0| wto 
Mi\ John Stockii or m^er, fix humired and forty poundi tta 
flilUiagi 4irtin|^ ibr value rtceived of himfelfi and placo k 
to account, aa per advico Atmi 

To Meflh. Baitly and Edwardii Your humble ibrtaa^ 

Merchanta in London. yt$Jkit 8mitk 

Liverpoo1» March 141 1803, for 6000 piecea 
of eights at S3{4^« per pkce* 
Al dooblo uiance pay thia my fourth bill of exchan|e^ 
iMito llTt John JervUi or order, fix thoufiuid piecea of eighti 
Mexico^ at-5344^. fterling per pieoe, for value received of Mr* 
Jofeph Munti and place it to aocounti aa per advice from 
To Mr* Matthew Marlh, Your humble lervaiu, 

MofchaBt in Leghorn. Htmy E4kimr4lu 

ABillo/Ddi. 

Xmm mK mm fy tiffi pt^tnu^ that I John Britoui of 

Londoo» merchant, do owe aud am indebted Mnto Henry 

Hqfoeai of Southwark, falter, in the fum of four hundred and 

for^*«nioe pounds, of lawful money of Great Britain \ which 

Aid fum I do hereby promifc to pay unto the laid Henry 

Haynei, hia heira, executors, adminitlratora, and aliignt, on 

Or before the twcnty*fourth day of September next cnfuiug 

^He date hereof, Witnefa Oky hand and iVal, thin fourteenth 

^mj of March 1803. 7«A« Brittt^ (j a). 

Sealed and delivered 1 WiUimm Smith. 
%Xk the prcknce of ua, J JUmms Hmri/M% 

A Bond, 

tCmw mil mtm ty ihifi frt/tttts, that I John Drew, of the 

l3i«iri(bof St.Gilci, «n the county of Miiidlcfcx, carpenter, 

^m held and firmly bound to Samuel Price, of the city of 

NVeftminftcr, in the county aforefaiu, vintner, in the fum of 

ti«» hundrad poOndt, of good and lawful money of Great 

^ritalot to be paid to the laid Samuel Fricoi or to hia certain 

Voi.L Rr attorney 



3U 



or »f«iciiA)n-» AccouwT*. 



wattKMA la II (pwifyinx ■ fwnw^ debt bctweco tbe pwtb% 
yet tht rec«ipi ftudt m a rtcdpt lii full. 



fy Pnm\S^^ Halt}, tfiuf JIt/Ji. 

A ptiMllMliry mxr !■ art encaKCRKnl foi' ■ fum oT nworj 
la be pMi) «i a cciuiii ikiiii, ot <ifi ilcitiaivJ i when (he (urn 
It ill b« |MiJ on dcDuud, (> u 'tiM (I'clciiflr, and thrre iK«iii 
imaCluil (kuiaoil, bum U otheiwtfe oliirg (be MiM^r il 
Id tx |UMl la • ihtrti pcilon, w wbcic iticre » a pmalty, to 
la ibM caii itia*r muCl U • dtmaiMl. 

A l»lt n a Angk UmhJ, whImuI auy raniliikn. 11 ■ iKffoQ 
Mluumlfdjto liiri>r<1f lnt]rt>i<;ili(iiinuiiier bjrbtUbiflK {um 
M Aftj pouMti, aiwl tif tbc Tanic iiili UmL hliMi hmI bll 
li(H« liir tlir piyiMHt 1(1 ilw Lid l>iin, iii > hiMlitd pamdi^ 
wtibPHi I'llcnioiE llir |>cr(<in'« name In t^hom be to bonad la 
tlM pcnilijF. i( lluU •wvxihrlcfi be Ukcn u a bond ^aiall 
him (iff Ilw faitl TiHu ami pcMliy. 

J(.i itHii iMi jIjIII i)>. Ic «■.,-.(*: IJo fv't «,i f,mif4 

,.,.„,. Ail , J ;■■-.>, ,h> p..,...,.„ W,,,,-./ tb.ni.ujdf 
,,• (; />,!■■•.- (.i.oll,,, |,cll. r,,, J, I m. 1- .( i-...^,.! lull liy llK 



I" 



II ,11 !.)» Ill,, Ijill, //,,/ / ,Ui h.,.l r,.r<i;,larcn 

,t III.' I, III hf, / lh.,H ,.,<■, /,, CD lU. ; uv .1 it (,.-. I, ml, 
(:Hi<>l.i„ I; i..„./,„,l-,.- „i, I Ik,.I«/- C n I-jI. tff,.;l> 
I., ,,p.,ul l;m .•■a:;; <„, / .1H h. h.n.l myjclt u. CJ}, lUl U 

ll.ill ,r./:i-t iitl. — ciit.i-i III rliric )ilii:<ltk Ijinda ilic drawer 
ol th,' hill, :ii>d<i>iil1iiutc3 ;, ^<i.><1 l,j||. 



Of ISi/l.uf i:.ni<. 

r 'x.luriKc „ :, vi'MtiiiK ,.i 
»t..i n..,Ncj', :i,„| hj. (lit-,. 



kTti ;i(iioiig nK^R'hinli 
cilii oJ iliu ijrawcr ijc- 



OF MBlCHANTa ACCOUNTS. 




thein, or each or cither of their heirii execucon, adminitm- 
ton» or alBgniy fhaJl well and truly pay, or caufe to he paid 
unto the above-named Thomai Smith, hit executon, admi- 
niftrators, or afligns, the fun) of one thoufand poundi, of 
lawful money of Great Britain, on or before the twenty-fifth 
day of December next enfuing the dare hereof, then thii obln 
gation to be void, otherwife to remain in full force and virtue. 

A Penal BiU. 

KnmumUmiM h thtfa preffnts^ that I Andrew Jonei, of the 
borough of Southwark, do owe unto Edward Mills, of the 
parifh of St. Clement Danes, Weftminder^ the fiim of one 
hundred pounds, of lawful money of Great Britain, to be 
paid unto the faid Edward Mills, his executors, adminiftra- 
tort, or affigns, on or before the fifth day of November next 
enfuing the date hereof, for which payment well and truly 
to be made, 1 do hereby bind myfelf, my heirs, executors, 
adminiftrators, or aifigns, to the faid Edward. Mills, his exe-% 
cutors, adminiftrators, or aiTigus, in two hundred pounds, 
of like lawful money of Great Britain, firmly by thefe pre- 
ientt. In witnei's whereof, Ace. 

Andrtw J$nity ( A j ) . 

Of Receipts. 

A receipt is a difchargc for money owing, and is a bar to 
^11 fuits in law and equity. When given itt/ifli 9f^ll demaHtit^ 
it difcharges ail debts between the two parties prior to tlu: 
^te thereof. 

If a receipt be given, it is good, though no money be 
paid, except it be obtained by fraud, iu which cAfo relief 
Uiay be had in cijuity. 

A fcrvnnt may give a receipt in his own name for his 
mafter, if he be acciiftomcd to receive or pay nwncy for his 
mafter*s ui'c, or a wife may give a receipt for her hulband 
in her o'.vn oanoe, and it is equally valid. 

Rr a If 



P4 



M Mnnm^nrn k€^/^Mfi^i 



0/ Vtmt^ljyy N^tn^ and MIm. 

t4* \ff ^f»U\ i(* tk Ihn^ pciUifu ^f trhf^ff tlnnd ft n- p4^hk^iff far 
iti fUtti tnUf ih0ff mull U n ti^tf}nn4, 

t^kiHtwkiifjF'it UimU)i UiMtU>:(\ lo t^tP4hrt try Ml ifi ihf^ ii$m 
hi Mif p$ni4nkf utH) iff ih^ Un*i^ \nh MA^ htmUtU «M bl# 
Ii6)m tot fiff p^ytmni of i\u5 tf*u\ (ntp* ih ft Mwlr^A ^rMA4#| 

tl^ f«;f lh<« (4^ t\tm <iri4l t^ftftlfy. 

ip j'ti^ In /I // '/.t hfi , J Of I hit puftftpvl f^^hptfinf I ItinA rtf/pif 
tit {', t^^^'^i, (>ii}ftfhft I'fti'-ft/, yft fht^ f« R ^ftf'f\ K»»l \f/ rM 

//'/• fhm 1$l I'fFfth l'fif*fnfti hnltn/i I lifnt'tifp ht h ty tff t^ t'' , M 
tf Hi*- h>ll }tP^ / //W/ /,fiy tn t; h i»/,/, , M i) If 1,"^ //>'/,# /« 

/'P ippnhl him ti^Hht ^ /if* / //// ,ln hind of/ltlf In f'h^ ll'(t9 Pi* 

0/ /////^ /// irnhiniuti. 



or MVVCRANTft ACCOITNTt. 315 

ticrMy paiTes m money 1 thrfc billt mt ilr^wn fomctliiMt 

|>siyi«bk' At figlui loinrtimfi At a certAiu timr. An inUnd bill 

of cxchADip" it nf tho nniure of a letter, And is dr^wn by out 

nicrthAnt up<M\ Another in the lAme conntryy At, I7 AB of 

Brilhil i4>on C I) of London ; but a fi>ivign bill of cxchAngo 

it ilrAwn by a men hAnt of one country u|>on a mcaliAnt of 

Another country. Thefe forcinn bilU Arr of more confc« 

q\)rncc in the eye of the Iaw ; a foreign bill t>eing refufcd 

to \yc Acrepteili An ai^\um niAy Ik hAd Agninft the drAwer« And 

every )>erf(m who indorfei a foreign bill becomei Tmble to 

the ^^AVinent a* If he were the drawer, iKCAufe every indorfts 

ment it in the nuttire oC a new bill ( but the indorfer ii not 

liAble to pAy if the drawer cau N foinul t but if the drdwer^A 

hattd cAnnot be proved, the Acceptor nmy ctm^r u|>on the Uft 

<ndotter% If m \k\\\\\\ only fij^tw hi* uAme ai the luck of the 

bill, the Acceptor of the bill inAvfill up the indor(cment| or 

the IvAre figtiAturc will |>Atk in Iaw for An indorfen^etu. 

There \t a n)nteri.4l diifeiTuce iKtween a bill ot exclmnge 
psiyAbie to a |)e\fon 4»r h^rtt\ mA one pAyuble to » (>erlon #r 
•rnifr, A WU pAVrtblc to « iicrlon or l>caicr U not nllij^nablei 
few tt> enable the mvcpior to biin^j Mt^ ai*)ion \l the dumcr 
rcfufw pM'mcnt. \\\ a bill prtvuhlc to A M oi' hcntr, the 
acceptor wyAV fue in the name ot hint to whom it \% iWAilct 
pavfthlc. If A \m\\\V bill |>Ay,ible to AH or bearer he lol>, 
<ttul h>iind by 4 lb;u>^r, pMymcni to the (li^u^cr will 
"^^rmnity the HAuk, yet A H nwy hAvc aw «ohon of lro>-er 
^g<^inU the lindcr, but not A|{Ain(t Any pci ton (o whom the 
S^dcr hA« juul It liu' vrthmbic conliilrnuion, — A hill of ex- 
^Wge p.iy;<blc to a perfon or onlcr m;n' hIwwv* be n(rij*ned| 
*rtd the Acceptor c«u brinj( hi* AO\ion in hl.iown immc. A 
l^ill payablr \o or\ier in wiihin the culVom of mc^hanl•, a|uI 
»«»y he uej^otlrtled Aiul rtflij^ncd hy curt«un. 

If A peUon accept* a bill, thoujjh the date of payment \\ct 
|»ft, he cann«>t return it, but he may brin|t *» acU<ui tor 
il)f moncv, if the bill be trndcicd in time. 
A fervMitt CADnot accept a hill for hU niAftcr, cxcrpt ihrra 

bo 



jtl or uBBriiiiii'n ArcovRTi; 

A t»-f.d mij be Kwid itioMKh ti (ofiMim Wfe L*io, or I 
Mh Lii|ilt(h, iir ihnuith It Ik of ■ (h>'>Mul mKrptttaUoa* 
■«, il A bmit biHiMI bi B m jmj t font of moMT' u A 
f wbcfvM K flwulJ be in B>, hrri: llw oblifxtina (t good, anJ 
iIm J*ivrmJ»m tmd. II a bond l<e ininliAn) in ■ flmx Ml 
nuiciiil, 11 •ill no- hitn ihe band . bui il it be in 1 nairrW 
IMfi, it ■ill nuke ihr bfifitl rind. In fbon, ill bondi, oU>f»- 
llont, bl'U, fntiiittthj nmtt, tec when in^dovbt tntct, 
vc aitrajr* •nHrpnWd In fi* our of the patty to wbom ihc 
nmamy fa mm. 

Thefe wc the (Kindpal le{«l prcfcdcnti trfcd hj mercxntile 
RWa, to wliiiti I dull n^d ■ power ix letier of MlMncf, ■ 
bcinjc tn iimII gcMnl uic \tj *lt ikitiijxion* of pcapfet 



«l Letler ^ jtltonuy from oiu, or ficw, to jWfi!( 
Mtottnh and raaivt * 



) 



JCmw »8mnh tbtfi frtfinn, that I Ed«nl Slokcf, of the 

{Mrilh o- SI. Am»ii-w, lI'.llwfM, l^n.loi;, HiifiMUi. f-.r F^K^ird 
.Siiiitli .;;i.l I'.i.ii l-it... '., ii|.li',lDM('i^,<ifll.';p:iI,(llof'}t. Luke, 
Mi.lill' Im ] I1..V' ri]4<!r, uri'^ii III, loiilliliilcd, and 3i)]x.]i.Ii:d, 
Ri.ii ill. h) tl.'li- |,irl<iiL', ii^ik.', i.icbiii, c'lirni.iitc, arnl^iv 
J.O,. 1 11.) Iiiujil Hi ill > I;m.,iii, ot ilic jwridi ol' lit. Jatiici, 
t:,tikt.r.-.r], III ilir l,ij,| ,-ninty cf MiU.llcfcX, watd.fliakcr, 

III)' |"r 1 rrn' :irnl l^iiful artnijuy fur me, in my name, 

Bnil"tiitiy1'i:irilJ [lj I<» 11:., iii.hii djiIio.^ihI on rjiir bclmlf], 
to :i<;,iifl ..inl fen I- uil a.i.l <-vi ry -.,, > .loiii :.ri.| a-xoii/.t. wafi ill 
aii'irv.rypirl. ii :iri - j.tiloiTi, 'a , li wlj„iii J [r,i wt] j.jvt lad, 
VI ili.iM (11 ti.ay h.ivt imy ii:.ii..ii'li'vii ui iltJiIiiigs w*.itfocvtf, 

fiii'l I ii>|>:oii.ili, :.'.',iii-, and .l<[crii,iiie all (lir|>iilci and 

ilill.irii'.tiji.,l l,JV(..,r fli.illai::. lu'Wr.,: IMC [<Ji Utjuivl^nf 

Olli'i (,.(,oii or ijiiIliib wi .(iMrvtr, aiil I" cxcmlt all I'lJl 

tici ,,, ii,f-nj,„Mii-,aii.l«iiiiii;;sii'.lit tli<:f.,id Ikmy BrnM 
(li ,:l jil<l,;i: ii.xfiraiy, and lo alk, (Inn .lid, Inc for, icuivcr, *iiJ 
rULiVC, lu Jiid tor jjiy [01 uiii ] ult, ol and ttuiii all olid e^er]' 



or mkhciiantii aocountsi jif 

it it nut giwii tliua 4 coiulition m^t to ufc « trndoi till or 
low giouitd, 6ic. i« uuhuvhil, being aguini) (he public goodi 
and tlicrcfore vDJii. \\ hen a Uoui dcpeiuli iipoii a licediand 
the deed btcomcn void, the bond i« void alio ; a coiulitm 
to indemnify u perlon tVom any legal piofeoutioii it vok^ 
being aguinil L\\ . Coiiilitionn of bond* are to be not oaly 
lawfuli but |)i>flible : if no time ii limited in a bond for paj^ 
ment of money* it is due piefcntly, and payable on demainL 
In a bond where icvti ul |)ei'lon« arc bound fn»trmiiY% the 
obligee hati his option, cither to liie ull the boi\dmen together* 
or all of them apuit, and have feveral judgntenti and cKecu- 
tion«, but he can have fatiifuAion but once ; but if a bond 
be made to three to |iay money to one of themi they muft 
all join in the action. An heir ia not bound by a bi)nd, 
unlef« he be exprcllly namedi but the adminiftratori and 
executon are. 

A bond may be made from one to any number of iierfoni, 
or from any nmnbn of perfons to one. If the furnante only 
of the drawer l>e fnhfcril)ed, it it fytKcient, though tlu:re he 
a blank for his C'hrtlHan name. U a bond h;M no date^ or a 
laHe date, or an im)K)lIil)le date (ua the thiiiirtU CiAy of 
February), yet if it be fcalcd and delivered it ii gtH>d ; a 
perfon cannot be charged by a l>oad without delivery of the 
bond to a creditor. 

Where a lx)nd is made for the payment of a fum of money 
by inftalmcnt!), the hoKler of the lM)nd in fome cutci may 
conte u|)on the drawer for failure of the fir it payment, but 
in other cafes hr cannot fue for the nu>ney till the lall p;»y. 
ment Kvomes due: ua lor inl\;uu'c>, it A givcii a bond to U 
to pay Ao/. in the folKtwin^ mani\er : >iz. lu/. to lu* paid at 
a certain davt ami to/. a\ another certain day ; in this cale D 
cannot fue for the cUbt till the lall jmyment lH\(>ineii due, at 
the ao/. is n)(f ntionod as an entire debt ; but if it tte expreilcil 
to pay lo/. at a certain day, and lo/. at another certain day, 
making in all tol. the ci editor may fue upon the bond o\\ 
failure of the fiv^ payment. 

A bond 



aiS OP M1l1l€HANTS ACCOVflTfl; 

L_ i ' . ' ,.. ., .LI.. 

A bond may be good Chough it containi falfe Latin, or 
fdlfe Enj^ifli, or though it be of a doubtful interprctatioUf 
as, if A bindi bhnfelf to B to pay a Aim of moiicy to A 
<whcrrai tt fliould be to D;, here the obligafion U gornf, nnd 
the fihtHdum void. It a Ixmd be interlined in a pl.K c not 
matcriat, it wil( no^ hurt the bond ; but if it f>c in a material 
party it will maicc the Ixind void. In (bort, all bonds, obliga- 
lion»9 biiliy promiflbry notei* 6cc. when any doubt -arifc*!, 
•re always interpreted in favour of the party to whom the 
money i» (iue. 

Thefe are the principal Icgnl precedents ufed by mercnntile 
men, to which I ftiall add a power or letter of attorney, at 
being in nioft general ufc by all defcriptioni of people. 



td Lciier of jlliorney from one^ or two, to JettU 
Accounii and receive MoTiey. 

Kfipnv ail men hy ihrfi pre/ents^ x\\?x I Edward Stokef, of the 
parith of St. Andrew, Uolbcrn, London, chinaman [r>r Edward 
Smith nnd jolin |;uiii<!, npliolflcrcf'Rjof the p;iiifli of St. Luke, 
^1ii|(llo(rxJ h^ivc nifidr, onl.iincd, conllitutcd, i\\n\ np|K/ititcd, 
aiul do hy the /if* \i\vU:ul% tn^kr, ordnin, confliintr, and ap- 
point my Iriciid llcriiy linmn, of tlio pniifli ofSt-Jamc]!, 
Cicrkctiwrll, in the fnid connty of Middlrfcx, watchmaker, 
ipy [or our) true and Uwfnl artornry for me, in my name, 
and (m my hcfrilf ( oi Un us, in our names, and on ruir behalf], 
to a<ljiifi and fcttlr ail arxl rvf ry a( count aud arcounrji with all 
and cvrry pcrf* n an i pcilou*, wi.h whom I [oi wt] oavc had, 
or fliall or may have any tianiai'tiooi or <!caling«j \^atf</cver, 
and to romptomifk', 'i\nrrj and drtrrniioc all difputm and 
diff* rrnrt g \\\A have oi (liall ai lie hetwri n inr [or \n ] and .injT 
othrr |Hf (on or prrfcns wiiondoevcr, ar;d to execute all I'lth 
drMi% infirumrntR, and wiitin;;'!, as he the faid Iktny Hrown 
fl) dl jnd^c ntcc/rary, and to afk. demand, fuc for, icc.ovcr, «ind 
rcctivci to and for my [or our] ufc, of and liom all and every 

3 per Ion 



« 



OF MfiRCHAIfTa ACCOUNTS. 319 




niA)' become indebttd to me [of In]' bf^inif9^^\ 
whatfoever, nil aM \tv\rry the debt and debN^ fiim»indftNha 
of money by them refpeAivrl;)* due alltf^winfy indltilvfth 
pound fi)r any fuch dcb( or debti, and to take itft iIihMm 
whofc For the fame, or othert^*ite to adjuft and fcftit the famt 
in foch manner and upon Inch termi at he thefaltdHemy 
Bn>wn flull in hit ditaetUm think fit; and t^ nott*pil)niient 
thereof, or of «ny part thereof, to take Tnch rourfe fer reroeer* 
in^ the fame as to my [or our] faid attorney (hall fee m meet t 
anil upon receipt of the faid debt or debts, fum or fuitis of 
inonty rffprrtively, or any part thereof, acquittanees or ether 
fufficient dilchitrgrs for me, and in iqjr name [or for ut| in 
our namc^], or in his own namei to make and give for what 
he (lull fo leccive, and generally to do, ne|{otiate, tranfadt^ 
and perform all fneh other ads, matters, and things, for ifiCt 
and in my behalf [or for us, and on our behalf], in and about 
the premifcs, as tuHy in every refpe^ as I [or we] might or 
could do if perfonally prcfcnt; hereby ratifying and confirm* 
ing, and agreeing fmther to ratify and confirm all and what* 
foever my [or oni ] faid attorney fliall lawfully do, or caufe 
to be done, in and abont (he faid premilcs, by virtue of thefe 
prefents. In witncfi whereof, I [or we] have hereunto fet 
my hand and feal [or our hands and feals] this twentieth da/ 
of March, in the year of our Lord iBo), and In the fortjr- 
third year of the icign of our Sovereign Lord George the 
Third, &€•♦ 

[or, Edt\Mirii Smithy (■•••) 
7#/»« /nase/,] (;. J.) 

A letter of attorney may be executed by any perfen, If of 

full age ; and a nuin may give a power of attorney to his wifo» 

- - I - - - - . . ^ .- . — >^ ^ 

• The worJi inctudcd in ciotcheti bclon| to the powtr wKca glvfii by 
Edwar^i Smith and John jAnin 1 in otltcr i^rprAt thft frtm i» iht fiMM iS 
vbtn |iven hy Edw«4 itakci. 

Vol. I. 8 a «C 



h «S(, 




CHAP. Vlf. 



Of mensuration. 



SECT. I^ 

X»F St'FKBFICIAL MEASUBC, WITH THE METHOD, OF 

1 I 
MKASCRING MASONS, BRICKLATER^^ CARPE^T^^^ 

SAWYERS, PLASTERERS, PLUMBERS, PAINTERS, AND 
GLAZIERS WORK, AND THE PRICE OP ^ACH ; ALSO 
THE PRBCB OF EACH COM^OOlTr, Al^D THE WAGES 
OP JOURKiKTMSV. 

SeFORE the Warner prooeedf to mcnfantion, it is nccef- 
fiuy ch'dt be ibould aiideritani duodecim^lii, or, a& it ::- 
pmerally called, croft iiiult«pliGat;un« 

Tbts rule if called dtiodecima.s i>r:raiife the n:tnibcr3 
decreale from the Icfr hand in a twciv^f/ld pr^poi tion ; t^.c 
firil niifnber being feet, the ^ext i giriher ;iicho, and ihc 
next namber the twelfth pant of an iuc'n, Uz, ' 

By tbii rule workmen and artificers c?lr =.p (he contni's 
of ibeir work, and omtriptj ictt^ inch^fi, an<f yznu hy i<tt, 
ii'Chei, and parts, without reducing then, to one <vrv>n-<ina- 
tioc, as in common arithrrictic. in tins rok i:/:iirs ?-- 
fimiefiroes called ^r/Wi, the parts are call dfecmuny rl-^t re 
divtfioo thirds^ &c. 

Af^ I- Ur.dcr the rau!tiplicaQd, write ?he ^orrcfp m . •• 
Heftm'nnions of the mulciptier : viz. fctt under feet, i;: 
'ndcr inches, Ice. 

S s s %, Mill. . 



». Mi(h)(i1]t c'tiy teim m ibe •■ii>1li|)lic»n<l, brj nninx *t 
ibe l'>«cfl, hy rhe fnl Pitw mult'pDer, >n<l write tbe rcfult 
of «arii antltr In nfjwAnreUiin, <ibhi»i gin emry i (of 

all hi %tm prwiMft l« (heiwrt hii(*wf din-mmitiofi. 
In ihf &■*» Bi»nn«t mnli'iily •••■7 «"" w «« rowlti- 
i hy (l« inrb**. in tkt muttiflllot, »nrt (n ih« pc^liift 
orr»rhirrm nne pl«r fiiflhw I" itit njbt l>iiiJot iJwi urm 
in ihc in<ilii)>l«ci"il. oi>fcrt<i)( m rtrry i to ihe pcst biglicr 
ilranmin*ti o (or e»»«y I* M hrhoe. 

4. PnmeJ in 'be (itne nuiuicr W'lh ihe fc<A idt, jnd tbi 
otlxr tktb'inia.iiKMi«, if ihcra be any moic, *ni uie iaia ol 
Um produft* »iU be ib« piodud rni>iireii. 

SMimfir I. HultipV Id fset 4 ImAei aid s puu bf 
7 fc« I lodM md 4 pwti. 



79 11 Q h 6 Anf-aitr. 

In thii Ciimplc the j part* ire firft multiplied by 7 feet, 
■nil the produA ii a inchei 1 ■ parii i ihcn the 4 iiichei are 
mullipUed by the f feci, ind (he prodiifl ii % feet 4 incliei; 
then the 10 feel arc multiplied by the ; Tcet, and the produA 
ia 70 feet. Then I multiply by the tJ inches, faying ( 
limci 8 ii 4O1 whiLh ii 3 twclvea and 4 over, the 4 I (et 
one pJKce funhcr toward!, the right hand than the tnul^pli- 
eand t,, and ihc 3 1 pl.ice utiilei' the Icconds ; then I mul- 
tiply ihc 4 inchci, fayiug 4 limn 8 ii 31, which ii 1 twclvM 



\ - 



•^u....^ cm. MXBfumATiQir* 




.Ju 



aad8,tlir8 1 6t mider the ptitf and the t under the inches; 
then i &j 8 timet lo is 80, which is^6 twelves and 8, the 8 
I ict under the inches, and the 6 under the feet.' In the ■ 
iaroe manner I nmltiply b3r die third and laft figure 6, faying 
6 times 5 is 30^ which is % twelves and 6* the 6 I place#oe 
iplace farther towacds the -right hand than the firft figm of 
the laft prodttd, and prpcccd in the fame manner as befixe^ 
aoi die fipn of ^ the prodnds will be the anfwer. 

I have gWen this example at fomewhat an unnece^i^ 
length, in oider to inftm^ the kamer more fully in die 
nature of the rule ; but ft is generally performed in three 
lines only, when cpniifting of feet, inches, and parts, as in 
the following example : 

Exmmfli s. Multiply 6 feet 4 inches and $ parts, by 4 feet. 
6 inches and 9 parts. 



Fc€t. 


Inches. 


Pants. 






6 


4 


5 






4 


6 


9 






*$ 


S 


8 




3 


ft 


A. 


6 







4 


9 


3 


9^ 


?£. 





5 


9 


9 



Anfvotr. 



Kctc. As the foot is divided into 12 inches, fo each inch 
is fubdivided into 12 parts, called feconds, and each fecond 
is again fubdivided into 12 thirds, and each third into 12 
fburhs, &c. 

^•$. What is the fuperficial content of a-fquare piece of 
gp:onnd« meaiuring 39 feet 10 inches and 7 parts in length, 
and ip breadth 18 feet 8 inches and 4 pans ? — /fnjkuer 74J 
feet 6 inches 10 feconds 2 thirds and 4 fourths. 

i^. 4. V\ bar is the area of a floor in Icn^^th 24 feet 10 
iocbcs 8 feconds 7 thirds and 5 fourths, and in breadth 9 feet 
4 inches and 6 feconds ? — Jn/nver 233 feet 4 inches 5 feconds 
9 thirds 6 fourths 4 filths and 6 fixihs. 

Seconds, 



JV 



or MKt'vixrxon. 



I 



SKonibi ihxdi, br. an uroaHv tnathol bjr tirn ar fhrfe 
frnn Qfokr* placed over (he RfUrc* : thm, ihc uTocr to ll)e 
..... I ■! Ill I'll iirit iitm 

taB foeliaQ M nprrocd, • ; j ics 4 ( 4 6 ^ tt 



Menfitr^ikm, in Htncrjl, ii liw art of mcaiuTui| *nd |At- 
■MliD| ibc nxjcnitkidc and diincnfioni of bodwi ur Agufc*, 
anrf u ditl4cil [innciinlly incu ihiit putti uUatl itaW^Mfr 
Jurt^ /mfrrj^^l Mt\\rt, u\A/»bJ mt^att. 



P^ft'llMi^. 



•^SH 



I. tinf^l w/rrf U flm[i)c mcafurc bitni|tli, wMmrt 
brradlh (ii d'-pth. 

•. S'.fttjiti4l midffar* tMtid&t of Icnph aad Vn<lili tnlieJi 
ngtiher. 

;). itUdrnta/uri canCfl* ftf Icnjrh, bltttlth, and depth) 
oflihiclihfrtjfK-r. 

4. A )i(iini hai nn p.irti nnr diiiienrtons, nciihcr m length 

f>.>l brr,.<lll). 

5. A Ime li i» only Icnglli, widioiit ar)y other L'tmenfiqiii. 
(>. A ii,'.)i< li«<^ I>(>,i11 ill the r,inic (liKflloii, and u the 

flioTttH iv.iy lic:wc<-ii >|v t^ii cxucniilic^. 

7. A luivi: iiiic c..niiiiu:i'Iy ih.inges iti liireftion. See 
//■'■ 

«. P,it;.lltl Unci arc alw.i/j at the fame diftance from 
r.Lih ritlitr. .'iee_/5t. '■ 

7. Oltliijiie righi liiit'i (li.inge [jieir diftnnc? and meet 
ill -111 niiRle. S.f /J^-l- 

IV. All angle ii ilicmreting of two linei. Seejf^. j. 

M. )i the two linef which fi)rm an angle be pcrpendiculv 
tet.ii-li (iihcr, ihey then foim a I'i^lil angle. Sec ^.6. 



i 



OT ji wCT i Tm >g^ jii 



• i». JtaifdirCiioIaMibcMKpcrpcMliariarte 
they form fHnc it ottei «■ cftifBc JBg(^ vl&di 
frcatrrorlc6d»Bar%facai^lc* Scc>§f*9 avi lo^ 

13. If a« aagic be kfe rfiMi >pghc gigkf '^ » nrfltJ at 
acute angle. See ;^. 7. 

14* Aa angle tlHf ii gfoner dm a ri^ angle is cabed 
ao ufatule aogle. Sce>|^*&. 

15. Atrang!e»afig«gcciw»imrrfgptkrtlg<eEac«pgHi 
has Tarioot iiaiiica» Jixuwi i pg to dK foe of it» aa^es* 

i6« An cqaiiateni triangle kas id three idea, and csak 
ieqoendjT kf three jBflea, cqad to each other* Seej^.9. 

17* Ao iMcekt triasgfc has •olj two fides eqioL Sc« 
/g'. 10. 

iS. A fadene triangfe has its three ides and an^es on* 
equal to each other. See fig. 1 1. 

19. A riglit^Mi^ed tguagfe has ooc ri^t angle* See 

ao. Ao obtiife4og!ed tnaog^ has one obtnCc angle. See 
ai« An acotr-aogled tnaogle has all its angles acute* See 

as. A figure of fnnr fides is called a quadrangle, or 3 
qoadrUaSenii figure, and is ertfaer a parailelograifi, a fquare, 
a rfaooiboid, a rhombus, a trapezium, or a trapezoid. 

23. A iqtiare is an equilateral rei^ngl::. having all i:s 
fides eqval, and all its angles right angles. See fig, 16. 

S4* A rfaombosd » aa obBqae-ang'ed parallelogram. Sec 

a5. A rhembas is ao eqeifateral figure, baring all its fides 
eqoi!, hot its ang9e5 are obHque. See Jig. 1 9. 

s6« A trapeziusB is a qtiadril^eral fi^re, but Id oppofite 
6deM are not paralcl. See^. 19. 

27. A trapezoid has 00 1 j iwo oppofire fides paralkL See 

s8. Plane figores having nrorc than four fides, are generally 

called poljgoos, hot the/ receive particular nanKs, accoivfing 

s ta 




I 



f m ttwlr Ml* I tbitt * p(rir|[an »( lift Uei ii 
wHld • f / U»t »m, ■ IgWHvl liB fidn •■ tr.*^#«, a AKura itf 
(cvtn (lit* ffi ttfMgtw, clRln Cdc* m WI^ m , mim btoi * 

totl'C Gilrt I H(r n^M> 

■9. A circle ii ■ fimit tgutw balMMktJ bj' out rim'ar 
tine, »tttrf thr ri ntntUtmrr, which m every itbcrc tqiuily 
Mum from ibcccnin. bMj^. tt. 

30. TW rvliii* of ■ drvli tt ■ rifhi Um Artwu Fmh ihc 
mtrrs ui ihc rlfdimrnrnn. 

31. Thc(Ji«t>«)ii 111 ■ tiiritU aright liot dnvn ilmngh 
Uk (t/iirr, aiMl bouiwkd at each toil bf ihc cUcbatlrifwet 

]i. An irc o{ n circle il Injr pait uf iIm cimiaifnancc. 
3}. A (.iMNd b a ti£lu liM jiiiiiing tb« twv Ktinailliu of 



3l. A (rKmern rtf ■ drcU II any |Mrt tharaof, 

3i AU^M ir.lt Htitlit emit. 

jh. A IVflur II a part of a cut I* taiiltlMrf an4ir pM tf 
Mm ate, and iwn radii drawn iii Ihr rtntrt. (k« /(f. U. 

17- A (Hi»'lr»i,i ii ■ |,Jli)f .,f . (.r<lp, hnriin iiiiF qinrfrr 
of ill. (iiiLiii.ltrLHi- li)r it; ^ic, itiid III Iwo radit Are per- 
pcnilin.lir r.. c.d. oihn-. See/^.jj, . 

tH. riic (iniinittjriKt of eviiy orrle in gtoiTWtry » fup< 
|M.([il ri< l.c iliMilcd mil) i6oe.|i(il pufti, uticd degrcci.md 
caili ilinuu litliilividcd iumfn) minute*, each minute into 60 
fetritiil", w\ fii (111 j htiice a femitircle contain* 180 dcgren, 
• M<l a (jiLi'liiiiii ijo (jfffitri, which form a righl angle, lod 
hdlf a .|ii.i.lr.i)(, i^llcil III! ..n-iit. coMtnini 45 dcgr«<«| fc( 
the irEaliiic nf evely rinlii-linc angle i* an arc of a circk 
ciinainul liiiwcen the iwo Unci, ithtcbform iho an)|le, Al 
|fiiiiit of ihr ,iii{{le bciitg in the crnlre of ibc circle, and iIm 
niii.lin ii( d.j'iirs rnni.iined in the arc of lbs circk ^M* 
th.m.,(.„c..f.he-n).le. .S.c/f/.aj. 

30- In tx.iy liKlitdiinlcil Tri,.ng'e the fide oppofltetlit 
right allele i< ..illed ihe hypolhenufr, aod the oibar tW 
fitUi, the itffl vt the Kianglc. 



OP MBNStTKATIOK^ Jaj 



40. The heijrhc or altitude of a figure^ is a Fine drawn firom 
the uppermoft fide or angle» perpeiidicvilar to the bafe. 

41. An angle is generally defcribed bj three letters: that 
letter which ftands in the middle (hews the angle intended* 
Thms^ in figure 24* £ A C reprefentt an angle formed by the 
line £ A, and the line A C ; and the letters D A £ in the 
fame figure ihew the angle formed by the two lines D A 
and£A. 

PROBLEM I. 

TO DIVIDE A GIVEK LIKE INTO TWO EOPAL PARTS. 

Fig. 26. From B as a centre with the compafies opened to 
any greater length than B C defcribe the arcs at m and n ; 
then (the compafles being flill at the fame width) from A, as 
the other centre^ defcribe two arcs cutting the former arcs 
in n; from the interfc^lions of ihefe arcs draw the flraight 
line m C n» and it will divide the given line A B into two 
equal parts, at the point C. 

probl;em II. 

X.O DIVIDE A GIVEN ANGLE INTO TWO £(^AL PARTS. 

'Fig. ft7* From B as a centre with the compafies defcribe 
the arc A C ; and from A and C with the radius defcribe 
two arcs interfering each other at m, then draw the lintk 
m B, and it will divide the angle ABC into two equal parts. 

PROBLEM III. 

TO DIVIDE A RIGHT ANGLE INTO THREE EOSTAL 

PARTS. 

Fig. e6. From B as the. centre defcribe the arc A C. 

Then with the fame extent of the compafies, from A as the 

centre* erofs the arc AC in n, and with the fame radius from 

C, as the centre, crofs the arc in m : from the points of in- 

' yot. I.; T t tcrfeaion 



or MntiuRATioii, 



urUAum m utd n, dnw ihe rigtn luiti m D ibd ii B 



PROBLEM JV. 



II 



Lint, *VD «r a ofviv mtraMVK. 

FIj. f), \m the £lvcfl Irfw be A U : ih«<i from (be foiou 
m aikd n wilb ■ rMtiut c<iir«I in C. the (i'ca i&ftiK4^ tk* 
ftfibathc jrri r aixl o, upoo whkbdrM ibc Ink C D. w4 it 
vIB be pu-ltel ta ihc lidc A D. 

PROBLEM V. 

/• i«icT « Mtfiirtiit u( A( rioK t siVl« rofirr 

tw 1 ulvaw Ltiis. 

/;/. 30. Let tko (ivm line U U C, >ad dir %wtn foUu 
At Take two MiuaJ diiUuca A m aiKl A a, tul wltb 1 n> 
dltn (Tester Uun A m, from ni mid a ■* centm, iakfibt 
Hn am, cuitinf each other ol r i fium Aiifltf Ar, audit 
will be pcrpcwlkiiUr to ihe lliie BC^ tbai tliupcrpeiKticd< 
ljt(r,fmtariKlii .ingk Willi .it 1, J>jtt '.i tIk li.-.-: iS (,. Tlirrc 
Jie many (itlicr wAyt ufiiuwinn petpciKiieubri to a ^vco, 
liiir, but the WO way ii to ilr^u them by a fijuaic, or Otbet 
fnailieni.n'riiil iMllniinoit Un iImI purpofe: I fliall, homew, 
|ivr .trKHlirr Prolilcin, lu <lraw a pcipcndicuiar froni a glfcn 
juiint out of thr line. 

I'ROIJi.l.M VI. 

Ill I.Kr fAM. A PKRPtM>tI:tn.AR >I(}M « OIVRM POIVT( 
Kf.Aat.V iiI'MniTi: TO THK I ;j|i or a OtrlV LIHl. 

A'^f.^i. I^t tlic f{ivrn point be A, ml tli€ finta \int B Di 
tlitn Troin A draw any line A in, (o inect B C t Met* A m 
at n, and frnm n at n centre, with llie ndiiii A n, defolbt 
Ihe are A Om, cutting SCin D| then draw a tin* A D, m4 
it will be the per^ictiikaUr rcfjuircd. 

moBLW 



Of itsmnBATiOK. 329 

^sssamsBsamBasaBaamammmmmmf 



PROBLEM VII. 

TO DIVIDE A Gimr LtHC IHTO ANT VtlMBBft OF 

KQUAX. PARTS* 

/7^. 32. Let the given lioe be A B, then from A di aw a 
AC,aodfiKn» B dmr £ P fwrallei to A C : on cacb of 
thefe parallel lioes poiot <iff a^tBany parts as tbe.gt«eo lioe si 
to be divided laio, begiootng at A io the ficft Utte, and acBin 
the iecocd liue ; theo iom tbc oppo&ie poiots of dtirifion io 
each lioe, bf the iincs A $, x 4,^ ^ kc. asd ibe^ «riU di- 
v.dc the line A B as requiretL 

PROBLEM VIIL 

AT A CITCy POIVT IV A OlVftir Llife, TO MAKE AK 
AVGLE or AVT rit.OM>*BD HUMMER OF DECREES. 

F//. 33. Let the given point be A» and the ^iven tine AB ; 
dxn from A, as a centre, with a radius of 60 degrees taken 
bam a Moe of cbordt, defcribr an arc m n, oiittiog A B in 
■1; tkea taikc tbepropofed ottmberof dcfroes with tbeoom- 
fa^aUcmibehmt lioe of cbordt^ and apply tbe coaipafcs 
ifmrn^m to n ; through the pomt n, draw the right tine A n, 
2nd it will forte an angle with the line A B, of the uamber 
of d^rees required *• 

Angles of loore than 90 degrees (hould be taken off the 
Isae of chords 9t twice. 

Or, the aaigle mav be made with a divided arch, by Ujfiog 
the ccolre tothc point A, and its radius on the tine A B« and 



A liBCclchordf IS alwravs ^cfcribcd upoo rbc pimir. fcalr, which k 

i i iiaBM i ir «r hn^t ivenr, or w€tod, aboyt cwnvc toctoes loiiS* to ^ 

attiiewiiikiinfifii ■aiMHuiii aiakcik: Uicrc mc aUiu ucbar Uaat 

ckc kaie «f ok an Ccomcuy, » a luae «f liiMi, of UiB§ft>, fe- 

Ecoia^DBau, riMmiU, wjd a Iuk <it «|i»al ^«ns ; 1 Ihail (*%< 

tbr 6p:Yc of one uf tbcir faut», auut iuc lucioud of ''**>#* irftT^ ^^ 

iarcial lines opoo k, with tbc tt(o lor whicb tbe^ aic tppl^ctl, wbeu 

I cx<aeicucatofTs%oauQicu3r- 

T t a mark 




OV Mfy«UBA'^|pll< 



mark at n, the number of dcgrooi propofed from .the nrch. 
nnd draw the line A Pi I* before* 

^ ;PROBLEM ^IX. 

I /» A ii . . T / ■ .II.-- 

Jtjf,i33« D^feribe thc*«cc i^ l),with the compaAei o^nocl 
m the nidiMt'Of to dfgrce»iA tht lint of chordt, taka tbo 
widkh of thD«rcia' n, 4ind apiply that dlftance to the Um of 
choidiv ftod Uwill fliew. the number of degreci In the anglo. 

U tht arc of thi aiiglo oxcecd 90 degrce«« it muft be 
taken off at twicei ai befo4'«. 

Ofi the angle may be meafured by tneani of a divided arch 
as the angle in the tail! {iroblteni ^41 conftrufted. 

PROBLEM X.' 

, ' » ■ ■ •■ \ 

TO FIND TH^ ORHTait Of A OI«CX.I. 

. • ^ . . M ■ ... , ... 

- ''if* JVtlA Ihticirolo A B C| ilefisribo -any lino, u A B« 
whifiti )• ealled eheivdi fnom the midd^ of whidi Mna draw 
the perpenilirular C I>, which will ' be the diameter of tho 
oirclo* and.biiiuft CD in the point Oi which will be tho 
centre* 

PROULEM XI 

TO DKtrRIHK THK CIKCUM rhK KNCR OK A «iaftK» 
THMOUGH TUKKK OIVKN rOIWTI* 

JFIj^. 3$. Lft ihc |;ivtn points be A B C; thrn from the 
Uiiddlc point li, diaw two cliordi* or two right liuev to the 
othrr two pointy A C 1 bifcft thefq two linei by perpendicu- 
lar liiitii meeting each other in tho point 1 O will thea be 
the centre of the circle; und with the radius () A, or O B» de- 
<cril)c the fiitk ABC, and it will pafs through the three 
given point n, 

rROBLUM 



or Mf^^nATiov. 




PROBLEM XII. 

. , . !/ . •• • rr\ 

TO MAKl A RfiOULAR PENTAaOM ON A GIVEN tINI« 

Fig. 36. Let the given Hne be^AB^ ' Drsw B m ptrpendi- 
cular to A B, and equal to half of it. Draw A m, and pro* 
fluce U till m a be qqu^l to B m« With a rft^ipf c^^J*' to B n 
d^cribe two arcs, iqterfc£tin^ each other in ,p poii^t ftpm 
A iind B| ai ccntrea. With t^p fanQe.riidluf, frbin't|ie poJAt 
pf.iptfrfeAion. 0, dcfcribe the 9rjCun;^nbipK.^ir9)!^A,9pi 
^ and about thecircuQit'ercQC.e of thiji cicclf ispplj; ^i^^il^WR 
A B fiv« tv9ci» And it wUl dcfcribq the %iu:c /({fji^df^ . 

PROBLEM Xllt '*'-'--^» -^ 

' TO DIICRU^ AN MRXACbW V^oVt A 'oIVIK' LTNYf'' 

■*j '• I ■ ..I ' I ' 'i ** 'f •■»" •' ' ■' "* 

Fig. 37. Let *thc given line be AB, iThen with a radiijs 
equal to A B, from A and B at centrei defcAbe two inter- 
fering arcs. Fron) the point of interfe£tion O, with the 
fame radius defcribe the thrle A B (5-) then apply the line 
A B fix timei round the circua)fcrence» aod it will form the 
figure required. 

If each fidie of the libove figure be divided liito two parti, 
a ^ure of twelve fides may be formed ; and it ^Vflde be 
divided into three parts, a figure of eighteen fides may be 
formed; thus i| appears that the radius of a ciixle will di« 
vide thecircumfej?€nce into fix equal parts; half the radius 
willd|videu Into twelve ; e^ual parts; aod twice the radius 
will divide it injto three oqual parts. 

, PROJBLEM XIV. • 

TO tiKife* A iioHr tiXK aq^Ai. do amt giv^n arc 

or A ciacLK. 



Fig^ 38. Lct|thc' given arc be AB : through the point A. 

and tlie centre df the circle, draw A m, making m n ^ual to 

I o( the radius n O. Draw a line A P perpendicular to A m, 

then through mB draw mP; ihen AP will be equal to 

the arc A B« 

FROBLBM 



or MuiavUTioir. 



I 



rRODLfcM XV. 

■• MAIt AMT ttaHL** PaLV«OK •» A 0tr*W 

lIHft. 

/^i/. ji. Lit ibc given line be CDj dnw CO Mirf 
t)0, mhing ih« uigln *l C and D, ndi equal w lulf ifia 
tpfft "I iKa tin'yitun I f">^ Ifi* CMirc O wild (W ndiiM , 
OD 4ffrribc »<« clftlcAUCP, then ■ppl)' ihc IImCD 
fantlntli'ly rnowt ttie eSttwijiintiKt, tnA it li doof. 

Sif. Tli« •njtln of ■ po'/jcon m fouitd In ihh nuniKf : i 
^kttult lb* wlutc ](io drjirnt, li|' itic number of fidci in (Im , 
pttyi^i, (Oil ibp 'ivntKPi will \k iSc ingliB «t the centre, | 
wblcli angk TulfiraAcd from lOo degree*, ibe icouiniler 
vUl be the «n^« of ttic pul^gon. I 

CmfSifurtK Iri* rfumltr nf Tirfrrfx in thir %igte, ant 
at the Crnlre ij mmry ngidur Vulijgon, Jron ikrte 
iiiia to iwelvi:. 



s..\. 


h.lyK.m. 


Aftjk 




ofOCD. 


.1 


vxl' 


iVo*" 


6o»~ 


'"3'^ 


4 




Vo 


90 


4S 


I 


Pcrii«i;'>n 




loS 


n 


Hcxnguii 


O'j 


ISO 


i 


HrptngDri 


^M 


iiBt 


<>** 


0«iK<m 


45 


'J! 


*7i 


V 


N'>iM|[un 


40 


140 


70 


to 


DcciiKon 


jh 


'44 


7» 


II 


Ktidecagon 


3* •. 


147 A 


J3.'r 


11. 




.?« 


i?o 


7f 



i 



OF MENSURATION. 333 

PROBLEM XVI. 

TO MAX! A riOUftI IIMILAR TO ANY OTMIlt OIVIK 

riOUftiK* 

/i/. 39* From any anglci ai fuppofe A, dnw dUgontli to 
each of the other angles ; then to b c, one fide of the ilgarti 
draw a parallel line B C ; and C D parallel to cd, and B D 
parallel to e d ; and it will be the figure reqxiired. 

PROBLEM XVIL 
TO »aouci A COMPLEX Ftouai raoM oki itxa to 

AKOTXBRi ar MIANB Of A fCAIt. 

f^. 40 and 41. Divide the gWen figure tnto fquarei, by 
eroft-linei, then divide another paper on which jrou intend to 
draw jour figure* into the fame number of fquareti and obfervt 
what fquafei the fevera! parti of the figure fall In, and draw 
fimilar parti in the correfponding fquareiof the other fi^ure^ 

PROBLEM XVIIL 

TO OmAW A TatAMO|.R IQjIAL TO A OIVEN TaAPS* 

tlVM* 

Fig. 4a. Let the trapexium be AB C D t draw the diago- 
Bal B D and C £ paiallel to B Dt meeting A B* produced in 
the poim B; join D£; then the triangle A DE will bt 
equal to tho trapexium A B C D. 

PROBLEM XIX. 

TO MAKK A TRIANOLE KQ^AL TO A VtOURK OF FIVE 

IIDBS. 

Fijif. 43. Let the figui^e be ABC DBA; draw the two 
diagonali D At D B, and the linei E F| C O, parallel to theitu 
mnd produced till they meet the bafe A B| produced to F and 
O ; join D F and D O, and D F O will be the triangle re* 
quired. 

In the fame manner a triangle mny be madci equal to aay 

right*lined figui'e whatever. * 

4 PROBLEiM 



/ 



334 OV MP.NfiUltATTON. 



PROBLEM XX. 

TO MAKS A TKIANOLB XftUAL TO A CrVCN (MKOI.I'.. 

Fig.^ Let the given circle be A^ draw the rnditis A O, 
and the tangent A B| perpendicular to ic ; on the line A B, 
take A B equal .to the circumference of the circle ; join 13 O; 
Chen will the triangle A B O be equal to the ciicie. 

BKOBLEM XXL 

VO MAKa A AICTAMOLEf Ot A P AR AI.LKI.OCjR A Mf 
BttUAL TO A CIV8N TRIANGLE. 

Fig.\i* Let the given tri.iugletK ABC».bifcA the bafe 
A B in ip^tlirough C ; draw C n o parallel to the l)afe of the 
triangle AB; draw the line m n and BO parallel to each 
other I and the reflanglc mnOB will be equal to the trian* 
glcABC. 

PROBLKM XXn. 

■TO MNKK A tQ^Atl! Xr^rAr. Vo ACltyKN RBCTANCit.C. 

Fig. 46. Let the given reSangle be A BCD: produce the 

fide A 11, till B E bi* equal to B C ; bifcA A K in the point < ), 
on which ;i8 a crntrp, with the rndini O A, defrribc a fcn^i- 
clrrlr A ( i K 1% and jnoducc H C to F, on whirh dcfcribc the 
fijnair H V O H, and it will he efjual to the rectangle. 

It) tliis manner any light-lincd ^\^\\T^ may be reduced to a 
f(]narc. 

PROBLEM XXIIL 

1 > MAKf A MMJKK l-ur/\l. 10 I WO U I II I' U SIMILAF 

fV^. 4)t Let the two timilar li>;uret l>e P and U, which 
Aic tqnarca: let the two (ides A Ji and B C be perpendicular 
to (;ilI) other; join their cxtremitieH A C by a right line* on 
which <lcli;iil>c the fqnare K, which will be equal to the two 
lijuyrts J' arifl C^j.iViii logcthci. 

All 



OP MEKSOUTION. 235 

Ail £33iiar Bgara maybe added togetiier in the (ame 
n-^zinaer : fcr zsy two fiaiOar figures, coofhii^ed upon the 
k^ o{ anv nght angle, are equal to a fimilar figure con* 
^ni6icd upan the bjpotbenuie. 

PROBLEM XXIV. 

TO MAKE A 5<^AaE EQJJAL TO ANT NUMBER OF 
S^^ARES TAKEN TOGETHER. 

Fig. 48. Draw two lines Am, An, perpendicular to 
each other : on one line mark A B equal to the fide of one of 
the giTcn iquaies, and on the odier line mark AC equal to 
the fide of anosfaer given iquare : then draw the line B C, 
which will be equal to the fide of a fquare, equal to the two 
former given fi^uares taken together : then mark A D equal 
t:> 3 C, and A £ equal to the fide of a third given fquare ; 
the3 D £ will be the fide of a fquare, equal to the fum of the 
three gi?en fqnares taken together. 

Thus amjf Mumher of fimilar figuies may be added together. 

PROBLEM XXV. 

TO MAKE PLAIN DIAGONAL SCALES. 

Fig. 49. Draw a line of a convenient length as AB, and 
iSifided into eleven equal parts * ; form each of thefe parts 
wxo a reAang!e of a fufficient height, by drawing parallel and 
perpendicular lines ; divide the altitude into ten equal parts, 
if it be for a decimal fcale — but if it be for feet and inches, 
divide into twelve parts j through thefe points of divifioa 
draw parallel lines the whole length of the fcale ; then divide 
the length of the firfi large divifion AC into ten equal parts, 
both at the top and the bottom of the fcale, and connectthefc 
pcnnts of (Uvifion by diagonal lines as ihown in the figure, 
and the fcale is finifhed. 



* 0«ly four parts ue laid down in this icalc for mn\ ;jf lo.ni. 

U u . Th( 



236 OV MBUfURA'TlON. 



The ufe of tbeSi diagonal fcalei ii, to take olf the dtmcn Aont 
of three figuieti and if the ftrft Urge divifiooi in the fcale 
from B to C be uattti the iccoiid fot of divifioni from C to A 
will be the tenth parts of an unit, and the divifiont in the aiti* 
tude from D to A will be hundredth parts : if B C be tensi 
A C will be unittt and AD tenth parts: ifCBbe thoufands, 
AC will be huiylreds, and AD tens: for example— if it 
were required to take off 143 firom the fcale, fix one foot of 
the compalTet, at the figure a of the largeft divifions at the 
boctofla of the fcale, and extend the other foot to 4 of the fe« 
eood fmaller dtvifioos, and on the bottom of the fcale ; then 
for the three unks Oide up both points of the compaifcf in a 
perpendicukir line, till thq* fall upon the third longitudinal 
Nnei midoD that line, with one foot of the compalKa renoabi* 
mg fixed, extend the other foot to the third diagonal Ene, and 
jrou will hare the extent of the three figures as required* 

To nwqfiire the Lengih of any Lusr. 

Take the length of the line, between the co re pnflb, and 
apply it to the icale : fuppofe it contains above three of the 
large divifions, then iiet one fool of the coiupafTcs on thr 
point 3 of th<r large divilioiis, and r(ip|)ofe the other foot nf 
the conipafTci to tall between 4 and { of the fccond divifions ; 
flide up the compalles by a perpendicular nmtion, keepioj; 
one foot on the line of the large divifion 3, till tlK other foot 
fall on the intei fei'tion of one of the diagonal linc^ which 
f'nppofii to \yc four ; thid fliovvs that the length of the line 
incaluieJ is 344. 

PRO B L KM \X\'I. 

TO MAKE PLAIN' SCALKS (OR TWO IlOVaBS. 

FkT. 50. If the Icale t>e a decimal one, after dividhig it into 
any propofed number of large divifions, one of thofe divifions 
Riufi l)e fubJiviilcd into ten parts : but, if it be a duodecimal 
iicale, one of the laige divifions must be divided into twelve 
parts, aod ferve to ukc dimcnfions for feet and inches. 



OF MRNSITRATION. 33^ 

The mofl proper form for a fcale of equil parti is that 
vrh^re the diviftons are marked on the very edge ; and are 
generally made of ivory, the edge being made thin for the 
purpofe of pricking off dif ifioni 00 the paper, without te 
help of the compafTes. 



PROBLEM XXVII. 

TO MAKE A RIGHT LINB, THAT SHALL BE A MEAN 
PROPORTIONAL BETWEEN TWO OIVBN LINES, 

Fig. ji« Let the two given lines be AC, C B ; Join thent 
to each other fo as to form a right angle at the point C : join 
the points A B, which will be the diameter of a circle 1 then 
defcribe the circle BCA£, draw CD perpendicular to 
A B, and M^iU be the mean proportion required. 

Note, ^he angle AC B, defcribed in a femicirclei it aU 
ways a right angle. 

The chord AC is a mean proportional between AD and 
AB, and the chord B C is a mean proportional between B D 
and A B. 

The fquare of the hypothenufe of a right angled triangle 
is equal to the fquares of both the fides, as fccn in Problem 
XXIII. 

The thvee inward angles of a triangle are equal to two 
light angles. 

Triangles that have each angle equal to each other are 
called fimilar triangles. , 

Tojind the Ai^a offypervial Figtoas. 

The area of a figure is the menfure of the furfncc^ without 
any regard to its thicknefs or depth. 

The area of a i'uperficial figure is the number of fquaro 
^nches, feet, yards, &c. contained on its furface. 

Square yards, feet, inchts, &c. difer from the fame mea- 
(ures in length, as fccn in the following table ;— 

U u • l^ineal 



.1.^3 



nr MKNNt^WATION. 



f.inml Mnijnrf*.\. 

J 2 Ituhct I Foot 

3 I'cct • t Yftnl 

h let* I ...••... I Frtthom 
i64 Fret or 1 r t IN)le 
i;| Yiirdi r • • 1 or Koil 

40 t*olc« t F\tt long 

8 Furloogi t Mile 






o Frrt •••... t VamI 

'^ft Fcrf I Frt«h»Mn 

t7ti Fret or 1 f t Tolc 
10} Ydrdi r 1 ot HotI 

1000 i*olf« t FutUm^ 

64 Furtongi).. • t iMiic 



PHOHLKM XXVm. 
TO ritto rn$ Atkk ot a rAHAi.t.iit.0f4iiAM, a motAnK, 

A MUClAKOl.i, A KHOMIIVIt OH A HHOMttOtO. 

The ArtA of noy of thrfc flgvirfu in fotimt l>y (he following 
rule ; 

R vt.ir. Multiply the length by the bre«fl(h (or, if It he a 
rhomh\i« or « rhomlMid, by the pcr|tcn(ii( uUr bright * ) tnd 
thr pi^Hlurt will Ik the Area. 

Fi«. 40. Whrtt In ihf nrrrt of a fc|«{«rr, one fide whcr«of 
i« (» fcct^ {tml tlic other lidc 7 li*ct ^ Anfwcr 4A (ce(. 

6 

4t frff 

PKOHLKM XX1\. 

Ill . iR. \Vh;u m thr ^ir^ o( :< rlmmb\ii,(hr Irng'h whrrn*! 
n t .• Irrf, (^ inc |»ro, an<( the prtprmlu \il.it hn^lu frrt, i«^ 



!nc hra '^ 



Vcri 17 \ mi Ik' 

to 4 ^ 



•»«'H (*iihI»« rni •mil. uI.ii Id iIh l«.»(v 

rHOlUTM 



OF MISNSUnATlOH. 



339 



JJ' " ■ i I ITTT-i* yr . -ffT 



••»- 



P U O H L K M XXX. 



Fi«» 17. Whnt is the area of a rhomlxiid, whofc length it 
5 chainsi and ao links ; and (icrpu^diculai heighth ao chatnt 
5 links. 

Ih this pmhlem the ehaini 
and links :ne nuiUiphe<l by 
«aeh other ns dn imnis as the 
links are alvvnys decimal pa its 
of the cham, as mil be (Ikowii 
hercatW, and the pnxliK^ is 
the aniwcr in fipiare chains and 
linksf w)iuh is divided by to to 
bring them into acres, as there 
are i« fquarc chains in an 
acrt ) and the decimals arc 
multiplied by 4 for roods, and ^^'^^ 

thofe decimals again multiplied by 40 for perchcsj bec.uifc 
4 roods make one acre, and 40 perches one rood. 



ao»Oj; 

a 600 
1040 

10)104,1600 

io>4a6o 

., 4 

1,7040 

a 8, 1600 



Acres. UtHHl. 
to I 



Pcrchfi. 

a8, t6oo Ant, 



PROBLEM XXXI. 



TO FIND THE AREA OF A TRIANCLR. 



Fto. 9» The area of all triangles is found by the following 
pics : — 

RuLK I. Multiply the Iwfe by the perpendicular height j 
«ml half the prochnfl will be the ai-ea, Hut when only the 
Jthree fides of the triangle are given, the area is found by the 
following rule : — 

Rule a. Add the three fides together, and from half the 
fum fubtra^^ each fide fcparately ; multiply the half fum by 
the remainders of the three fides continually together, and 
the fquare root of the produift will be the area of the tri- 
angle, 

ExAMrt.fc 



•14** 



fllr Mt(Ni^|tnATfi»f^« 



y 



AN(Wf»r 4c)<» N<<!f 



• '/ iy §2 «^ 

_. iny » u It 

^4 



i6 





• • • 



11711(1)6.71. 



*|R 



4 

«7«7 1 9f ^OQ 

7 I i.ju)Ho 



AhiVVtl t ^0,78 fr^^ 



PHOIU.KM XXMI. 

f CI ftNP AN V ONk t)th)t Ut> A tIthH t AN(4t,||l|^ tUfANMl H^ 
M AV tNu <t MU (U MH M ilVilalhDa, 

Im cvriy lij^ht (tit^UI tiuni^tp, fh«> («|Mrtie ii( (tir hyp** 
fhf niUti u ptjurti fci hath ihr (qurtiitf til i\\c two lrjjii| t(q Aiowii 

TlirirftMi?, ID fiiut ihe hypothr^iHirfc, ^dil fh<i r<|iwir< «f ilir. 

Atu! 



OF MKMIVItATION. |4t 

And to tlnd one leg, fubrr4^ tho fquAre of tlie other teg 
Ifom tiie l«|uaro of the hypothenule, and tho ft]U«rc root of 
the diflfcrcnce i« the leg rei)uiii3il. 

£xAMt«i«it I. WImtji the hypothenvib of a right an|(t<4 
triangle, whole Iwfe ia 3 j feet, and pcrpcnJicuUr j6 foot f 

• ftp <)Q 

\\{(^ loH() 

499 ^(6$ feet. Anlwei. 

Ex AMFLK a. What it the perpendicular of a right angled 
tii44igle, whole Imfc ia 40 yaidii, and hypotbenufe 5oyardi ^ 

40 50 

40 JO* 

^-^ i6oo 

oooyaidi, Anfwcr. 



:i^ft, 3. Whi\t isi thf hcij^hi of a fculing ladder to reach the 
lop o\ a wall ati Icet in height, auJ acrofn a ditch 41; feet ia 
Wcailih ? Aniwcr 50 <cei, 

Qucftiuna ol thi* luMurc are rcfolving by the foregoing 
IVoUen^ * the benight ol the ladder being confivl^red a» a hy* 
pothcnulbi^f a right anglej triangle, and the height of the 
\sall and breadih of the ditch ai the two oiber legi of tlit 
triangle. 

PHOHLEM XXXin. 

nV) FIND lilb AKCA OP A laArKXOlD. 

Rui-8. Multiply the i\\n\ of the wvo parallel fidei hy half 
the perpendicular dilbnce between them, andtheprodoA 
uill be the area. 



•• 



3431 O'' KfENSUTlATIOK, 



IixAMPi,B I. What \$ the area of a trapt^aoid, whofc two 

parallel fules are 8 feet and i% feetf and perpendicular dif- 

tancc 10 feet ? 

8 
II 

ao 



Anfwcr loo fecr 



PROBLEM XXXIV. 

TO FIND THB ARKA OF A TIAHfiXIUM. 

RutH. Divide it into two triangles, by a diagonal line 
drawn from any one angle to the oppofite angle, then find 
the area of thel'e two trianglesi by Problem XXXIL and add 
them together. 

N§ie, Two perpendietilara drawn from the diagonal line 
to the other two oppjfite angles will be the perpendiculars ot 
the triangle, 

PUOHLKM XXXV. 

lO KIND TUli AHKA Oh ANY IRRECJULAR FlUUtth Ot 

ANY NUMUhK OF bIDIiS. 

All irregular ii^ures conlilVmg of more than three fides 
aic^ to he iliviJal iitio trianglca or tra])rziun\8, t|icn lind the 
ana ot cai h of ihrfe ti iaiiglctt or trapc/iuma l*cj)araicly, anil 
aiitl ilu-m lo^m'thcr, and ihc fiun will be ihc area of the whole 
li^;me. 

A'i'/i', J'.very figine may be divided into as many iriangUsi 
except two, us the iigure lias lidea. 

'J'huh, a tignrc of live fidcii may be divided into three tri- 
angles ; a H^me of fix fidea, into four triangles ; a figure ol 
ei^Ut fides, uiio lix triangles, ^.e. 

PROBLF.M 



OF MENSURATION* 345 



i^. «• How fnany fquare ftet does a circle containi the 
ctrcoaifemice of which it 10.^956 yards ? Anfwer 
fi6.i9a66. 

The operation of thefe problemi ii purpofely omitted for 
the exercife of the learner* 

PROBLEM XXXIX. 

To FIND THI LSNOTH OF ANY AKC OF A CiaCLI* 

kuLE I. At 180 it to the number of degrees in the arci 
ib ii the produA of the radius multiplied by 3. 1416 to the 
length of the arc. 

RvLi •• As 3 is to the number of degrees in the arc^ fo 
ii the produft of the radius multiplied by .05a3A to the 
ieogth of the arc. 

j^. !• What is the length of an arc of la degrees 10 
niootes, the radius being lo feet i Anfwer ••ia34J. feet. 

Jt|r. ti What is the length of an arc of 30 degreeS| the 
ndius being 9 feet ? Anfwer 4« 7 1 14 feet. 

PROBLEM XL. 

TO FIND THB AKEA OF A SECTOR OF A tlECLB. 

FiG.aa. Rule t. Multiply the radius by half the arc 
of the fcdtoTi and the product is the area. 

Rule a. As 360 is to the degrees in the arc of the fee* 
tOTi fo is the whole area of the circle to the area of the feAor. 

NHi, For the femicircle take one half of the whole cir- 
cle I for a quadrant^ one quarter 1 for the fextant, one fixthi 

SxAMPtE. What is the area of a feAor of a circtei whofi;^ 
radius is i j feet, and the arc 30 feet ? 

iL 

Anfwer aai; feet 



X X 2 o^ 



'^ 



or MIKfOkATtOK. 



PROBLEM XXXVII. 
TO rtlTD TWI biAMtrii ot tui rimc*M>i«>wct. or 

* CUCLI, Tiri ONI riOM 1N> OTRIK. 

RvLt ■• A* r bwii, foiittttdUnMttriotiM ctrouiB- 
hranca.— Ai ai u to 7, lo ii (tie drcumfmnoe la tbe itii' 
mncr. 

Kvit*. Aft 113 u lB3{{. (o ■* Itic tfimiccet to ihe cir- 
cmtHtRDcc— A« ]{( bw 11^ ii> U the dreimftfou (9 



R«ta 3- At I b to 3.(416. (o b the ditmeur to the dt> 
nmftrcncc.^Ai 3-1416 bio 1, (0 ii ihe cimunfercncc M 
A* dhnetcr. 

^. I. If (he dUweicf ot ilie urth be ^^{t miki, u it 
nearly i*^ wfaii 11 i)h citcuniftrrnni. fuppoGflg it wrre ex- 
•Aly round i Aniwrt • fooo-fljiS mile*. 

^«. s, Whii b the dUmricr uf ihc ctnh, Tuppofing ihe 
cbcandtrcDCt: ■ jooo mila ^ Anfwcr J^ijl mda. 



P R O lU. K M XXXVIII. 
TO nnv TKk aiBa or a ciacLt. 

RvLi I. Multiply h.-iir ihe cirrumfercnce by half ibc db- 
meter, and the prwdiifl ia fhe aiea. 

Rum a. Multiply ilic fquareof the dianwter by.;^;^. 

RuLK J. Multiply the (ijusre of the circumference bf 
07958' 

RoLi 4. At (4 ii to II, fo it ihc fiiuare of the diatneW 
1(1 the trca. 

RiJiK J. At 88 it to J, (o it ihe Itpue of the drcum* 
fercnrr tn the tret. 

C"- 1- Whiii i( the ir«t of a circle, whofc diameter ii j 
feet i Anfwcr 38.4846 feet. 



fUS 



^ 



6.19266 

The 
\c 



TO Fi3ra T 

} ia the fmiuSt # 
rngthof tfaearc:. 

RvLE s. Js x;* 
i the ftoanBt 4r 
ngthof ttie<BCr 

j^ r* W!nc s 
xinates, the 

j^.s. Wlnrk 
ufioBbeiiig^Ar?- 






TO FIND rWt AtC^ ->» - iifstm^ » .-—* 

' r 

or, ib it tbe ^ifbolr amacol tfi^'Tw^^«^^4 
jr«er. ^or thr fcnwei >rtr riHie ^mK V^g^ 
(e ; for a qindrafit, one/pMPiSBr ; V iie^^ 

Example. What in the^5f»Wf>f '. <'*^-^ -#'-, " -•-' . "^ -^ 
adius if 15 fleet, and the '>rr -^^ f«9»f « 



• 



7C 



^ n> anamninaii. 

^. t. WiMl li ibe am dr a qwilniRt ind 3 fcmkirck, 
whofe r»BM It t) Au otdi * Airfwer, ttw qnAnal 
I }>-73k6 fact, wd (enflabtte 16 s^6{a feet. 



PROBLEM XLI. 
la rivD rot akia or a tifiNiiiT dv a cieci.*. 
ilutV. Fbdihe'ucaortheyiof oftticSrcklijrUiclAft 



TM ttM arn oF the triangk rnnn«4 by HKdJftd'tif tlit 
fagpnenl, and (he radiiii fif the feAor. 

Then ibe fmn of ihefe twfl will be the antWer, if (he frg- 
tnnii ii'urcsicr lliin tlie femkircle ; bui if tile frgmeof be 
Icb thia a fcmfcircle, the (liffcimcc will be Ibe anfWer. 

Tlie forCf-oii^ proMcini will tic found fully faiEcienI U 
inftruftlhe learner in ibc neitiod of mwfnring nwy kind 
of f«p«fci« wtutctrcr, » ibere ii no figure bit may be re 
diKctl to one or enoM of fhe fortgomg flgurtk 

OF MEASURING ARTH-ICEHS" WORK. 

Mii/on,- llori. 
To mafunry belong all forts of ftonc-worlt, anti the mi* 
fiiri'S of ii i) by the foot, either fnperiicial or folid. Stone 
walli, cnlumni, blocks of ftonc, Sec. arc meafurrd by the 
ibiid foot I but fl-ibi, cliimtiey •pieces, pnircmcni, tic. irc 
meaftired \>y the fupuficial foot. 

T/ic Prim of Malh„>: Work. 

£■ •' ^• 

Ncwcaltleftorie, ^/«.;l>*J;V ... .0 i la 
U'oikmanfliip lo^nxa, ptr fuperfual fa^i. from 

bil.io 016 

Von\aaA ttont, ftr luht fMt o 3 * 

Worlunanfliip to ditto, ftr faet J^ptfficM, from 

iO</. Co oai 

PiTinj 



Paving in Pentfattid fioDn Bcn^ i§ mek 

Ditto a indi duck » . * ^ » * . » -o '% ^ 

Furbeck flooe, pa/iog, ^ foot fttferficial^ 
from 11^. to t>f4 

Bremdi ftoDC, psmiig to terraces, fer foot 
fuperficitd ••••••«.«.«Cf^ 

Portknd fione, cbitDJoey-^ieces and ibJbfi, from 
I \ inch thick to 3 iocbeB, per foot fttptrficUd^ from 
x/.6</.to o«$ 

Marble ciiimney-|»eces veioedy ^rr/#9/ fttii^ i 15 o 
Workmaofltf p to ditto, /ir /•#/ fopcrficlai^ from 

3X.61/. to o S 6 

Blilt and white marb]e» an inch thick, per foot 
ftiperficial ««Og6 

Bricklayer^ Work, 
BiidL-work is meafured by the (quare rod of s6 feet^aod 
a half, and the brick-work eftimated at a brick and a half 
fhick ; if a waH be more or lefs than this ftaadard thicknefst 
k triufti>e reduced to it, by the fottotving rule : 

Ru Li£. Muhiply the fopctficial content of the wall by the 
number of half bricks in the thicknefs, and divide the pro- 
4lud by 3, atffd the q^iotient will be the fuperficial contenu 
of the waH, at the true ilandard tbicknefs of a brick and a 
half. 

To take the dimenfions of a building, it is ufual to mea- 
fure half round the outfide, acd ai'o half round the tnlide ; 
the furo of tbefe two me^ures multiplied by the height, gives 
the fupcrferial content, which mufl be reduced to the Itiiiid- 
ard meafure, in order to afcertain the price. 

Chimoies are fometimes meafured as if they were folid^ 
dcdnfting only the vacuity from the bcanh ro the rrantle ; 
and foroctime? they are meafured round for their bread :h, 
and the height of the dory is their height, and the depth of 
the jambs is their thick acfi ; :l. :h:i z^\c co dcdualoa is made 
for the fire place. 

a The 



I 



348 ot utxniATtowi 

TIh rbiniMf flttftst wUdi «ppcir ilwvc ihc boUAiit ■■'^ 

■ w f ara J (oand for ibrir liraidib, utd nablpllcd bjr fhdr 
bfiglM (or tbc CuparAcut ranmi ; kuJ ibe ihkliDrii li k- 
rTMinicd lull t bhck miirc t|un II rraUjr if, on ORSum flf ibe 

All wiiidawi, 4oOT-*a]n, &c. are lo be AeiaSiti m mm- 
liumg br ihr inaKriaU, bat not in mnTuiiDK for wivkmaa- 
Aup. Ttwn ate alfe fnw other lUvwuKct, m duutilc Rm> 
furc far fealhtf'd gtbk cndi, kc* 

AlltlkcMkminibrtckKnrkHinMfUfcJ l>]r tlte ftnl Itfturc 
iif il>| ferr, whlrfi rimcun* t;*! Iqniio fen i bcao:, «hcn 
tbr cmrniu of brttl-mnk U (m>nd In ((lunre feci. It ii divUed 
b]r «;a (ihsfnilMQU:inj[nc2lcflc4).aiKl (tirqtMicnt if rhe 
number at {t^nn radi 1 which n id be rcduccit u twilifd 
nEcTm b]P ibB riinner rutc. 

TUlnt li Rearuted by die Tquare of 10 fetfi maUn( o« 
hundrad <i|iura fan in carh Tqairt. 

BrirVwotfc, at ^ff- r*/. £. /TI; 

New-plate biick«, l;iid dry, wiilnJI nuntar, 
ill ivcll', &L 88a 

Kniigh greyflork britk-work, in (uriy-walli, 
be. from 10/. to IS 

Ijtlidur and monar only, Iq biickwork, from 
3''o 3 'S » 

L;il)uur only to Jiiio, ffini 1/. 61. tu ... i 8 a 
Plain lilin^, al ^r [quart. 

New plain tiling, from a/. J/, to .... 1 10 

Labour only, from 41. tu • { 9 

PWic '/ MateiiiiU. 

\.\n\r, ptr hunArtd a 14 

Sand, ptT Itail 056 

Momr, ptrtead O 16 

Pointiiig 



\ 



OF MSNSURATIONi 349 

mmmmmmmmmmmmmm^mmmmmmmmmmmmmmmmmmm 

Poiollng mortari /#r /m^ • • • • • « 1 it p 
Prkkif fir hundnd, accordin|^ to the quaUty, 

from 3/. to • o »o 6 

BrkUayeTf ptr ^^y^ in iummer ••••040 

Ditto* 10 winter • • • o 3 10 

Labourer* /#r di^ in fummesi from ai. bd. to o t 8 
pittOf in winter •0*6 



^» 



Carpenters* and Joiners' Hork, 

Moft large and plain articlei are meafured by the fquare of 
10 fifty each fquare being 100 feet; but mouldingi and 
Other omanaeoti are generally meafured by the foot» running 
meafure* 

In meafuring flooringi no deduAioni are made for hearthig 
on account of the trouble. 

Fahitiona are ipeafured from wall to wallf and from floor 
)o floor, and no dedudtiont made for door-wayt. 

In meafuring roofi, the length of the houfe in the infide 
with two thirds of the thicknefi of one gab)e» it confidered at 
the length s and the br^dth ii equal to twice the length from 
the ridge to the end of the rafteri. 

For llaircafes take the breadth of all the ilepi by a (Inng 
from the top of the ftaircafc to the bottom, whicli multiply 
by the length of one ftep. 

For wainlcoting, take the compafi of the whole room for 
the length ; and the height from the floor to the ceiling for 
the breadth, deducing doorways, windows, &c. from the 
inateriali, but not from t)ie workmanfliip. 

For doors, fliutters, &c« Thefe are meafured by the foot 
fquare, allowing for their thicknefs, the number of pannels, 

Prices, 

Flooring, vX p%r fquan JuptrficiML jf, j. d, 

)4tbou^ and nails only, from 6i. 6i/, to « • o la o 

Rooft, 



JfO or IIRNftURATIOK# 

Labour Mid iN|ili ooljrf ^rom {i« 6i« to • • o i { o 

P«rti(ioiif| %%p9r /quart, 
labour tod naUif from {i#4/. to » • • • • ss o 

Doorf, %X per foot Jquart/ypfrJUist, 
DmI ditto «•.•*•.•»• o I V 
TwOi^nelted ditcot tccordbig to the tbkk' 
ncTii from 7i^*to« •.•••••• o o n 

Fottr'ptnncllcd ditto, fron; 9|^* to . • • o i o 
Stfli'feimef •nd (tflieif at ftr/otufrftrfUM. 
tk4 <btio» Ao|(l« biiogf wiib wciglili^ puUicif 
lw« from li* 4i/« lo •••«#••• 9 » 

PkyUf^TM' IVwrh, 

Tliiftorin' work U of two kindf x s\z» pioiAeilof uoon 
latbf , Mid rcfideriii|{9 wbicb if pItUUrinK upon wtllf? 

Thry trt vtltied diflbrcnti]f|»rbc contontf tro ekber 
found b)r the <i|i)«rf fooi^ or the fi|iiire of so UiU or tfio 
fijuare yard { but mouldtngit f^* «'^ inoafumad by ruooiflg 
mcarura. 

DeduAloni are always mad£ for door^wayi, trC'placc^ftec. 
but run ior tviiidow«. 

Limt wliitei)ingofic<r, ^ifr^^r// . . , . o o i 
Colouring, anrwiMm^ f,cr yard ....003 

Rendcrin^j rough, one a«t, ^/r>4f// • • o 3I 
Ijithing only, ptryarA ...... o o 6 

Lathing and ()Uiftcring, //r><ir//, from 5^. to o 1 4 
Dirco, to L'eilinK*9 f^'^nn n« a/A to . 
Outfide lime and han*, /^r ^^/Z 
FlatiUrr, ;><r lhuI, . • . . . 
Tir Utht, ^/r bundlt .... 

^Ut^ fn gallon ..... 

Whijcaing, //r /^;j/^ . , . . 



1 (> 

O I o 

o B o 
o I 6 
004 
jP o a 



OF MKN^VMriOftT. 351 



It •.<«•»«»• 



Saicj/crs* Prices. 

T«irdv« feot dcflli and (uitteni hvft6^ prr d$M€ti 

cms, from axt 9//. to 'o 3 o 

Teii*feet dUco^ from ai. 7^. to • • • . o • to 

% 

All extra cuts are charged after the rate of three (killings 
per fquare of 10 feet. 

Plumbers' fVork. 

Plumbers* woik is mted by the cwt. and fotnetlmes by the 
Angle pounds for there is no method }*et difcovcrcd whereby 
lead can be ca(l of An uniform thicknefs. 

SheeNlead is of two fortSf called caft Iheetleadi and milled 
lheet«lead. 

Solder is charged by the pound, and leaden p:pes hjr the 
yard or loot running meafure. 

S)ifiet*kad ufed in roofing, guttering, &c« is frona 7 to 
itlU weight Ui each fquare foot. 

Pric9S' 

if- /• '• 

New iheet-lcad, caft at 71b. weight to the foot, 

j6crcwjr» and labour to ditto 190 

Safh weights, per cwt 199 

Solder, perlL loti. ; or, fertwt 4 13 ji 

Leaden pipes, /^r ctu/ 1 10 o 

Small caft pipe, from half an inch to two 

inches dianneter, petfictf from 9^. to . • o a 10 
The new patent copper (heets, coverings, fer li.oiio 



IFork. 

Painters* work is meafurcd by the fquare >-ard : tOd the 
sneafuring-line is forced into all the mouldinjm ,%nd wherever 

tbt bnifh goes. . . 

Yy Wmdowa 



« 



)5^ O? MBS9SII1IATIOK. 



lA* 



Windowi we done by the piecci and ddh-fquares by the 
dozen. 

ChiinDcy^piecc9» Tariegated or fiuicied colours &c« by tho 
foot fqutre. 

Onumeotal figures nouldiiigi, Ice, by ibt fool nianin*^. 



Prices* 

CqpnmOQ paUiting in oS 

Once, firjmnt ..003 

Ditto, twke «..oos 

t>ittO| thn:e tiroes 4 •.•••••007 
Sifli frames *^<^ *ui oil, Mi^ • • , « o o 8 

OittOt twice inml*.. 010 

Safliiquaretoncein<nl,/fr^«aM • « • o o 8 

IKtto^t^ice . • 010 

Caftments« .4 006 

Glaziers* Uork* 

Glaziers take thdr vlimcnllons in feet, inches, ^nd parts, 
aiul compute their work bv the Iquare foot. 

In taking the leui^th and breadth of a window, the crofr- 
ban between the fquares are included; and windows of an 
oval or circular form are nicafured a^ if they were fquare, 
taking the grcateft length and breadth, on account of the 
wafte in cutting the glafs. 

P!ate-g!ais, cut lioni 1 foot to a feet, frr/f^t 

Ditto fi*om 2 feel to 3 feet o i 6, 

Beft Ratcliffe crown ^bfs, ^r/fft/^t^axidl • o a 4 

SECT. 



OP MBNSUHATIOir. 353 



SECT. 11. 

OP MBASUniNO LANP; OR SlTRVBTIN^. 

Before I proceed to the prtdiee of furveying, it ii oeceilar^ 
10 n^eotioQ the ioftruineota ufed in meafuring land. 

I . Of th Chain. 

The chain, called Guntefs chain, confifti of too equal 
links, each link being ^Vv of a yard, or tVv of a foot, that 
is j,^ inches long ; and the whole chain is 4 poles or at 
yards in length. 

An acre of land is equal to 10 fquare chains. 

An acre is divided into 4 equal parts, called roods, and 
leach rood into 40 parts, called p$*rches or poles. 

The length of lines meafured with the chain are fct down 
in links, as integers, every chain being xoo links ip length ; 
therefore, when the content of a piece pf land is found in 
fquare links, cut off 5 of the figures on the right hand for 
decinnals, and the reft will be acres ; thofe decimals are then 
multiplied by 4, to bring them into roods, and the decimals 
of the produ^ multiplied by 40, for perches, as in the fol- 
lowing example : 

Example. What is the area of a rectangular piece ot 
ground, the length of which is 1300 links, and the breadth 
940? 

1300 

240 



C2000 
flO OO 

3.iaooo 
4 

.48000 
40 



^nf^vcr 19. 20000 3 Acres, o Roods, igPerches^ 

Yy* a.O/ 



't ttia iliHi ililii iit t»>niilla !•( ■% jilaiii n . I4li^«l!itl (i.nr.t i»| 
Any llillV|;l|^hl |l^(9« lUt^i lui4U0Mlt(|l i|llF<: it^e. U\ lit- illlo 
itl 4 |i«ll AImI lolfci:!, hy V^liiiU \U^ liilil|3 ia Iik Ijiicil In .itiy 
ililfilMf f U blli ullM » flill«Hl <i| WMiid ill lil iPlMvt M» ^l|gr». 

|.'i|ii:t Mil lllC Ultlf. Olio IlilfS ur lliis Il4l«)ts U iitrlilcti IiiIm 

|tvri4l r<}iii«l p^tl». I«>f ihf |i|if(ipfi» <tl »lM\Viii^ lint:* ((• imU 
ilm{M|ini iiiift ilipoiliPi' Uii<»Mi ilt» (ifiiti« U Ui^itiMl iniii 

lUMiHifv Ml' ukiiiK atij^lroj fci. Thvt p i« ^t|a ii nprtitr And 4 
< iiiii|i4lii OM iiiifs iidp <tl f h0 ijitilf , IM |H«iii( otti ilifs dir^lKtM, 

Uliil lU llii» lf|ti|«s Ml \\\p iAtiW \Ht(\lU»klt waU fPff^\it\ iMlM 

)>iiihi» ui \U$ <:om|iar» ar «vriy irniuvt. 

of ibP liriiPi Mli ill (lip (Atm |i|flliP| illi-l iliJll C:dj^(» Itl i:4Utf4 U|i» 

Ms\^U\ p\\^ff u( itiR iiutrif. 

Ill uAi)|t iltin utitr, 4 ilipri (>t |.ii|iPi ii iM Uf wp(r«4 4h*I 
f|it0Ml (iiKMitUi with ihi^ U'f^\m Mt (titi utilp piriUil ilii^ii 

I hifw, lit kl |i iIh- )><|>Ct Owiiii)! i%liii.ti la |ii tnti4iiilill it ta 
•liyi llial il limy llifKh liUlJ iitiMOllij M|*Ui| (ItU |ia|ii:i llm 
|il(ih iA III 1*»' iiirt«i h. 

ill laklii|^ A Ihivry at nhy |itfi> fi n |Miittl U If* Ite illftiU ult 
l)tP |iii|ici til flriitilf; llmi i|.<il wli(.l0 Ihft uMe itt li«rtl, wttkti 
ia 1 4llril (lu* /f.tl.ttH i itirti lit llldl |jMitl( lU a )>ilt| li| (HlO llHtl 

ijMlir I t>i|i)>.ilUft, iiit«l III il <i]i)i)y ilin fiilu Ul piIj^c ni lln.- tn 
ill ^, Miiiviiig iiiM Hill, r ji.iii ill ilio iiiili ji .ittiiiii. till iltriitiijit 

ilii li^ttrj \ •III |ii II riti uitr (iM^li i.t itii, til M VMii liiivry, im 
iiiitii iillit I II iii'tiLali'.i i.tji.lj iiiiil) liuiii itii- II illiiii |i.itii( 
ilnuv tliiit al< It.; llii Ii4ii>iill'ij ol l|ii9 liiilrt , lliriiluiit 
ili>- intli « itttmi ti|ii>ii lilt, iLitiKii |i.iiiil ii4 iiiiilii', lill yi.u 
I'd* MM itiiMiliri <)ti}'li,t.i liiiiii. iilfii r (>t ,• I, :iiil i1tiit« « line 
linin till U.ililHt |Mi||,t alnii^; ||i# III}*! ni Ih* ii Ir t, -ik U Im . , 
ii^rthiittl luiJli ihi. laliit. li!l V'ili Im.l ill i\l» liiilt iMilti ll.i 

iUliuii. 



OP MP.NSURAT10N, J55 

^ution, to rcpn lent ihc bearinv.s of as nuwy ;»nj;lt's or ohjrrti 
at nijy be ncccilaty, atul nu more ; then imal'ute from (he 
itation wlierc^ the tabic ia fixed t<» every uhjeft which you huvc 
vicw<id» und lay the ineafures ilown upon their vcfpe^ivc 
Unci on the pnpcr. 

If It bo requiif d, av it fun^trtlmcs is, to take n furvey from 
more than one ftation ; renuivc the table, and by the help of 
the ttnnpafi, fix the table in the lame politlun aa beforci and 
martt another point on the paper, for this fecond ftation 
ptntt I and from thence draw lines to ns many obje^h at 
tftay be ntceffary, marking the ditlance iron) the flation u 
bcibrt* 

tn uflng the plain table, choofe fuch a point for jrour fla* 
tioli ai (hall have an obje/^ both before and behind the 
itation point, if it be pulFible : and in moving the table 
from one ftatfon to another, it will be necrfHry to prove that 
It bo ftraight in the line towards the objed^, and alfo that the 
diftance be rightly laid down on the paper. To know whethei* 
the table be fet ftraight in the line, move the table about till 
through the fights of the index, you can perceive either the 
fore or back object ; then go round the table, and look 
through the fights at the other end of the index, to fee if 
the other objed\ can be perceived ; if it can, the table is in 
the line, but if not, the table niuft be Ihiftcd acconling to 
your judgment. 

fo know if the table be in the right part of the line, that 
Iti if the diftance has been rightly menfured, fix the table in 
the fame ppfition as at iiill, and lay the index aUmg the (la* 
tion lines then turn the table alxuit, till the fore und bark 
objet^^t api^ar through the ii^hta, and the needle will point to 
the fame degree as at full ; then lay the index o\cv the tlatiou 
point, and any other point on the paper irprelentinir :\\\ 
objt^ which is feen from the (lation, niui if (he fame objeot 
appears llraight through the lights, the tl.ition may be de< 
pended upon as right, but if nor, the diilancc mull \>c cxa- . 
tuined and cqrrc<Sted till the laid ubjc<^^ can be Icon* 



250 or MrNSiUHAYIOHf 



O/' /A{/>iw^« the Pap^r on the plain TalU. 

\Vl\cn the pajKr it lull wiitteni nod h i» ncccfl^ry to cot)< 
tmuc the phn upon Hiioihcr flircti ili«w « line through the 
lanheft |K>int of the laft ihitioii line* then t«ke the iheet ol^' 
the table, and Ax Huoihcr flteec on» druwiog « line upon it 
in the mufl convenient part tor the reft of the work i theu 
lokl the old flieet l^k» ilote by the line drawn upon it s 
ap|>ly the edge to the Vme on the new flieet of paper» and iit 
thry lie in that piifition continue the laft itation line upon tWo 
new Iheet. and alio the reft of the meafurei, beginning at 
where the old flteet left offi and fo on from one (heel Hi 
another. When the work is done, the flteeti are to bo faft* 
enetl together into one plrce» i\nd the |lne« In each flieet t» 
be accurately joined together. 

It mutt here be noted, th^t the faid joining Knee upon thf 
old and new |hret»» mutt have the lame inclination with regard 
to thcpolnu of (he con^pf*. 

3, Of the Theodolite, 

ThiA is A hiau i ucular ting divided into 360 degreeii wuh 
an nuli'X^ w ith ojHrn lightf, or a triefcope moveable upot) tha 
crntic i alio a con^i^aU to point out the bearingii ht. The 
y/\\\Ae 14 ti.scd by the crntre npi>n a ftand. 

When \\\\^ inllr\iniciu i^ ufed, a Aeld-book ii neceiTiry, to 
note do\\n <ill iucaUMc&» a^i^le^ ^c. to be remembered when 
the plau la ihawu. 

In uiin^ \\\U iMthnnirnt, any llaiion may be taken at a 
jmt^t^il mod i'oiudtienr. hut it ii hett to take a (Utit^n from 
whiih moll oUjei'ti van hr Ireu; aiul it \% nercllary at every 
nrw \\ix\uM) to ll\ the ThroJolito in the fmne |M)liiioi\ by 
niiMiu of viewing the loir uul hack ohjciUii, and the com- 
pati J }\\ ill ulHii* thr plaui table ; rr|;iileung in the lield« 
lHn»k tbi- lunnbri ot ik^uv* cut otf by the index in viewing 
cai'h object. 

The 



OF MKNfiUnATION. 357 



Th« beft niethud of u(iii|r thia inftiumoiic w Co drAw a 
Urgf circlcj quurter iu And mark upon it the number «)r'dc* 
grMi cut by the index, In viewing each obje^ i then by 4 
pamllei ruler, drnw frwm ftution to tUiioni linea {mrullel to 
the Unci drawn from tho centre to the rclpe^tivc potati of 
tht clKumfcrencc* 



4. 0/tfwCr(i/s, 

Thia inftrument ia only two pair of lighta, frt at right 
AAgIca to t-ach other upon u RAtY with a (liarp point to Uick 
in tht ground. 

The crola ia very ufeful to menfure fmall and crooked 
piecea of ground. The method of meafuring them iathia: 
mcifaro a bafc or chief line in the longoll direv^Uon of tlui 
picMt from corner to corneri and, while mcaAuing ir, find 
the placea where (^rpendicular linea Ihould fall upon thia 
linei from the feveral corneva and l^ettdH in the piece, with 
the crofa, by fixing it upon fuch parta of the Hue that thrmigli 
one pair of the lighta lH>th ends of the line may be (vc\u and 
through the other pir of light*, the corrcfpohdinj; lutgie m 
anglea may be feen, and then meafure the length, &ii\ 

There are alio feveral other iaftruatcnti ufctl in furveying : 
aa the Circumferentor, which refemblea the Thcndolite both 
in ibape and ufe ] rnd the fciuicircle ufed for takinj; anglei, 
ikC% and :he reianibulRtor, for uicafuving rondii and ttthcr 
great diftancei, on level ground} it hu^ n wht^rl of 8| feet 
in circuihference, upon which the machine turns and the 
diiHiQce meafuvcd ia pointed out by m\ index moved rotmd 

by elock«woi k. 

Levela are inftrnmenta with telefcopei or other light?, ufed 
to find levelt, or how nnich one place U lnk>htfr than ano« 
then 

The ofTiet-flntT ia ten linka in length, and ufefuI for mea« 
iurlng the otfteta and other Ihort diftancea. 

1 There 



iW^^ «f M» 


M\f* 


^^^^BH 




■^ 








n(.A 


rWm , for by |J«n«>"K •«' 


1^, lU 




■r* n«f7 cilri >h olixh t< 




- • 




rlAtn 


iiwr, puucuMr 'n l« 


i,,MA*U«lr<.ct(.|iih(r. 






f >wr (nil M • M4 W>Ht > 




.;*< 


4)(l*<ii(i,fcc titf'tx.iroi 










:vif, i| 






, ^iU. 



t^unn «-/ titc lueld.U<Mk. 



_A_ll7k «<i_ 



90 



Pay'i hedge. 



tQ [iruwit't (ymd. 
IP Sh«ep pen). 



OF MBNSUnATlON. 359 



Herci in this fyftcin, the book ia ruled in three columnij 
the mldille one i» for the ftntionii anglei, bearln|{t| diAancei 
mealbredt &c. and thofe columni on the right and left ire 
for the offif ta on the 1 ight and left fidea, which are fet againft 
their correfponding flguret in the middle columni and alfo 
for fuch remarici aa may be neccflary to note. 

Thui ^ I in the middle column ftanda for the firft ftation 
where the angle or bearing ia 10* so\ On the left flde againft 
JO links ia an offaet of it linka to the red houfe. On the 
left at 0| or the beginning of the principal linei ia an oAct 
tt%i Unkaiand on the right of the ikme day*a hedge beginai 
nt t4 on the right an otftet to the fame hedge of 40 linka. 
and at 50 the fame hedge terminateai and at 040 an offiiet of 
•0 tinki on the left. 

A line la to be drawn under the work, at the ^i\d of every 
AatloQ llnei to prevent conftifion. 

Notwithfttndlng the fleld-book ia In very general ufe, yet 
« nnore readjf methtnl ii to draw by hand a rough figure rc« 
ftmbling that which ia to be meafured, and write the dU 
menflmia aa they are found againft the corresponding parta 
of the figure, Thia method may be prudtlfcd in moll cafe^i 
where the furvey ii not exceeding large and intricate. 

PROBLEM I. 

TO IIKAaURE A tlNVi Oa PUTANCK, WITH THR CHAIN, 

After l\uving fet up a picket or ftaiion-ftuff at the end of 
the line to be meafured, two pcrfona are to begin the mea- 
Aire at the other end of the line. One perfon i« called the 
lendery and the otl^er the follower. 

The leader, having one end of the chain, proceeda forwards 
In a ftralght Ime towards the ftation ftaff, (u* ob}vc\ rill he 
has advanced the length of the wh(Oe chain j the follower all 
the while ftandin^ ft. II at the beginning of tiie line, holding 
the ring, at the otler end of the chaiiii in his hand. When 

'A 2 thtt 



iftn np Mf'.W.til/HAllOfy. 



■■HMMHHMM 



ity ittr NIowrt iVf«v)Mij hi9 hiiml fo fiff Hj^hf, #»f Iftflf till (b# 

Ut\\ttwh4 irtfft Urn )ti the (Aiu^ \U\P wifti f t*«F /tmrh u$ t^ mcM- 

tlM' f hftm (hr i'()H|i( |iii»v)d«fl wuli tori /^»)f«ll ciMnHtf ^^t flmt 
puipfiif ;• i hf" t^tit^t Uftvttig tt»« ttrttiw ill lifr ^ftnwtHf rt^ 

Wftffff m»il»ilr» l«y ttiotirig biitrf^lf tmt^ tiiniy tnUf (ill h«> 
Ut\hn*i tiff) li/liiiwfsf und (be^ fiifl nmik tMitb m mff> tii»«i 
)mv)n{S tliPM^firef'hml ib« rlmini Aiid Outk 4lMWiiAM/fb» 
lirriiWf «» hitttt^, ilie fM^iMWer tnki^i U(/ bin Atr^Wi mt'l fbqr 
t^ifl* fMtvf^m (( ftiu/iiiei fhdiM Inii^fb < ihm \hty tmti^m i(y 
(i^i tilt III) fbe t«ii nrrowiv iifi$ In ibe bAiid(» of tli« follmvvr, 
Aiirf (h« kfiiiler in MdvMnrert (o (lt« 0ttd uf the «l«v«fliti ebitiM 
%vtf Itf/tit »ii iim/w ^ tbe yiiiwer iUeh fefl4» or bfiitgn rtif t«A 
Mfrmvif m lbs Inifle^i »hA ihey prtn^tud oti Hn bcfeftf. Tbyn* 
f bf" Mrmw» 0re rbiifi^ii (turn i\m tnui ty (b« ofliif «( fb« fftd 
of «v«i/ uii tbniiin. 

|'MC)I»m;m If. 

tn tApp Aim I, tin AMM nPAnttiim. 
|,r» ( ' |l |,i fM/ii .,li)«/l5, .mm! 1*1 it lir i»fjiiitril III l.iltr tli- r 

I //'//// ///./ /'A//// 7/////r 

n=UMl, |,lrtl.« II rff ll.r lU.iMM (i, .IM<1 ri» fl |.}„, fti f|„. |K,J„| .^ 
Dm MHn|>f«H;c, ii, fl |,i,},., Millie |MpM,»oh|M»fMll lb«» |»fnt.f 
f * . UiU^ |»v »|if li.lf n\ t|,j4 j.imit Irty tl,r li'liM U\ f.ljjr i»{ <h 

i'Mlf ^ „n«| IMMI U ^|,.,Uf, Ihll fi.Mll,.,,^ f|,r j,„i„f (,, nil „,„ 

"»♦)"'», IK M»n |„. I*., I ll»i»,iii/h iUi figl.in, ibrit hy fbr A«iM 

riinOrtri 







09 MBliaUIUTIOM. 36 1 

fwmmmmmmmmmf Ji ' ^ ' i 1 i mmmmmmmmmBSSBSsss? 
manntri draw the line C O from tho objedt focn at C| and 
the angle COD on the paper, will be equal to the anglo 
meaflired. 

a. inth ihff Theodolite. 

Turn the inflrument about till you fee the objeA D 
through the fights, and there fcrew the inftrumcnt faft : then 
turn the index ttbout» till, through the fighti, you iVe the 
objeA C I then the degrees cut by the index upon the ring 
of the inftruinent will fliow the mcafure of the angle. 

3. With th0 Chain onlf. 

MciAire one chain length, or any other length from the 
mglCi to both objeAa C and D, then meafure the diftanro 
D Ci and it li done. Thii muft be traniferred to paper, by 
making a triangle O C D, with lengths proportional to tha 
coiTel]pondlng lengths in the figure. 

VROBLKM in. 

TO SUaVk^V A TaiAN(]iUl.A« PIKLD. 

1. fly /At* Chain only. 

Let the field to be meafurcd be reprclented by the triangle 
ABC, (fig. I.) then having fet up marki at the cornerA 
(which is always to be doi^e, when there are no objects tu 
ferve as marks) as you meafure along the line from A to C, 
when you have arriveil aliout n, wherr you judge a perpendi- 
cular will fall from the angle li, plant the crofv, or any other 
it Inftrument ) nnoving it from one place to another, tilt, 
through one pair of fights, you can perceive the marks AC, 
tnd through the other fights the n.ark H. Then meafhre the 
Itmidnder of the line from n to C, and alfo the perpendicU" 
kr nBt thus, having the bafe AC, and the perpendieutar 
n B, the area is eafily found. 

Or the area may be found by meafuring the three fides of 
the triapglci as taught in the foregoing le£lion. 

Z s t a* i7> 



<fl« 



Mt MMnfrKATHnif 



■», /ly fttklHi "Iff M W>"» .Inifltt. 
•nil k 4».M b; ai«f.<ln|| -Ay ••»« 'f^^. ^d ulwig Ikt 
liA tol««<« '<•«"■ *• All, HC. *fwt th* Mfl* K) or, 
(lib, »mI <!.■ (wij ii<l)>i*'>i anxlMi H AMi m' 
MAandn. 



IM* o n I. V. M IV. 
f* Manr a im b •>» r..(n mom bt tbi omu. 

10 ilM M4 l» ntprtfaMwl H ftw *i^.*.l-» « 

A»CO (fl*.i.) ».-("»* fi"'" A lot, wi.i 
■Im«u(mI, 4t>Ul«i|| fU DiM («<4r< im liUi>xli). -v 
In NiMfytiiig alwiil ihU flii||m*l IIm*, •l<a« 

fhf »f«a* cr lb* (an UU«{tfi A ItC ind A ' 

• lMi«il»)f:(l<«i fMllwWMii'llwUi|»<ltl« AUu Cj- 



• nnfit.KNf V. 



HVMVtK or tlMl IT 



I^ Ihr r.*l.t lir ri-)irK&>itt.t I7 ll>c flpi'* AllCDftl'0 
(Ag. 1.) T*l>« n vitw otll'f n«l'l, *ti<l rnn(l'l«« (impNH^ 
bfll bf di«iil«d liiliiliMiif|lM lU'l irafitxtiKiM I indArtfll 
liiln M ro«iiy lii(rf«iuii.», tin) rw hw hlanf|lti M pttlM> 
'Utiit, tt>h Ajinta ti illvulnl tnln l«» ir^/lii«it« AlOOr 
(iUKf, afidthtdixriKlo l-UU. 'tUtn ilw ataaa <<*» 
(WA Irajicxlnin* an found ■•)' incaiii '>f llt« 4(*|{mMlaACr 
FP, ami [irrti*ri(lt«il»t< Hn, ii|(i, lio, |i IJ, Mittltwllt 
Prubtem. am) ihir vm •'( ttre niai'ft^c. Iff t It* bak Cft 
am) periH-fldkiiUf '|I', «• •'■ I'Milrin JIJ. '(Iw Aw if 
t1w£> IWD irH|ic4iuni«, «i<l lrt<u)|l<i )« llta «w at Oil w 
r,«liL 



OF MENSURATION. 363 



Ute* The meafurea of eiich line may be wrote agaiiili 
the correfponding fides of a fimilar rough figurci dt nwn upon 
paperi or in any other nianner. * 

Figures of this fort are, in fa^i divided into triangles ; as 
each trapezium is divided into two triangles. 

PROBLEM VI. 

TO SVRYIY ANT FIELD WITH THB PLAIN TAT.LE. 

Fio. t. Plant the table at any one anglei as at C, from 
whence all the other angles can be fcen i turn the table about 
till the needle points to the flower dc iuce> and there fcrew it 
faft : make a point on the paper for C, and then lay the edge 
of the Index to C| turning it about the point d till through 
the lightt you fee the mark D ; and by the edge of the index 
diraw a Hoe DC; then meafure the difbnce from C, where 
the table is fixed, to the mark D, and lay that difbnce down 
00 the paper, on the line C D. Then turn the index about 
the point C, till the mark £ can be fcen through the fights, 
and draw the line C £« and meafure the diftaoce fi*om the 
ftatioQ C to the mark E, laying the dithincc down on the 
paper, on the line C E : in the fame manner find the ptifitions 
«)f the points A and B; and lay the lengths of tlufc linrs 
down on the paper, on the line C A, C H : then join the 
points by the lines C D, D E, £ A, A B, B C. 

PROBLEM VII. 

TO STXtYlY A PIBLO BY MEASURING BOVNP IT. 

Let the field be reprefented by figure A B C D E F (fig. 3.) 
lUving fct up marks at the angles A B, &c. plane the in* 
ftmmef^t at any point A, and turn it till the fixeil index be 
in the direAion AB, and there fcrew it faft; then turn the 
moveable index to the direction A F, and the degrees cut otF 
will be the meafure of the angle A : meafure the line A B,. 
planting the inftt umcnt at R ; and there in the fame mannci 

4 obtain 



■ 

I 



Ci llicn r>«aiort iK> dtdtncc CD, aiMl take the inttrDf 
tlwo Rv^luic DB, uiiil tUr ihc ait|[te 8; tfa«n meafitri 
C Fi uhI taU tlK tiiKlc F i avd Uftly, luoritrc tbe difiaoci 
FA. 

Taptore iho waih i — uMall ih« tniranl inglct A&C,Aae. 
(pgctbei I uiil ii' ito inxk be rinhi, lb* flun will be ujoal l» 
twice 11 muij hghi aiijtln u ibt Agtira hit fidu» cxerpi 
(oar li^t anilM | l>ut nlKii ilitrc it «n an^lc tW hemii ^ 
vtrik, ■* at F, tad yau ntufufv (lie oulwar^ aiiKln, fubwGI 
ft rn»i toui' ri^ht an|ln, or 360 degree*, and itx rcanabdcr 
wiil be lbs iawan) angle. 

IrllrsJ ol taVinn the iti«:.ii! a'u-lrf. you trtv MVe iho 
nuiward an)(lc], by prodm In^ one fide of eacb angle funbft 
out, lu fern III the ligiire; and If the fom nf all thcouivard 
»ng\rt be Ftjiial to 360 degrees, or 4 right anglai, the WO(k 
i« lif^hi ; liui uhen one of the anglat rum inwirdi, ai P, 
lubtfHa it from the fiim uf the reft, and the rcmaiBder will 
be 4 nubt jiiglci. 



PKOIILEM Vlir. 

II) suavlLV A IIKLI) WITH ClOOKIB HEflOlt. 

UtABCDr. belhcnuiieofthcfiilJ, ('i|;.4.} St 1 1^ 
m.iikd "iUiiii ibo field, at .ibcti, dividing It into aa few fida 
tis iH.lTiblc. TliL-n lirgiii ni iiiiy (Iniion, ■$ *t », anil lucafun 
along ihc imaginary lines ab, be, cd, da, t.iking the obeB 
IS yi)i) nieifuie along the linrt, at a, m, n, i>, p, Set. cithtT 
with the olTiet flaff, or any other inurnment ; which are to 
be ndded to the area of the figure. The iitta it found either 
by meufnring a rfingonal from b tod, wltli pcrpendlcul.irttO 
a, Ifi. or by uking the angle) at the four corncis a, b, cA 
as befor;' (iireifted, « — ■ ■ 



OP uisxsc^jLrtam. ^65 




jy^/r. The area of the ofiMfs » faoBod 
for Boding the area of a triaogie; ortakipg^e 
of the perpeodiculars, for the meao ^iitaoce of 
thus; the offset from o to B lorms a triangle whok 
dictihir is p« But diat from B to D aMift be aieafured bf 
addiag the two perpendiculars togetber, aad tsJkJng balf the 
im for the mean diftaxice of t^e hedge horn the fine be, 
which is to be maitiplied dierebj. 

If the meafuremeot be takeo outBde the oCsets, they smt 
tbeo be f ubtraded from the area* 

PROBLEM IX. 

TO 8URVHY ANY PLACE JiY TWO STATIOJTS. 

Let the place to be meafured be reprefeoted by the hepta- 
fpoai figures ABCD £FG (fig. $.) ; plant the plaia cable 
at m, for the firft flatiou ; then tun: the ta^ic abost, lift 
through the Bghts you perceive d, the other fiatioo. Draw 
the line m d on the paper, along >vhich lay the fidudai edge 
0I the bdexy and then fcrew the table faft ; turn the fights 
found m, to all the objeds ABC, &c. fucceffively^draving a 
dry line by the edge of the index to each, as m A, m B, &c. 
Next, meaiure the diibnce on the ground from m, tbc firft 
Ibtkm, to n, the other ibtion, and there plant the table, and 
lay that diftance dowq on the paper, on the line m n ; then 
Jay the iodea by the ftation line m n, and turn the table 
about, till througli the fights you perceive the other ftation 
«, and ihcrc fcrewr it fail. Laftly, direft the fights fuccef- 
€«eiy to all the objeds ABC, &c. as before, drawing Jincs 
horn each, as n A, nB, &c« and the interfe<aioas of thefc 
with the fbrnoer at the points ABCD, &c. give the 
of the objeds, or bounds of the figure. 
The Umt method mu& be purfued in furveying with the 
tb ce do H te,, or any other inftrument for taking angles; 
attineiy, mcs^urin^ the diftance mn, planting tlie inftrument 
firft at 00c ftatioD^ then at another ; placing the fixed fy^h'i 

" in 



I 



007 ab|oa« MUH <*>■ ^*% ^**( ''■' **^ '■"^ 

Ttak iM«rT*iMM Wi« phiiarJ, the Inwrlaciwa «^ ife 
|i»m ffm% As bo— ii of liic IfUMt m lirtmc 

II aw iIm •brattl cuHMt be fifcn fttm l«n» Ouioai, tfam 
mom taUMy msr ^ ■>'*4 1 •Uty* a^fanng ibt cAmw 
ffoa am IbuoM w iWMtiiv, P^"K '^ inSbamm m iIib 
fM« poMon x ewrjF ftatkMi. uul bunt ndi OinM aU' 
binsg avoy obfuA ihtf cm be Croi JfoiB i% br uk<p| Hi 
•nfrfv pntnoHi litl tbc ptm sf c«crf ob>ra b« iWirtnl cJ 
1^ tlwbuiicaiMuof iwuw iHME tiuM— chtmo'duMiite 
Uller. 

TIm itiiioo* n>>y (k uIu^ ciilicrwlthui Acbwiiwlo/tbc 
tffarc, nr 10 oar 6dr, w m ■ dtllMirc, and (rktoul Unr 
UMld»alibe A|[>ue. 

In (hi* nviiwwr fOffsitnlv* Tiirvrv* mty V tiVcn, of 
UiRi tliiitfi, wiOmiii o.tering itirm i or ■ fiirvf j m»)r be 
ukLM '.I ;i •.rjiiniiy, »r aiiv |'jrli ol 3 coimrry, by ukiug V*<t 



Rt marks. 

. . ■J'A.r -i.l ilie anglti J^l-rcii ilic rtiitlrtos rhat we i»f««fc 
r..ry, alwiy. ii.caliil.n|- ll.c <liaiiiK<. li'>m Aaliun (•> (UWO M 
,. i';;ht Jii.c. Jri iiiealuiiiif{ uiivol llic ll^iioii (iittanc«t,Bvk 
v.licrc tlieli: liiic^ iiieLt Willi f\y diC'.;bc^, liedgei, [m4^ 
i.vuieli, or i)ilii:t iciii:iiku'iil(: ijijjr.cls, liy nKii1Ulin| ^ 
i.ilhr.tc t'luin llii: IlaiiiM line, :ii (1 vih':ic tlie fKTf>«ndiciilir 
1 1 I'll. 1: tiifi iii.it Jiiic : and .11 \«ii iiiealiirc alotiij any mai 
il.,(ioi. line, take die '>lt'Hi£ 10 ihe end* ol all hcdget^ «4 
i» ,iny iwiid, lioufc, livuki, if.-, aiitl Ix cjrclul to ia.'f 
II .iikk III 1I1C intcik£)io[i6 of all licdjfei with ilie HaiiMiliHi 
tii.i! •j.ni may Liiuw wi.erc lu iiicalurc fruiii wiica yixi UMK ' 
('. ("^iMiy (licfc paiiiciiljr places. By futli nican* sll yMi 
UiiMi tiiiti arc tu be itiLiiluretJ, aail tbc lituattOAdftf 
|,l3cei ttdjoiriing to tbcm determined. 



OP MKNSURATION. 367 



«• The inner parts of the i'urvey niuft be determined iii 
like nwmieri by ucw ftmion lines i taking inner ftation* at 
tfaofe piooet wliere you have the greatell cumniand or view* 
JMcifure thefe flation lines as beforei and note all the inter* 
feAions with hedges or other objects. Thus you may furvey 
theacyoialng fields, by taking the angles that the fides nuke 
with the ftation line at the interfedtions ; and meal'ure the 
dilbincei to each comer from the interfedtiuns { for every lla- 
tloa lino will be a bafis to all the future operations, the fitu* 
acioii of all parts being entirely dependant upon them ; 
thweferQ the ftation lines fltoiild be us long as itoUiblci and 
Ihonid be fo contrived as to run along the hedge, or bound 
of fome fieldi ur to pafs through iome angle. Thefe thinga 
being odjufted, you muft take more inner ftations, and divide 
andftibdlvide till you come to fingle fields* repeating the fumo 
work at the inner (bitions as at the outer ones 1 und tuko 
notice how one field lies by another, to place them properly 
in the draught* 

3* When an eftate is fo fituated that one part cannot be 
fecn from another, it mull bo divided into two or moro 
portSt and each pui t furveyed fcpurately, as if they Iwlongcd 
to different owners j and at lall join them together in the 
plan* 

4t In laying the lines of diftances down upon the paper, 
it u necefltiry to have a fcale ot a proper length. For this 
purpofet you mull take the length of the whole eftate in 
clMim, and conlider how nm\y inches in length the map is 
to be, and from thefe you may know how many chains theie 
muft be in an inch on the fcale s thus, if the length of the 
elhle be too chains, and the map is to be so inches in 
length, a decimal fcale fliould be ufed ; and each inch on 
the map will contain lo chains in length, a tenth of ai\ inch, 
1 chain, flee 

5. When the ftations are long, a good inftrument fliould 
be ufed for taking angles : und the plain table may be ufed 
for the inner ftationsi oa it it a quick.and ready inftrument. 

3 A 6. When 



36R or Mi;KAiti\ArtoK. 

r\ rrv other nsmdi kiibli! obji^i In tlitlr pmptr fitunttmi. 



lMU)ULt:M X. 
iH nvktnr A t.AKDv TRArr ar lanoi or a cctUNtv. 

tt In ihoofinK ytmr ft(itioiu» let thtm b« on the top of 
fomcrniinrnct^l ii«| high hllUi mnmUainti t<»wtni chiiivli 
llvrplcR. Arc. m\\\ furh nn mnutiaml the grcttteft vltw, mul 
('All he Irrn ( 1 om r;n'h t>thri i nnd ni f^r diRnnt frQn\ cacU 
othm- t)i potUUIci Kiiile o t)CAconi nr flrtg, of h diffisr^nttivloyrt 
flt rrtrh« to be viliblf (Vom thi! other AAtioniift 

t. Diint flii|{i Alio At filch of thoAi pUtic« yCiii (Itfmld «Ur» 
t\ng\)l(l\ in your pUn^ Axing thrm npnn th<« tt«pi of fhuirh 
(Irrplf >, hoiUb, Jkri nntl thunfi^h)!^ then\ to other pktitt When 
ncwirrtir. 

^ *rhrti f'tviti iMic (t;t(ion tjikc M ihr anglfi bftWren the 
oiliei (lAiiim «ndeMch ttf ihofeimiks ohfrrving tht dilTei 
ent ntlouit ttt the tti^i^n, nnd note thcnt do^rn ht tiM pimi 1 
fionnhf oi)»rj lUiivMi irtko nil fhr nnj()<> Mwern the tlrO 
rtrtttoh rtn«l r;^\h of ihr foiinn hmiKjii :uhI note Owmo doxui 
m thr plnn .tlio .i^vuntl ilio l:un( titlouirit in;trk ; it it W 
'*••« rit}«?v. fhr unr.lt^ M^AV nlli» h« tjikrn i>oo\ ;» fhii\l ll.iiion. 
\\\\u\\ w\\\ (kwc «o pro\< thrwiMk, if ihr tlVn* hne* iiunlWi 
rAx \\\\\\\rv\\\ llir t;Uiu* poiht. Thr inlh\u\u^nr tni talking .iokIc* 
towrt he ntl rxiYnlinj; jh»Oil one. A ri»t \nnfrirmor U llw IkU 
ol liMii ot fivr f<*t't iMiiiu* \fcilh irKfii^pir ltv;ht"% 

4. It IS not i\v'n lUi V lo mrininv rvnv <hdrttu't>, IvrM^ft 
MU OtMi«M\.it\ linr i'rin^^ rKAi'Hx \a\A down (lOOi ;0)V h'rtlr. 
i\\\ (hr othri linrn will hr |M\\)\oi(ion.d In it: t^it t'ometiwc* 
>i !;> nnvll^rv to n^'Ahnr Ihr dilt.in\v o( a plnvr in luiln 
:*»\»l >n incrtlnnnjj h»n|j ditl.uuT>, il uill nol W rurtrt rnoWfjh 
«o n»rrti»iic rtlooji the hij;h nnidiii hVMMton of ilioii w-indiii)i'>i 
but Ihr l>od wnv in, to OK^afuiv in a itiMi^hi hnf, o\TrhilN 
nul dfllc<, .lo^l ,ill ohlt,iv'ki». tl poihlilr » hut where it » o<>t 

|s)lhhlc. 



or MEirtuaATiuir, 369 

fiSbltiAilrib purtiiaHift be mtirttred by th« niMlkod or m««- 
Airing IpMMAUf dilbuMM. A good Qomfaft U iilfo neccf* 
i^ty^ It ihiw thf btarbig of the Iwo ftationi, And to dtr«ft 
you C|» g9 Amight when you do pot (jm ilir ftAtionn. 

{• JPiwn M your ftitimui and in the wbole progiTf*, 1^ 
jvfiy tuiM in obftrvlog «11 re maiioble objcAH 1 »f, towni, 
MftiMi f4Wi^H windnMliif rivuletiy bridges. &c. \c. 

#• HnriOiU^n your ol)(frviCloM IVom tlio m«ui ftntioni 
n4M^ Pfimmni the vrhoti aMjntry, thcii procef4 to take 
jbwr fttliOttf I IS in Amreylog Urge «ftttes ; and from th«fc 
4(Mr ftf^M* dittrrmioe U^ pliu^ pf «i many of the remain- 
JAg feowi^ |s you ain I imd if «ity reiunliii tlie fuuntion of 
^vU^yo^OMnottiiXei tAkienioris umer ftAtioiis ; and thus 
peeMWl tbiwgt^ 'Al Jthe (^nii taking 000 lUtion after another 

p |4iHyi lake the pofitton of die ibtion line, with regard 
eo ite llotiKl of tlve compafii by an aftronoinical {^nx^efii a» 
Jt^lovt t j^ABg a ptumbet in the fun, over fotne part of the 
ftatlon linei and when the fliadow ol the phmtbat line runs 
ilo^g thia ftation Jiuc^ at that moment take tlic (\n)*« ^Uitut^tci 
ihe^i having his declination and the altitude of i\\c plnee, the 
ig^ulh will be fo\md by fpherical tri^mumicit y ; for the 
aitmuth is the angle whiuh the ihiion linr n).\ko« with the 
meridian: and thui the mrrldian nuy be dnwn tlunitoU tlw 
inapt 

puoBi-KM xr. 

TO iVRVttV A TOWN, Oa <!ITV. 

The proper Inftrument for thi* purpofc ii the plain tuMe ; 
«a tbe diftancei are not very greati and every |>art (IkuiKI br 
laid iown while in Cf^^M. 

Take ihe Itrft Aatiun at themeetinfr of two or more ol 
the principal ftreets, in order to get tha longf(\ lt,itioti lini*:. 
t)Mn draw the lines of dirrAion to reprefet^t thcle (Vret* ri: 
having choien objr^!*, menfurc the ftrce t«, and l^y the mru 

\ A "i tui'cp 



37P M utmntmhrton. 

ftifct down from s fe«le, on the Imei on f he |M|Mr« uWn^ 
offtru with the ll«ff| to ill txtKUnc* and wMing* ht rib 
flrwift Mid to mII rentarlmblc ohje^ i tbtfn fdVe Miother !•• 
lion in one of the foregoing IHieff and retNWt the pfoceff . 

ThiH, (fig* 60 having chofcn A for the firft Aalion, dnw 

tiro linei in the diicAion of the two flrceti niretfng there i 

and meafiire A Bf marlifng the flreet on the left, and Uy the 

Imie mcaftire down on the plan \ let B be the fecond llation, 

from which draw the dircAions of the flreetfl mcetini^ there 

ineafure from B to C, noting the cnd» of the ftteeti at n and < 

a« jo^A f«fs them \ and lay the fame meafure down on th 

p1ao« At Cf the third flaiiony take the dirrftion of the fltcct 

merfing theret and meafure from C to D. At D« the nei 

llation« do the famet and meafure D E« noting the crofi lira 

at p; and in the fame manner take the direflioni of all \\s 

prioeipal ftreett, laying the meaforei down np^m the pl^r 

Then pnireed to the next fmaller ilrcef 9 ) and hiftlyt to th 

lanct, allcy^^ coiirls && ufing the iame procefii fbroaghoi 

the wliole. 

AVr. In taking the furvcy of a town there ii no ncceffif 
for h^vin^ tth')tf\% fix*-'! up, «« xV^tf ^f ^f.n?ra1^)' m'^rV 
cnoD^li to fTvc a* o^j'.'l*; fiicli f*i til*' *\*i'>r% 'iT window; « 
bcufe)i| ^r 

Ok PLANNINf;, CASTINC; VY\ asd 

niviuijM;. 

10 LAV f »0 W l» 1 M r i- f, A V OK 4 ^ fr » V F V . 

Wlifii the fiirvrv »< taken hy »hr pbiii » jM**, .i roiijrh «lr « 
f»f »hf plan !«; ahr^'ly fli^wn on »lic p:»|Kr ; »nit wh^r« tl 
fiirvry ii t;ikcn with any othct inOitiinrnt, the plan i« to h 
dra«^r» from thr nKafiircf l^kcn in thr fuivcy : fir ft, i lo'ij; 
draft t% to Iw dr^wn on paprr, inwhuh .i\{ thr hnn ar 
angles nniA be l»id dov.n in the fjtiic order in uhich th*. 



Ot MKMBURATXOK. 37 1 



wen UkcQ in the furvey } laying down flrft the angleti then 
the Itsgthi of the lineii with the pUcei of the oflfseu ; tl>en 
the oAeti themfdvcs. All thefe fliould be done with dry or 
obfcure iinei ; then n black line drawn through the extremi* 
tiea of all the lineii and the offteti will be the bounding lino 
of the whole plan. 

After the principal linei and botindi are laid down, proceed 
to mark the fniullcr objeAii till every thing be laid down thit 
11 neceffiiry. 
The north fide of the map or plan \n commonly placed 
vpptrmoft. And in foroe vacant part • fcule of equnl parts 
tnoft be drawn. All hilii muft be fliadowed, and all hedges 
coloured with diifcitnt colours ; all hilly grounds fliould be 
drawn like broken hilli snd valleys t ioot*pathi are repre- 
fented by fingle dotted lines, and roads by double onet. 

In taking large lurveyi, all oblique lincii fuch as aro 
meafured up and down hilli, muft be reduced to ftraight linesp 
by making a proper allowance 1 for which purpofe there k 
generally a table engraved on fome of the inftrumenti, 

VllOBLEM II. 

TO GAIT UP THB CONTCNTI OF A TXXLO. 

This is no n>ore than what has been taught in the fiilt 
fedion of this chapter, ft^v finding the contents of figures 
whether there be triangular, fquaie, fuurfuied, polygonical, 
or circular figures, by the proper rules there delivered ; then, 
having found the area in links, nicer you have cut off five 
figures on the right hand, the remainder is acres. The five 
feparated figures are to be multiplied by 4 tor roods, and five 
figtires cut off from this produ^ are to be muhiplied by 40 
for perches* 

In pieces of land bound by winding hedges, in meafuring 
the ofisets, all the pares between the offsets ara accurately 
meafured feparately, like fmall triangles or (rapeaoids ; but 

(onetimes 



»• ' ^ 

iMPc^ih } Ni thii Uft imibM) U mm v^ry <mji^^* 

Uut in v«ry brge fur¥e>>. <iiui \vher« ther« are mhh> iWi4i» 
|K« U»A v^4X «^ iiod^iti^ ib« €txnir4Ui cif iht wM« U i\> ky^lv 

»imm mh) iri<An]j[Vs «aJ fiu^) the 4)C4 of f«ch ii^|mM<)y» 
»ml «tM tho^i^ lfi|Kcihfri itv^ la |»k^v« ihe w«rk, divide thi; 

by dinwing mm Ima m Uw fim \ wA tfih« ^^fmifi^vi wm4 
by thi* toft wtiM N i^^mI itn tb«i i^mUflU I^hmWI by ll^ 
ioriutr Awth«d» Ui9 \v«ili i« t i|{bi 2 Imi tf thfy k)i#w» tbe 
^ork vmA b» «««R)ittMi «nd r«v«)^>|MKHi liU (hoy «MMaf)) 

Uuf ihe iiiii^f difti^Mby in c^lU^ \t|i the v^icm^ «h<«a 
b^m ihe tii«)e« «if i)h» i^ore U>ii^ UMfv«k)^ or «4' m^y «M.b«r i»ih 
gu)4r Amp* ) in whiph c^i^ (ueh Ii^mi^U oi iU« ti^^^Ht amiA 
b# fvd\w<il to ftvAij^ht linvii in the foltawin^ manner ) n^ak* 
a I'uwil Uwv wiih 4 |Mcc« of horfe-h<)ir» ai\il v^hAl^Uwe^ or 
i Ant iw M\\ o(!\cr cUltii i'u^O;tiu v, \i \\w\\ >v kl| kit^^ (h«; hiUU'- 
h<«u « \ui\vlcU 4( luU ihtichi thru 4j\j^)> ihc WuVt^*u iw i\\v 
ii\H>ke%) lH»muU 01 ihw ln)*utf t ia uuh 4 md»uu*»^ t!\<i! iluv.o 
ixiiii&al ihv; ciu'vt whtvh <krt on ixt^e lulc ih« h.«u a^^^y (^ 
c^uaI to tin? )\<ui« ol lUe curv^ oh the otbei ttiic ih<r l^ir ; 
then, by aukin^ hvt> |Ai^»iA» iUaw 4 Aiiii^ht hut iu lUc Ui« 
itiMuxu (Jkt* lUc hotirh><n, whiJi will he 4 lli4i||hl tuir u^ the 
ii^\ut;. t\\\\4\ t\^ the iui>i^ oi^e. l>o the M\)w hv v\«^4y ^ ar\< 
t«iiv ot the tl^urvi tha4 lh« Itj^nte m<iy he \\k).KA«l mio a 

Thfir are iVwr^l nKthi^)i .»l |vit\»,,\>.H^ i!»\4 j t'ouk of 
<r\V.uh I Au)! lUi^iuiou : 



09 MltN«VltATlQII« $73 

¥irft« Rub the back oi the pUn over witli black lead 
powder» and then lay the black fide upon ihe (beet of |uiper 
on which the plan la to be copiedi keeping it fleady ) then 
with a bhmt point of a tnicer, trace over all the linea in th(« 
plant preffing the tracer lo* that the black lead on the back gf 
the paper imy be traniferrc^d to tl\e clean paper } then tako 
qS the plant and you will ice all the nvarki on the clean 
|iapor in black Uail, whi(;h n\uA be traced over with a pen 
And Ink, 9ic. 

Secondly. The plan n>ay alfo be tranaferred to anoU\er 
l^apert by dividing both rnda and fidea of the plan into any 
convenient number of ctiual parta, counting the cone« 
fponding pointa of divifion with lines i which will divide the 
Whole plan into a number of fquare«» or )>arallelogi'nu\a t 
then divide the |>aper upon which the plan la to l^ drawn 
into the fame number of iquarea or parallelogruma j next 
copy the paita comaiutd iu the fq^area of the «dd plain i'^ 
the eotieipunding fquavea of the new one. (See Itguiea 40 
«nd4i.) 

Thirdly. Another mctlu>d h by the inftrument called 
a pentagraj^h, which will copy the plan in any li^c re- 
quired, 

Fourrtily. The l>cfl method of any H the follow ing ; 

fix the old plan on the front of a copying frame of glatai 

with the face uppermott, (which ia a largf fquare of the belt 

window glafa, fet in a broad iVanie of woodi anil eoniU\K^e4 

ib aa to he raiied up to any angle whatwer), with the clean 

paper on the hiQ9 of the old plan being tinted to the fiame 

by feveral pina 1 then the frame being raiiVd «p facing the 

windoW| by mcana of the Kght fliining thr^Htgh tht) \\\\kt^\\ 

you will perceive every line of the plan through the clean 

paperi whkh ia to be drawn thereon with a pencil \ having 

copied that part which eovtra the glaftii the other part ia to 

he brought over the glafii, and copied aa befor«i and fo on 

throughout the whole. 

Then 



37i OV MBMSURATIOK. 



Thtn tuUe them Ai'iindert ind trace the linei with pen and 
ink ( and finifli the piece, writing fuch names at are neccf* 
fary. 

Thus the fined plan may be copied without the lead in* 
jury. 

The foregoing rules will be found fully fufiicient fo in« 
ftriiA any ordinary capacity in ail the praAieal part* of 
Hcnfuration and Surveying. — I have avoided every thinjj| 
that fuvourii more of curiofity than real utility* 



w^mm 



SECT. m. 

OV HOIW Mh.itiVnV,, MiaHIJHING TIMDI'.Hj DIQUINGj 

AMi OUAUIMU* 

1. Solids a\c fuch bndit-'fi ihar have irjj^'tli, hrcadili, and 
ih'u-kneia, 

2. A pi ifm 15 a folnl Iwjdy whoic i^nd* air fniular und n|iial 
liliiih ^guicB, and iu iidrb are parullelogranis. U is called 4 
liian^uiar piiiin when im endii uic triaiiglrs (ae tig. i.in the 
iolidb) i when iu ( luU uu f«juare&, a ftjuare prihn j when 
pntiugonit, a pchtat^onal pi iiin, l<-c. 

:\, A cube is a fl|iiarr pnfm, having (\\ npiul \\\\\Mt lidc« 
perpendicular ii* twcU ntljcr, (I'ig. a.) 

4. A parallclopiptrdnn \& a ligui« liavmjj lix mAangnlai 
fiilcB ; fgch two uppuliif lidcB being f<]ijul, und paialUU 

5. A cylifulci is »i round pulni, havii»;^ w.j t«|u:4l cji<lfs 
furicsendf. (Fig. 4.) 

«; ^. A 



OP MItWiVl lATIQIIt 37J 

6. A pyramid is « figurt th«t hm « right^lintd flg\irt for 
^« bafei ipd CAch of iti fidci ii « triai\|lf| whoft Ytitkta 
Mfl in « point «t the top, which ii oallcd the yemx of the 
pyramic^ «l A (<ig* sO The pyriiaud takei its name from 
the Igure of iti bale, like the prifm, 

7* A cone ii a ixiund pyramid, liaving a circular bafo. 

I* A fphere it that folid body bounded by one continued 
eoiivix iUrface, every part of which ii equally dilianl from 
Ibe centre. It may bo Aippofed to be formed by the revo* 
lutioa of e femiclrcio about its diameter, (Fig, 7O 

9« The axis of any folid is a line drawn from the middle 
of one end to the middle of the oppoflte end. Thus the 
axil of a pyramid is a line drawn from the top, or vertex, to 
the middle of the bale ; and the axis of a fphere is a line 
drawn through the centre. When the axis is perpendicular 
to the bafe, it is a right prifm, or pyramid j othcrwife it ii 
i>blique. 

10* The height or altitude of a folid is a line drawn from 
the veitex, or toj)) perpendicular to the bafe, 

II, If the bale of a prifiu or pyramid be a i^gular figure,, 
It is called a regular priim or pyramiii 1 but if the bate be 
irregular, the prifiu or pyraiuid is called irregular. 

la. The fegmcnt <»!' a pyramid is a part cut olf the top 
by a plane, parallel to the bufe, as C E, (tig. 6.) 

13. A.fruftum, or nuuki is the prt that remains after 
the fegmcnt is cut o^\ as K A, (fig. ^«) 

14. A xone of a fphere is a part intercepteil between two 
parallel lines. 

I J. The fegment of a fphere i« a fegment let than a 
hemifphere, or half fphere i like a c(Mie, whofc bafe i« the 
fame as the bafe of the fegmcnt, aiul whole vertex pafiea 
through the lenire of the fphere. 

i6, A circvilar fpindle is formed by the revolution of the 
fegment of a circle, about its chord, which remains fixed, 
(F\g,80 

^ B i7» A 



^ft OV MBNSHBATION. 

-i-pa- .11 - -i-i. - ■ ■ ■ ■ ,- mi -J.J -p 

17. A regular body is a fo|id« contamed under a c^ruiu 
number of equal and regular plain iigurea* 

i8. The faeea of a folid are the plain liguret under which 
it it eontiined« 

19. There are only five folid bodies which are regulaii !%#• 
which have each fide equal and fimilar : namely» firft» tlM 
; tetraedron, which is a regular pyramidi having four trian^ 
gular iaees. Second^ the hexaedron, or cube, which hat 
fix equal fquare facet. Third* the octaedroui which hat 
tight triangular facet. Fourth, the dodecaedron, wbkh hat 
twelve pentagonal facet, Flfthi the icofaedron, which h«i 
twenty triangular facet; 

N$t€* At fquare meafure it greater thin running mea^ 
fure, fo cubic meafure is greater Ihan fq\)are meafiire. 



The Table of CmHc M^afiire. 

• 

1738 Inches make i Foot 

a7 Feet i Yard 

)66| Yards 1 Pole 

64000 Poles I Furlong 

^ It Furlongs i Milt*. 



PROBLEM I. 

TO FIND THg aoMDlTY OF A CUBE, P Al AM k t OTlPknON , 

PKISM, OR CYllNUI^R. 

The fohility oi" any of thefc figures U found by the tollow- 
»ng rule : — 

RuiM. F\nil ihc area of one end of the figure by the ruio 
f*»r fiiulmg the area of a luperfices in the forrgi^ig fe^'lion, 
iiml multiply fuch area by the length of the tig\ue, and tht^ 
pio(luw\ IS th? folid »:onteots. 

FX'AMPI I 



or MSNIUIUTION. 




BxAMFLt 1. Whit is the content of « trUnguler prifliH 
wliofe 3 fidei «^ 3, f. and 5 feet» and length xq feet i 

36663 IQ 

♦ -J -J _i -^ ^ 

3 » I 6 Anr.15o feet* 



) 




Here the three fides of the triangular end are added toge- 
Ihefi and from the half fuin each fide is fubtraAed feparately, 
and the remainders, and half Turn multiplied continually to« 
fHher I then the fquare root of the produd is the fuperflcial 
oontentt as taught in the foregoing feAion 1 whicht rnulti- 
plM by the length, gives the folid content. 

Cubes, parallelopipedoni, and cylinders^ have their folid 
contents found in the fame manner. 

^iti a« What is the folid content of a cylinder, whofe 
kngth is ao fect^ and circumference 5I feet ? Anfwer 
48.I4S9, 

PROBLEM II. 

TO FIND THK SOtlDITY OP A CONK OR FYKAMIO* 

Rvii. Multiply the area of the bafe by the height, and 
one third of the product will be the content. 

ExAMFLK 1. What is the folidity of a cone, whofe 
height C D is ao feet, and diameter A B of the bafe 3 feet } 
(Fig. 6.) 

•7«S4 

2 

;.o686 Area of the bafe. 

ao 



3) i4i.37ao 

47.ia4o Anfwen 



3>» 



ExAMrii 



37l 0» MItltlUllATIOIti 

KAAMVtiiA* Wbat U tht foUd content of a'pfnt«|Dbil 
pyramid* tht btlgbt wlttnof U t a fitt, and c«ch fide of tbc 
bafc » iff t f 

i.7i0477 Tab. irea* 

4 

fi.il8i9o8 ArcA hnfe. 
4 One thii-d of the height. 

*7*S*7^3*^ Anfwer. 



PROBLEM m. 
to ttMH tna iottdttt or a irttfeae on otota. 

Kvt.et Miihlpljr the cube of the axta by «$At|6. 
BxAMPta t. What li the foUdltydf a fphere or gtobei 
whofe aali or diameter la t a feet ^ 

t% 

«44 
la 

S tH4 
9^4.7^^» Anfwrr. 



P n O H f. K M IV. 

lO FINP TMP ROMDITY OR •VrPKIIrtPc nf ANY 

■\S ' *•*•«• Multiply the Ubiilar area taken (mm fhr follow 

**|W *"Wc of lurfacei by the ftniarc of ihc linear cdrc ol iIk 
folld. ^ 



or Mr.NHUn4TlON. 



379 



a. For thv /?»//(/ Content. 

Multiply the tabular folidity by the cube of the lincni 

edge. 

« 






I 



4 
6 

8 

ti 

to 



ArtMrr. 



Tetrflc*(lnMi 
HeXAcdrim 
O^Uedrou 
Dodecneilron 
I Icofrtedmn 



Smrf^fttt 



»*73*o5 
6%ooooo 

346410 

A.f)Oot^ 



S*fiMtit9. 



o.tt7H{ 

1.00000 

0.47140 



KxAMPLK t. If the UncAi* edge of the tetracdroti be 3 feet, 
what ii it! fut face ntul folidity ? 

0.1 1 78 5 '•7.1»oS ^uuaic of the edge. 

^ §7 Cube of the edge. 9 

• ?<57o 

,1«i8t95 Anfwer. 



■^1 ■ ^■^*— . 



:^.t. What are the fuperflclei atid folidity of the oAae* 
^dtxitiy whofe linear fide \h t feet ^ Aulwcri ru[)erAciei 
13.8 J640, atid folidity 3.^7 1 10 feet. 

3^* 3. What arc the luperficics rtml folidity of the icofae- 
dron, whofc linear fide ii a inches f Anfwcr, fupcrfioien 
10*64100, and lolidity ! 7.453 jt inchen. 



P u o n L E M V. 

TO FKNr> ritfi CONVKX HUarAtX Ot^ a CYLtM)Xlt| ok TKR 
VI*RtGHT lUaPAOX Of AKY PRtsM. 

Rvii. Multiply the eircumferencr by the height, «nd the 
pi^uft will be the anfwet. 






ruonnKM vk 

Hi>«.te% Multiply tl\(f dWM\^fr»i^\^c^ ^r \ht h^ft hy iKt 
KvAMi^m t » tr rtw tlkiwf^tfi^ »r ih« h^lV >M? J r\?«u i^w^ ^ht^ 

i 



JX 



l»KOttLKM Vn. 

\\\ r\\\^ 1 »u row p> 9\^tt rA^Mi or a «r»uwt ott »-.\ k>*«> 

iUf» |M\mI\uM will W \\\\ ^\\\\X\:\\ 

feiijnwMt of ^\ t'phvus i« fbumi t vlf . In mMlfiplvh\ft \\%f^ 
hK\[{\\\ \)\ tl\e s>ou<i *>i' ligutenl by thie >fc\\\sW vtmimf^tiMH^ 

4 $J»* 



OP MRNIUnATtON. 38 1 

Jl^i i« What ii the fviptrlici«i ot* tht enrth, iti (Immetcr 
being 79571 niilfi, And the cirvumftrcucf tjooo tnilci ^ 
AiiiWcr iv^iy43i7So^4^*^*^ milti. 



PROBLEM Vm, 

rO riND tHK lOLtniTY or the IkOMfcMT OP A OONi 

OR rYRAMlD* 

Tht fegmcnt of a conci «i C B (Rg. 6.) or of n pynimi<i| 
may be conriitci-ed ni nn entli'e cone or pyramid i and thf 
(blidlty or fu|)erficici is found in the fat^e nmnneri and thert^ 
fore iKed not be repeated, 



PROBLEM IX, 

to FIND THR BOttntTY Or THR PRUITUM OP A CONt 

OR rVRAMID. 

Rvt.k t. Multiply the mean area of the end by the height 
df the fruftumi and the product will be the folid content. 

a. The mean aica of the endi li found by one of tlie fol- 
lowing rulci J 

Add the arcai of the two endi| and the mean pwportional 
between them together, and one third of the turn will be tho 
mean arra. 

Or, when the endi of the pyramid arc regular plain (IguitJi, 
|he mean aren in fb\ind by multiplying one third of the 
tabuLir number belonging to the jwlyg^m (in the table of 
muhiplicri, in the fupetficial meafure) by the (um arifing by 
adding together the fi^uait* of a (iile of eavh cnd| and the 
pr^dui^ of .the a fides. 

In the frnllnm of a lonc, the mean area is found by muU 
llpjying the fum of the fquares of the two diiuneterii added 
to the prod^a of the diamctcr?| by .a6tB| or one third of 

But 



\^%% or MKNStlRAttOK. 

But if the drcumfeience bt taken inftead of the diAmefetri 
the multiplier will be .ot6$4» » 

£xAMPLii t. What is the content of the frtiftum of a 
conci M hofe height is ao inchcBi atul the iliamcteri of the 
two ends la and lo inches ? 

Greater diameter ta Icfs diameter to \% 

I a 10 tQ 

bquarc of greater diameter 144 100 teo 

Square of left diameter 100 =* =5 

Trodttd^ of the two diam<teri tea 

7*^ 

y5.ags^ Mean area ^ 
^o Height, 

1905.9040 Anfwer. 

ExAMrt.F. A, What is the content of a pentagon frtilhtni 
whofe height is $0 feet, each fide of the bafe 31 atfd cidi 

fide of I he Icfg ctui i. feet ? 

2 2 



-J ol tabular area •</ U9 

'9 




1; r0i4i 

J 7.MP 
Mean area icHar^t 


4 


S.o 

Anfwer. (,44.81 {;i;o 


nj 



.'•Vv. \, What is thr ffiliiliiv of iho frniUunoF n mnc, the 
Jidgfit of which is 2 ij Icct, thr c licniiih letuv at tin: Riratrr 
end 20, and the Icfs end 10 fret ? AiHwer 4()4,ioq teet, 

ii^isf. 4. What is the folidily of nn hcx;if/niial linllnni, the 
height being 6 feet, the Pule ol the grrator end 18 inchci, 
*:id that of the Icfs 12 inchcp ^ , AnlwtM 14/18172^. 

ruoiH.EM 



OP MBN8UllATI0N« 383 

95SBS9SSS=======S99BBBMnSBB 



PROBLEM X, 

TO FIKD TRB 8VPKXFICAL CONTENT OP A BOAID OR 

PLANK. 

RuLB. Multiply the length by the mean breadth, 

N$ie. When the board it taperingi add the breadthi of 

the two endi together, and take half the fum for the mean 

l)r€adth. 
Example i. What ii the fuperficial content of a board, 

whole length ii ao feet 3 inchei, and mean beadth 10 

inchei? 

J> JDecimsls. By Du9Jtcimah. 

Feet. Inchei. 

BO«B$ BO •• 3 

10 10 



iB )Boa.go Anfwer 16 *. 10 .. 6 

16.87c Anfwer. - - 

When the board doei not run regularly tapering, but ii 
broader in fome parts than others ; take feveral breadthi and 
idd them together, and divide the fum by the number of 
them, and the quotient will be the mean breadth. 



PROBLEM XI, 

To FIND THB SOLID CONTENT OF 8QJ7ARB OR FOUR« 

SIDED TIMBER, 

^Ulb. Multiply the mean breadth by the mean thicknefs, 
***d that produa by the length j aod the laft produdt will be 
^^ TcUd content. 

'^o/<. If the timber taper regularly from one end to the 

^*^^^, t(ie inean breadth and thicknefi ii found either by 

3 C meafuring 



3S4 OW MBNSVUATION. 

meui'uring the mM\e of the piecc» ur by taking half tho fuin 
(4* the two endi. 

Hut if the timber does not taper regularly, take feveral 
tUmtnlionii and divide their fum by the number of theu^ 
tor the mean bieadtl^ or thii knef?* 

Kxamtm: 1, What la the folivl content of a piece of lim* 
beri the length of which ii «o ftet ^ incheHi tho breadth at 
the greater end a feet 5 incht», and at the left end 1 foot t 
inchei 1 and tiVickneft at the greater end • feeti «nd at tho' 
lefs end 1 foot inchen ? 

Us 10 

a)js7^^ a) 3 i) 

i.H7(; meanbrettdih i lo 6 
e*o a o 

1 ,87 f; mean tiucVnelii 1 10 6 
1*^7^ nteun breadth ! 10 b 

g,H7S; I to b 

^^»*^ I b t) 

«_«7j;__. ' 

;i.<;isb4(; ,< b a ,< 
90.^ length «o 6 

yo\ 19 (;oo 1 g I I 

y-i.o7op«q Anfwcr 73 o 10 1 



\^f , a. What is the content of a pine ot' timl»n . thr li-ni;th 
of wlui h h 90. 3H t'tr\^ and \Xi f nd» unnpial lijuare-s the tide 
•>t thr j»ic;itci being loj, and the tide ot ihc leU y^ Irec ? 
Anlwri ov^.P^H feet, 

PRORLEM 



OF MBMSUKATION. 385 



PROBLEM XII. 

TO FIND IHK SOLIDITY OP lOUND TIMBBX. 

The common rule, is to multiply the fquare of the quarter 
girt, or one quarter of the mean circumference, by the length ; 
and the produdl will be the content. 

The quarter girt is n geometrical mean proportional, be* 
tween the monn breadth, and thicknefs ; that ii, the fquare. 
root of their produ«^ : unikilful meafurera ufe the arithme- 
tical mean inftead of it, that is, half their fum, but this oc- 
cafions a very great error in the contents, and particularly 
when the breadth and depth differs much from each other* 

When the round timber or tree is tapering, take the mean 
dimenfiona from the dimenfions of each end, as in the fore- 
going problem, either by girting it in the middle for the 
n^an girt, or half the fum of the two ends ; but when the 
tree is Irregular, find the content of each part fcparately. 

^#/#. This rule gives the contents about } Mn than the 
true quantity, fo that it makes an allowance for hewing the 
tree fquare. But when the true cjuancity is required, it is 
found by the next rule. 

Example x. What is the content of a piece of round 
timber, being 9 feet 6 inches long, and its mean quarter girt 
:i feet 6 inches ? 

Dtcimals. Duodtcimtth* 

3.; quarter girt 3 6 
_3j H 6 

105 



10 


b 




I 

12 

9 


9 

I 




110 

6 


3 
I 


6 


1 1*6 


4 


6 



11.25 
9.5 length 

612 5 

1 Yo 25 

1 16.37 5 content 

3 C 2 PROBLEM 



386 



OF MCNSURATIOK. 



PROBLEM XIII. 

TO flND THE CONTENT OF A TREEf 01. EOUND PIECE 

OF TXMBERt MORE EXACTLY. 

RvLB. Multiply the fquare of -f of the mean girt by twic9 
the lengthy and the produ£b will be the content!. 

Example. What is the content of a tree, the length of 
which is 9 feet 6 inches, and mean girt 14 feet ?• 

Decimals. Du^Jgcimalt* 

».8 I of mean girt 297 

g.8 a 9 7 

fti4 J 7 » 

56 % I % 

' 7 

7.84 fquare of i of mean girt 7 ^ n 
19 - twice the length - ig 

7oJ(> Anfwer '4 8 « S ♦ 

784 === 



148.96 Anfwer. 



PROBLEM XIV. 

TO FIND THE DEPTH» BREADTIIy OR LENGTH OF ANY 
VAULT, CELLAR, RESERVOIR, &C. TO BL MADE. 

Rule. Divide the folid content l)y any one of the three 
dimenfions (viz. length, breadth, or depth), and the quotieut 
will be the product of the two other dimenfions. 

Example. What will be the length and breadth of a fquare 
rcfei-voir of water, to contain 5000 cubic feet of water, and 
the depth to be 20 feet ? 



* The anfwer by duodecimals 16 left in this qucftion than the truth, 
0$ aU the parts could not couvcnicntly be concluded in the o|)criition. 

2,0)500,0 



or MKNSURATION. 387 

ft50.oo(i$.8 Aafwcr. 



ik; 



308) a ^.00 

i^ir. a« A bowling-green, 300 feet long and aoo feet 
broad, U to be raifed one foot higher by the earth to he dug 
out of a ditch that encompafles the green, and is 8 feet in 
breadth ; to what depth muft the ditch be dug ? Anfwer 
7Hfect. 

Of Gauging. 

Gauging is nod commonly performed by the Hiding rule, 
or ganging rod. But I (liall here give the praelice of it, at 
wrought by calculation of the common meafures only. 

By gauging is always underftood the method of finding the 
content of any hollow veflel, and is moftly ufcd for finding 
the content of calks, coppers, &c. 

The rule is to find the content of the veflel in inches, and 
divide them by a8i, if for ale gallons ; and by 23 1 for wine 
gallons; becaufe 282 cubic inches contains an ale guilo:^, 
and 131 cubic inches is a wine gallon. But if any prefer 
multiplication to divifion, when the folid content is found* 
it may be multiplied by .003 J46 for ale gallons, inflead of 
being divided by %%% ; and by .004329 for wine gallons, 
inilead of being divided by 23 1 ; for dividing by 282 or 23 1 
is the fame as multiplying by thefe vulgar fractions 3 -J^j- or 
f^ \ and the above multipliers are the decimal fradions, 
equal to thefe vulgar ones. 

Ill veiTek of a circular or eliptical form, to obtain the 
content in inches, it is necelfary to multiply by .7854, and 
then to reduce them to ale or wine gallons. Therefore to 
multiply by .7854, and then divide by 282, or 231, is the 

fame 



38S or MRttSrHATtOK. 



Uiw u to multiply by the frA^Imn VV/ or ViV* ^^ ^^^< 
tkcinul fusion cqiul to tbdo vulgar oiict arc .00178^1 (01 
alC| and •003,^9999 for wine. 

PROBLEM XV. 

TO OAVclK k CAIK. 

There art fevcml mrthodi of gauging cartd iccocding c%i 
llitir Otapcis or the curvature of the ttde«, of whkk Ihrte 
are four general (brim, but the content of any of them majr 
be Hound by the fc4lowing general rule x 

Rtrt.ii. To (he fipiarc of twice the middle diameter add 
the r«|iiarT«of the head and bung diainctcn« Multiplying 
the (un) by Jf of the length, and that produtft multiplied or 
divided by the circular multiplieri or divifon» will g)v« the 
contcnit I or multiply the fquaret of the diametera by the 
iength «>f the C4(k| and tliat produA again by »ooo4| for ale 
gallonii or by •0005} (or witir galhrtii. 

KkAMFLa !• Rcqnirrd the contents of anycafki whoTc 
length it 40 inchrt, the bung diameter l)ctng Ui the bead 
(hmuetcr 04. that Inrtwccn the hung ntui head n^l inclKi. 

4 ^2 ^ 4^ «>^* 

^^"t < ^\h 10*4 






1.^-4 

4 > 

»)».^>^M iJallocb. itt.tcH^ Wine. 



stl 



rKODI.i ^; 



I 



OP MRNSURATION. 389 



PROBLKM XVI. 

TO FIND THK CONTENT OF ANY CA8K, FROM IHREt 

DIMKN8ION8 ONLY. 

Rule. AiUI into one fuin 39 times the fqunrr of the bimj^ 
diameter, 2^ times the fqnnreof the heml liiauu-tor, and a6 
times the pro(h)A of the two diameters: then multiply the 
film by the length, and that prodiid by .00034, and divide 
the laft produi^ by 9 for wine gallons, and divide b}' 11 for 
ale gallonsi or multiply by .00003 1\ for ale. 

Example. What is the content of u caflc, whole length is 
40, the bung diameter 32, and head diameter 24 inches ? 



3» 






a4 


3* 


3a 






24 


24 


^4 






9.) 


128 


96 






48 


64 


1024 






S7<> 


7(>8 


30 






fiU 


26 


9216 






zbSo 


4008 


3072 






11^2 


i(;^6 


39036 






14400 


1 9()(>a 








1 9968 

743^4 
40 

2972160 
.00034 

II 888640 
8916480 


2972160 

.ooco3tV 

8916480 

270196 






9> 


ioio.(;u.vo 


Ale 91.86676 gallons. 


Wine 


gallons 


1 12.2S16 


— ■ - • - 













PROBLKM XVII. 

TO ULLAGE A SrANOINO CASK*. 

Rule. Add together the fijuare of the diameter at the 



* The ullage of n culk is what it contains when only partly filled, 
and it is confidered in two pofitions ; ntmdly, either tUndin(|; on \t% 
end with its axis perpendicular to the horijon, or aa lying on its fide 
with the axis parallel to the horizon. 



390 



07 MRNSUBATIOIf. 



fiuface of the liquor, the iquare of the diameter of the ocareft 
eodi and the fquare of double the diameter taken in the mid- 
way between the other two ; then multiplj this fum by the 
length between the (urhct of the liquor and the neareft end, 
and multiply the product again by ,00041 ^^ ^^ galloot^ 
or by .ooo^l for wine galloosy in the lefs part of the caik» 
whether empty or filled. 

Example. The three d'uuneten being t4f t7» and t9» 
what is the ulbge for ten wet inchei ? 



«4 

96 

48 

<76 


*9 

«9 

a6i 

841 


54 

ai6 

370 

3916 


S916 

841 

• $76 

4333 
10 




4333? 

si66eo 
s88i6 






• 


»4'J53* 




4J33<> 
•000 4,f 








«733«o 
38886 








Ale ao.3io6 







Wine. 



PROBLEM XVIII. 

TO ULLAGE A LYING CASK. 

Ru:.F. Divide the wet inches by the bung diameter, and 
fi.ul the quotient in tiie column of verfed fines in tlie table 
of ( ircuJar i'cgments at the end of this fe^lioHf taking out its 
coi rcfjjondcnt fegment; then mutiply this fcgment by the 
vfholc content of the cade, and the proiiud again by i| for 
the ulhigc required. 

I'jcAMPLe. If the bung diameter be 3a inches, and content 
92 ale gallons, ^hat is the ullage of 8 wet inches ? 

4 3») 



09 MBNSUHATIUN. 



3i)8(.i;, whofe rab. feg. is ■is3;46 




A TABLE 

Of the jireas ofllw Segments of a Circle, 

V/YaSe diameter is Unity, and fuppored to be divided into 
One Thoulund equal ?ani. 



ll«ti,. 


Ar/a %. 


ii.ij:»i. 


-V,« S-s. 


//«jpt(. 


jlrta Sig. 


•001 


•000042 


■017 


■005867 


■053 


•016007 


■oo> 


•000119 


■018 


■oohi94 


•054 


•01645; 


•003 


•000»iq 


•oaj 


■oSes 


■OSS 


•0.6911 


■004 


'•00537 


■030 


■056 


■017369 


■00 s 


■000470 


■031 


■O07aoo 

■oorssS 


-057 


■oi7yii 

■oi8a96 


•006 


•000b 18 


■031 


•058 


•007 


•000779 


■033 


■007913 


■059 


■018766 


■608 


■000951 


'OH 


■ooij-^ 


060 


■01 9*39 


■009 


•001135 


•o?<i 


■O0H63B 


•06 1 


•0197 16 


■010 


■0C.1329 


•036 


■ooyooS 


■061 


•oaoi96 


■on 


■001533 


■037 


■009383 


■063 


■010680 


■Ola 


■001746 


■03B 


■00976^ 


■064 


■01116S 


•013 


■00.96, 


■039 


■01014H 


tl 


■011659 


■014 


■001199 


■040 


O10S37 


■011154 


•016 


■ooi4,^8 


■041 


■01093 < 


■of>7 


■011651 


■ooabB^ 


■041 


■011330 


■068 


•013.54 


•01; 


■001940 


■043 


■011734 


■of'9 


•0J36sg 

•oa4if)8 


•018 


■00310a 


■044 


■011141 


■070 


■019 


■00347 1 


■04J 
■046 


■01.554 


■071 


-014680 


■010 


•003746 


•011971 


•071 


■015195 


■o«i 


■00403 1 


•047 


•01339a 


■073 


■015714 


•01» 


•0043 w 


■048 


■oM8.e 


■074 


•016136 


-033 


■0046 1 S 


■049~ 


•014147 


■075 


-016761 


•0J + 


■004911 


■050 


■014681 


■076 


■0 J 7189 


■o»5 
•016 


■005930 


■OS' 


■015119 


•077 


■017^1. 


■005546 


•os» 


■«.Si6^ 


•07fi 


;oi8aj6_ 



3D 



3»> 



or HKRSUKATIOII. 



THE AKEJIS OF THE 



»..Jl. 


^AlA;. 


B^U 


Jr»S.g 


H^t, 


,!.«*, 


••79 


■098894 


•114 


•«49S>8 


■149 


t.;3i6i 


•080 


•"•943S 


;:;i 


•050165 


■150 


■074589 


■08. 


•oa99J9 
•03PS»o 
•031076 


•050804 


■151 


•08. 
■083 


•117 
•118 


•051446 
■051090 


•'S« 

■'S3 


■.v,& 


•o»* 


-03ib>Q 
■03s 1 96 


•119 


•o^«736 

'•Vol 
■054689 


■>S4 


•076747 


zu 


■ISO 


••S5 


■077469 


■031745 


■lai 


-156 


•078 '94 


■Hi 


■03.1207 
•033«7» 


■111 


■»S7 


•07»9»" 


•i«3 


•OS534S 


•158 


•079649 


■oa. 


•034+4.' 


•i»4 


•056003 


•H9 


■eSo^So 


■oqo 


■03501 1 


:;:i 


:o56663 


■160 


-o6iW» 


•ogi 


:VdS^ 


•057396 


■161 


-0S1846 


■«9» 


■Ml 


•OS799' 
•os^sS 


■i6« 


-08s 58a 


•093 


•03674. 


•.63 


•o8j3*o 


•094 


■0373«3 


•189 


•059317 


■.64 


■084059 


:^ 


•037909 
•038496 


•130 
•131 


■06067s 


::S 


•084801 
•085544 

■oSfeaSo 
■087036 


■097 


■0390H7 


■13a 


■061348 


■.67 


■098 


■03.;68o 


■'« 


'u6joi6 


•166 


■099 


■0401 76 


■134 


■of. 1707 


-169 


■08778s 
•088535 




■04087 i 


•IK ,■of>^^^ 


•170 


'lOI 


•041476 


■13'' ,-ofU074 


■171 


■0891 87 




■o-l'oSo j -1,(7 


■0(14760 1 


■'7* 


■090041 


•lo.t 


■04J6B7 ' ■i,,8 


■of' 5449 1 


■'73 


■090797 


•104 


■04119*. |i-ii9 


'0flt)l4Q 


•'74 


■o.JUi4 , 


■10^ 


■043908 ];-i4o 


■cf.6Bu ) 


'17? 


■09HIJ ] 


■106 


■044S" ; '41 


■06751 if 


■.76 


■093074 1 


•107 


■04^131) i-ni 


•of'h'ia; > 


•'77 


■01)3836 1 


•108 


■''4,^750 :|-i43 


■o68.,a4 


■>78 


094601 


•109 


■041.381 |-i44 


■o6.)6.( 1 


'.\ll 


095366 




■04700^ -14! 


■070318 


096134 


■V,l 


■047631 '146 


•07.0 ), , 


■i8i 


096001 
097674 




•04816a -147 


■07174' 


'|8> 


""'- 


■04a8(j4 


.4« 1 


07.450 . 


■18, 


098447 * 



or MSN8URATI0N. 



393 



SEGMENTS OF A CIRCLE. 



' 

-184 


^/•/<i Seg. 


*219 


Afta S9f[. 


Ihigki. 


AfaSig, 


*099flsi 


'127285 


•254 


•157019 


•186 


•099997 
•100774 


*220 

'ftfti 


'I28113 
•128942 


'256 


•157800 

•158762 


•187 
•188 


•101553 


*ft22 


•129773 


••57 


• I 59636 


•io»334 


•««3 


•i^oboc 
•«3»438 


•258 


•160510 


*(f9 


•103116 


••«4 


•59 
*ft6o 


•161386 


•I9» 


•103900 
• 104685 


•22c 

'i26 


•132272 


•162263 


*t9i 


•133108 


•261 


•163140 


•19s 
•«9I 


•lOOftOl 


•227 
*228 


•»3394J 
;i347i4 


•26ft 
•263 


•■164019 
•164809 
•165780 
•16666 a 
•167546 
•168430 
•169315 
•17020ft 


•«94 


•107051 


'229 


•136465 
•'373©7 


•264 


in 


•10284ft 
* 1 0863 6 


•»30 
•231 


•265 
•266 


•192 

*i9l 
•199 


•109430 

M10ftft6 
M110ft4 


••3* 
••33 
••34 


•138150 
•138095 
•139841 


••67 
•a68 

'269 


*ftM 


•Iii8t3 


••35 
.236 


•140688 


•270 


•(^1080 
•171978 


*toi 


*iift6si. 
•113426 


•^4»S37 


•271 


*•<)• 


••37 
•238 


•142387 


•27ft 


•172867 

'»737S» 


••03 


•ii4«30 


•H3^38 


••73 


*fto4 


•11503s 


••30 


•144091 


•»74 


•174649 


':^ 


•11584* 

•I 166 CO 

•117460 

Ml8ft7l 
•119083 


*240 
*241 


•144944 
•14C799 

•146655 


••7S 
•276 


•^7554* 
•'76435 


ISi 


'242 


•277 


•177330 
•1782*5 


•24^ 


•i47S»* 


•278 


*fto9 


•*44 


•148371 


•«79 


•179122 
•180019 


*BIO 


•119897 


•246 


•149230 


•280 


•ftll 


•120712 


•150091 


•281 


•180918 


•ft I ft 


•121529 


'•47 


•150953 


•282 


•181817 


••IJ 


•1223A7 
•123167 


•248 


•151816 


•183 


•182718 


•fti4 


•249 


•152680 


•284 


•183619 


•ftie 

'ftiO 


•I230B8 

*ift48io 


'250 


•>S3J46 


285 
•286 


•184521 


'251 


M54412 


•185425 
•186319 


•JI2 
•J18 


•«»S634 


•252 


M5C280 


•287 
•288 1 


•126459 1 


2iX, 


;ijS,49 


•1872.U. 



3De 



).w 



r\V UENSKHIlTinN. 



THE AREAS 0¥ THb 



lUlk. 


<«M&f. 


/.-ii-. 


W.MA.C. 


i4,iiu. A»*a,f 


>l« 


■SB 140 


JU 


I 10404 


3W '•SJS90 


■•«» 


189047 




»» 1.140 


360 ■•(4iSo 


••qi 
'•9> 


:;"x 


■•••»77 

■"3««S 


361 l»ssSio 
36. ,-ts64Ti 


•M 


■'93190 


■M41S4 


163 .■•S7M3 


■•« 


•3»9 


■••COIJ3 
■«ih03J 


(t"4 , ••58391 


;:3i 


■33'^ 


■lb6 i-atajso 


.19440^ 


■31' 


••«6474 


:ni 


''90337 


■3J» 
'333 


;:'.5'.;5 


:iSi» 


•99 


'197»S» 


■3U 


-•iijtkji 


'jt4 •.6)11} 
■jjo ••»4i;l 


■300 


-i9Bl6tl 


■3J| 


::SS5 


30 « 


■iqi)0fl( 


«■ f'SW 


•301 


•■00003 


■337 
■336 


■»3»M 


■"• ■"?'"; 


'30.( 


■•oou. 

■»0lB4i 

■sai7^i 


'..USBo 


■)TJ '■•«7»7» 
•J» [■•'«04i 


■304 


'339 


•»34Si6 


•30 s 


■)40 


■«IS47J 


•17( ••'9011 


V,of, 


'tuJ,f,tt, 


■ui 


■J ,'.4*1 


M''7 


■lo^'ioi 


,H» 


■i , J t'-l 


■177 '''7t''*^' 


M"« 


■Ju^^iy 


'Ml 




-,;« •.7..)>o 


M-J 


■»0f,4ii 


■lU 


■.t.ji..H 


.,;,, i-,,l«.,o 


■111 


■f07,/(. 


■Hi 


■i4 .iilt 


•,«o ■.,,«,. 


Ml' 


■at.b,oi 


■u'' 


■24i|(..y 


■,til .JJ+fl* 


•111 


•*oi,i*7 


'■'^l 




,K, ;ji;«o, 


MM 


•iM>,s4 


■MV'M 


■|«l :-"7'''77! 


•1'4 


'iiu>Hi 


, ■ H9 


■1.HUH. 


i«t i;?!*" 


■*'i 




■iW 


■«44v'iu 


-,«( .i«7>i 


■,.?. 


•»"*'M" 


:;.i. 


■*4?'.il 


■,Kf. 17.^.4 


't'7 


■«l,H7i 




■,4'.;ia,, 


■1^1; 1 iHll.tlJ 


■,.fl 


■.14H0X 


ifi 


■-M7'tli 


■,h;i i'lSi(.4» 


■,ly 


••IS7H 


■iu 


■MUii-' 


■,H,j ^-ttil.t-l 


•jiO 


■•iW/.f) 


I'tii 


■»4'jh; 


.,.,. .■•^..■.< 


't«< 


■■'7Wj 


r.ti'^' 


■»v'7". 


,,,, .■.«i...H 


Ml* 


••iB.;,! 


■U7 


■*i"''/. 


■.',' ■'»',;« 


■-<':• 


•..>,4ofl 


•.,(« 




■,,,, 1 ■■«.,,,. 



OV MKNSUHATIOM. 



395 



SEGMENTS OF A CIRCLE. 



ntight. 


Arta Se^. 


Ihij^At, 


•394 


•»«7498 
•a88476 


•430 


•395 
•396 


•43 » 


•289453 


•43* 


•397 
•398 


••9043a 


•433 


'191411 


•434, 


•399 


••9»3()0 


•435 


*400 


••93369 


•436 


•401. 


•494349 


•437 


*4oa 


'ms3^ 


•43» 


•403 


•296311 


•439 


•404 


••97892 


•440 


•405 
*400 


•ac)8t73 


•441 


•a99i5C 


•443 


•407 
*4o8 


•300*38 


•443 


•301210 


•444 


•409 


•301203 


•446 


•410 


•303 ««7 


•411 


•304171 


;^447 


•4U 


•30515s 


•44S 


•413 


•306140 


j -449 


'414 


•307125 
•3081 10 


•450 


*4i6 


•451 


•309005 
•310081 


iNSa 


•417 


j^4S3 


*4i8 


•3 1 1 068 


•454 


419 


•312054 


•455 


'4ao 


•313041 


•456 


•4«i 


•314029 


•4 57 


*4>* 


•315016 


•45« 


•4*3 


'316004 


•4j9 

•460 


•4«4 


•3 1 6992 


•4*5 


•3 1 798 1 
•318970 


•461 


*4t6 


•462 


*4a§ 


•319959 


•463 


•320948 


•464 


/-•♦*^^^31'9,\?.' 


••^65 



'322928 
•323918 

•324909 
•32CQOO 

•326802 
•327882 

•328874 

•329866 

•33085H 

•331850 

•33*843 
•333836 
• 3348*9 

•335822 
•336816 

•3378*0 

•338804 

•3;,97()8 

•340703 

•34»7W7 

\U«7«^ 

•343777 

•34477a 
•345768 

•346764 

•347759 
•3487SS 
•34975* 
•350748 

•35'J74S 

•352742 

•853739 
•354736 

•35573* 
.356730 

•357727 



•466 


-rlf/ r.l St(^, 


•3 587* 5 


•467 


•3597*3 


•468 


•360721 


•469 


•361719 


•470 


•363717 


•47« 


•363715 


•47a 


•364713 


•473 


•365712 


•474 


•36O710 


•47 > 


•367709 


•476 


•368708 


•477 


•■^69707 


•478 


•370706 


•479 


•37*705 


•4H0 


•372704 


•481 


•373703 


•4«2 


•37470* 


, '483 


•37 w^^'^ 


'•484 


\\7b7o2, 


•485 


•377701 


•4S6 


•378701 


•487 


•379700 


•488 


•380700 


•489 


•381699 


•490 


•382699 


•491 


•3H;',6i)9 


•49a 


•384609 


•493 


•385699 


•494 


•386699 


•495 


•387699 


•496 


•386699 


•497 


•389699 


•498 


•390699 


•499 


•391699 


•500 


•39*699 



396 f^y MKNfiirEATIOMr, 



In tliid tat>U (lie ilinmcur of clt« rirck ii i , ifid the whole 
urea *'j%i ,ij9 { th« figutm in the coltiinrit of k«i^h(e arc the 
lirij^ht tii (he (rgnirfiti or (he verfcd fiftc of half jci arc i ao4 
(ho(e in the culuinnf of area fci^nienti are the areas of the < 11 - 
ttilar fegmenif, wtiofe Ud^Uni ftand on the left hand hi die 
column of height!. 

Tlir uim oi (hi* table U to fnid the area of any fe|ineo( ol 
a circle^ by (he iollowing rule 1 

Kuti. Divide ihe brkglit of (h« given fegmenl by (lie 
dianfieter of tl>e circle, and (lie quotient i« r he height of Uic 
Irgiitent I and oppofite thii lieighCi in (lie (able, if the laliidar 
area, wbidi in (o be innUiptied ity the (^luire ol the diemetcry 
and (lie |iroduA will \ye (he area of the fegitient* 

KitAMrt.a. Wliat 1% the area of a (egnieiU of I circle^ 
wliotia height ia $ tocheii and tlie diameter go ineliea t 

30) {*ooo0(^>6 Tab. beigbc 

^l$544> Tab.ftgfMnt 

yx > tiquare^ the diameter. 
Anfwer* 76.980600 

— — — * lO 

ftioh, \\\ dividing the x/ivrn h'.ighf hy the diaineteri if 
tlircfuiiiieiit Hot) not iri minute in thirr |ilutet of dci'imaU^ 
then the incii for iliMt fra/tionitl {i4it oii^ht t/> Lk; prot^it* 
(ioiicd Uti 4» lollowt) : 

littWiiig h;un<l \\\r (:iliiil;ir afa, anrw''iifi(( to the Ai Ik (hter 
de< iiiuU III the r{iloiicnt, take the dilfciciKc hetviccn it afw! 
the nrxt following/ Mliiilar 4iru j whit h dilfricnrey miitli|>hed 
by I he ha^li«>iiul jmit feiimiiHii)^, (he jiiodiiift will he die 
i,in\r\\iim\n\\\ |;ioi>urii<in4t puil, to he added to (he hi A 
tabijliti 41 en. 

'Ihiiti MX (he l4(l exam|ile the <|iioticnt U '166, and ilierc 
U a lenuinder of \, the tabular luca oi the lr|fnicii( in 

4 .'-»^J544 



OF MBKSUIUTION. 



397 



.085(144 

.oS()d8g 

J 745 The difference 

a. 



48 



40^ I of the ciifference 
.086040 The true tab* area. 



SECT. IV. 



OF INSTBUMKNTAt JlRITHMETIC. 



Inftnimental arithmetic is the method of calculation b]pin« 
ftnimenti made for that purpofe, for a quicker dif|>atch of bu- 
fineibi and for the help of thofe who are deficient io common 
arithmetic. The moil common inOruments arev the carpenter* s 

mndih^ Mmgciuti rod. 

I* The carpenter's ruleconfids of two equal pieces, each 
m foot in length, connctSted together by a joint : one (ide 
of this rule is 'divided into inches, and cigltths of an inch i 
on the fame fide are alio feverai plane fcules, divided into 
twelfth parts by diagonal lines, for planning dimenfions in 
feet and inches. 

%\ On the other (ide of this rule, on one pivxe, are fet all 
the principal lines, which are on Coggeniall's iliding rule : 
pamely, four lines marked A, B, C, and D refpe^tively ; the 
two middle ones being on a llideri which runs in a groove. 

Thefr 






A, H, i' <»«»■ all r.»|\ul i lUul air laliwil \\iA\\\h Un*»» hwikuil: 
il).^ i.vtoUuia {\i \\\^K\\\ \\\i\\\ \\\w tu»m ) u^ lo, iwW0) ihf 

ilu tiMa^nii ot n\rs aiwl Uiubur, ThU liu0 ajfo way b# \\M 

I'j'on ilu' oiher |vui ot" U\ia lulu U a t^Wo of |iO\)n^U% 
<Uilhuu«i, uiui j^ciu'i-, ih^'wing the v»l«e of ia !oa«l» <H ^o fwbu" 
fi it itt tuulwri At all i^'ucM fvxuu tU|)(^no« ta vwo {hiUu>|i& a 

In tho ute of thv^lv) lihua it iiuU^ ho \\\\i\\y obf^rV«4« iMi 
mIuu uiu'. at \\w- \w^\\\\\u\^ of a lino U aeco\)UtiH) utMtVt thvu 
tlw ( \\\ xUti m'uKIW of \\\ii lino will Uanvl fi>r \^ «ni) ti\« i^a 
At ilu^ f'tui uf tlui Imewill Aativl tU* \\>o\ m\\yt\kp\\ iho f 
at tlu'- iH'gihuih^ v^f the \\\\s> ttatwU U^' lOi tb^ \0 \\\ t^cs 
i\\iJillv i«t \\\\^ \\\w will AatuI fi»t: iv>a^ Atut ^h« l«> *^ <ho *w*l 
uf iho liiu- io;M, v\;v3. ahil all the iiUvnv\«ili<^N divitionA aio 

Alltel ril \\\ \i\\\\vm\'UH\, 

Tht^ f i)ge of the I uW ia OivlvK U ^IrcimaD'vs w^H f«^^ Wit^j; 
ih\iil«^il iuioauhumlu^l ivjual p,MH: I»n ihia luenUuv ilimi t» - 
U\\\\i aiv tak/u ih tvM, au^l iUiUtuvia of a l\vM^ whivlv ia U\ 
hwuh thf Ktl way. 

■{. C ointoia lihi la A \i\w. i^t tii^uu a. (Aaillv the U\\^%: ai th;'- 
Ihivc luvi^Ki Thua o\» ilu' iaip»<>u I'i i\»Uj aiul lhtn%;lo»tJ iuii*U 

tu» t\Uthfl \UUli|U(Oh lis WW la Ui lVt\Htt)^l>\ i>k \li\iJvs 

nui\tl»(^i!i. tvi |»nloiiu tho luU o(' thuv \liuvl| Xx . It w«a4 
tvM»i\vih w\ l»v iiu^lt ou ihvi ».tr|»/nti|"'» nUi\ 

il». !M<> Im -i, w \\[\u\ \\\\\K'^ \\ip\ h(<htfv \^\ i^\ ',o» X;\\ a^\u% 

* uV. , wi aoV\«thv> s.tUI-., riW^x lis'. vIoOvuiuUU Imnv l^ivi* 
nK* M It (^ .i iv|\mi' n»K , w uh l.»v, uuhtui, lii\<^oh thv ti^U'^i 
Jva>jOt{ thui- uulxi imn\ip^j in v,us >;« \\\ \\u\\' ^'f .hr lixl. .*. 



OP MRNRUItATlON. 2^)9 

'•9immm''mm^fmtf^immmmmmmmmm^mmmmmm'''mamm 



Upon the firll l^cr o( thia rulr nie tluee lineH : two, lUBiknl 
A and H, for iuultiptym)> uiul dividiu)* i aiul one, inui Wctl M 1>, 
fer male depth, nit it krvm to gau^e malt. The iniddlr Una 
N ii upun a Uidrr, and id u double line*, marked at c<ti h rd^o of 
the flidrr. like that on the larpcntei** rule : thelo thiei- line* 
are all of the fume radiiu, or dilluncc irom i to to, omU line 
containing twice the lenj^th of the indiut. A ami H uro 
uumbered e«a^ly alike, luul the numl)er« may be increai'ed, 
or dcci'caicd at plralmc : thun the tirll number i ntay eitlier 
Aand for un unit, lo, or too, &r. or i, or .01, or ,uoi, &:t\ 
but whatever thr tirll luuuber is the naddle number will lie 
ten timca aa mui h, aiul the lidl nund)er 100 tin)e:i a:i nuicli| 
A« on the car|ienti:r')i rule. 

The 1 on the line M I) U opixilite ai f; on the other line;i, 
which are the eubir. imhc:! in a malt bufltel \ and the dixifum't 
oi\ thii line are umnbercil reii-ograile to tht»le of A and IK 

Il|Mm the lined A and H aie ievrr;d other nmrka and lelteri: 
chua, on the line \ are M D, for malt bulhcl, op|M)lite th«i 
aforefald number a 1 q 1 and A, lu>r ale. (tpptihte tBd, the eubii* 
inrhei in an ;ile gallon : and uium the linrB, oppi'tite 1 Ui i* 
W, for wine, ihe cubii- iui hcs in a wine i>,wll«»u ; alio S 1, lor 
ftpiare inscribed at .707, whii h ia the lide ol the fiptaie in- 
feribed in a cinle, whole diameter ia i : and S !•, for li|uaro 
equal, at tBUd, being the liile ol a fipiaie ecpial to (he fame 
circle! alfo C, for cirutnufcreme, at ,^1416, which ia the 
cinrumference of ihe fame circle. 

Upon the fecond face, which ia that oppoiite the tirt\, are a 
ilUler, and four linca marked D, C, 1), £, at one eml, and at the 
other end marked i'<»tv.yi/M»i»y, roo/, itt^u' i the lines C anil K* 
containini; refpet^tively the fiptarea, and cubea of the oppoiite 
numbera of the linea I), D : the radiua of the lii\e U ia double 
to that of C, and triple to that of K i lo that whatever the 
lirft one on D dt-notea. the lull on C is the ftpiarc of it, and 
the flrft on K the cube ol it ; thua, it i> be^iui \n uh 1, C ai>d 
U will begin with 1 } but if D Ivtgina with 10, C will begin 
mi\\ 1Q0| which il the f(piarc of 10, 'and l< with loou, th<^ 



400 09 MCKSintATIOll. 

cube of lOt and fo on. Upon the line C» at ^07916, it noiked 
a c for the area of a circle, whofe circumference is 1 ; attd md 
*^ •78S4» for the area of a circle, whofe dianoetcr is i« AUb 
\ipon the line D are WG for wine gauge, at 17.1 $« and 
AG for ale gauge, at 18.95 * ^^^ M R for malt round, at 
51.31 ; thefc three being the gauge points of round and cir- 
cular mcafure, and are found by dividing the fquare rooCi of 
•31. aSa, and ti5c.4 by the fquare root of .78J4; aUb M S 
for n^h fquaie is niarked at 46.37, the malt gauge point 
for fquare meafure, being the fquare root of tijo^. 

Upon the third iace of this rule are three lines, one marked 
N upon the Aider ; and two upon the ftock, marked S S and 
$ L, for fegment (landing and fegment lying, which fcrve 10 
ulla^ lUnding and lying calks. 

Upon the fourth fKc area fcale of inches, and three other 
fcales, maikeil/r^ varUty, jW^md nfsriHy^ and third ^tmritty ; 
the fcale for they#«r#^ wtrutv being on the iofide of the Aider 
on the third face; the ufe of thefe lines it to find the mean 
diimeter of caiks of each of the four differeut forms or Aapca 
of the fides. 

Bf fides ihofc line?, there are two otheis on the indde of 
the two firft ll'Jrrs, being continued from one Aider to the 
o:he; ; one or" thefe is the fcale or inches, from ! a J to ;6, and 
the other a fcale of ale gjUons between the corrciponding 
numbers 43^ and 361, which forms a table to ihow, in ale 
gallons the contents of all cylinders, whofe diameters are 
from i2| :v> 36 inches, their common altitude being i inch. 
5. The dias(onal rod is a fquare rule, commonly four feet 
long, and folding together by joints ; this inArument is ufcd 
both for gauging caAis, and computing their contents ; and 
this is performed by taking one dimenAon only; namely, the 
diagonal of the cafli» that is, the length from the middle of 
the bung hole to the meeting of the head of the caik« widi 
the Aavc oppofite the bung hole ; and is the longe A line within 
the ca& from the middle of the bui^g. On one face of thi% 
rule it a Icalc of inches to take this diagonal by, oppofite 

whick^ 



OF MENSUBATIOJK. J^l 



whJdi are placed the areas, io ale galloos, oi circles to the 
coiTefpaiidiiig diameters, in like manner as the lines oq the 
under fide of the three Aiders in th^ Hiding rule. 

On the c^pofite fiace are the fcales of ale and wine gallons, 
to ihow the contents of calks, from having the diagottia). All 
the other lines on this inftrnmcDt are the fame as thofc ca 
the Hiding role, and to be ufed in die fame manner. 

TheUfeof the Carpenter's Rule. 
PROBLEM L 

TO IfCLTIFLT tlUMBEmS TOOBTR£X. 

Scppofe the tiro nnmbers 24 and is ; draw the Aider out, 
till I on the line B is oppofite to 1 2 on the line A ; then 
againft 24 on the line B ftands 288 on the line A, which is the 
produd of the two nambers. 

Kctem In any operations, when a number runs beyond the 
end of the line, feek it on the other radius, that is, the other 
part of the line, which will be the tenth part of the required 
number. 

PROBLEM IL 

TO OlVIPfi VVMBEIiS. 

To divide 312 bjr 24 ; draw out the Aider till the divifbr 
«4 on B be oppefite to the dividend 312 00 A, then againft 
1 00 B ftands 13, the quotient on A* 

PROBLEM in. 

TO SQUARE ANT NL'MBEJl. 

Snppofe to fquare 12 : (ct i on the line B to 12 on A, then 
agadnft Z2 on B ftands 144 on A. 

PROBLEM IV. 

TO £XT«ACT TB£ SQ^AlB BOOT. 

Set I or loo, &c. en C to i or 10, &c. on D ; then againft 
eftry number found on Cfiaod&.its fqviare root on D. 

3 E 2 FROBLEM 




Of Mmomi oK. .407 

nnt, ftt lou on II (u ilic Krcrvtil nuabtr on A* and 

' tticwlinlt:(-o(itei)t on U will befauadthc ullifB ottA. 
Ift ar« ninny fbliil figiirci bclldei the ftxtgoing, llic 
pf whiv'li (^■iiiiiut be fomid by nay aAuil dimenQoiii 
M tho fluiirc, I'uili ai lliilitUi In:, The roiitcnMof 
Nit foimit by Iniiiicrflng them in wntcr, and mev 
the liTt of tlic water noLafionetl bjr ftich immcrliwi. 



S K C T. V. 

A THW or THB riVK OMOXRil OP AROUITJKTUMt. 

The nrl|in nr nrrhitcAiirc it nlmoft contvmihirary with 
thftt of civil fnciciy. Wlici) mnnkintt ffit the Inrlemencki ul' 
tlio WHiher, Bud, ronrcqiicntly, fbund the ncrctlity uf orrAiiiK 
Imbitiitioni for ftieltcr, f rIg mA rimvpnlenia fuon improvnl 
Itfclf into omimciit tiiil grandeur. A lew trcci pciliApi 
growing round in > eiii'lr, kikI leaning togcthir at the top) 
afforded the firft hdbitHtiom, being iiitarwnveii with twlgi, 
and plfllflfretl over with mutl. Thli gava riro, in aricr agci, 
to th« idea of colnntni. 

It it probaldc that the inconvenlciwc of tliefe hBl>iu(ioi» 
rtndered their uwncn dcliraut of hivcntlng fuch, that lliould 
anfwir every pnrpofc of the former fort, and poflefi fav«ral 
atlVBtitBgci .ibove Iholc 1 tliii improvenicnt naiurnlly gRve rlf« 
to the invention of tlic crufi bcaoM to ftippnrt the roof) tor 
. thb purpofe, thryhad, noduubtt rarunilc to thclrunkiof 
^' mui ihiiir/iluinni wcrcut oneelntrodvwd. 

jF The 



which oac cone, LO N, bit iti nnex in one pant d m 
dbjt&% ind ilie other OMC. LFN% hai iu venn F in (tM 
P fmoi af the tttifO. Ttac middlr tine O F it oUcd the lU- 



SECT. I. 



I 



T>ireA viGiw U the faculty of fight, vid u oodfioned t? 
thd riyi of light praceetTing fnim on Mijcfi, snd poffing 
tIniHtghdiC hBmonn siihecyr, where they fnim die tin>^ 

..I the ofjf.^ i,ri t),^_ T.nrli i.^.rt. ,,r l.nrfr,m of iJi* tyc In 

order to urulc Hand ivhicli, it u'ill l>e ncccfTary to explain the 
iJgiire and conflruftinii of the human eye. 

A13LT, istliecvc. ll is of ,i fplicrical figure, by which mtms 
it it cnfilj- mo^■c^l anyivay in lis fockel, by mufcles appointed 
tor ihat purpole ; ihe fore part at A (fig. i ) is more ronvei 
tlian any oilier pait. The eye is enclofed in three mem- 
bra nrs : the oiitermoft is called tht Sclerttiira ; the fccowl, 
the Tuiti.-i CUroiifes ; the fore part of which ii called ihf *«» 
wliirh confifls of many fibres, like fo many radii : the third 
nicinbraiie, or innermoll coat, is called the Rtlina, which is 
nothing but ihf optic nerve, fprL-ad over the bottom of the 
eyi; L iipon this membraoe ihe images of vifible objeAi are 
iorn.ect. 

Ill thefe three membranes are contained the three hu- 
mours of the cyci the litft, HAI, is called tlie a^afi 
humour, 



i 



OF OFTICS. 415 



huzDonr, which is a thin watery liquor ; the Cecand, F G O, 
is the crjfi4ilUM€^ m the form oi a doable convex IciiSy and 
more coorex in the back part : behind this is the 'uitrtous 
hunaccr K L. 

The ojfialliiie is moce denle than die vitxtocts, and 
'CLc Titreoos noore den£: than the aqneoos hamoar: the 
three hnmoars together fi>nn a compound lens, which re- 
fra^s the ray: of lights iflbing from an objed F R, to the 
bo:u>m of the eye ; and there paints its image p r, opoo the 
rtrisa, in an inrerted pofition. 

The ^ueoui homoor is in the &nn of a menifcas ; as it 
alfo the Titreoos humour. The fore part of that membcaofc 
calkd the fclerotica is cmilcd the ctrmea^ as at A, and that part 
adjcMniog b called the white of the eye. Wirhia the cornea 
is that coot called the wvta ; in the micidle of this is a hole 
O called the pupil, to let in the rays of light : this papil is 
coTitradcd or dilated by iereral maicalar fibres, in order \3 
let in more or leis hgfat, as foond convenient. 

D b the optic nenre, which, coming from the commoa 
fenforinm in die brain, b expanded all over die concave back 
furface of the eye, and thus forms the retina. Th?s nerve b 
not fitoated in the middle of the eye, but ties nearer the ^uSt^ 
£, in that part next the noie. 

The crytUlline F G has a ring xs^ fibres round iti edge, 
by which means it can be drawn ax>re or Icfs convex, and 
the difiance AC b thereby made greater or leis, in order 
to form the image p r, upon the retina, for didind vifion. 
Thb ring of fibres b called the Ugamemtmrn ClUarr^ the back 
pert of which b black, in order to flifie the rays which fall 
upon it. The eye b moved in the bead by feveral muibles 
In the fclerotica. 

If the image of an objeft do oot f all upon the retina at 
p r, the Tifion will be confuied ; if it fidl (hort, or nearer 
F G, as is the cafo with ihon-figfated people, then a concave 
lens that makes the rays more diverg^Dg wiH bring it to the 
retina. 

3G « 



4t6 Of OI^TICfl< 



If the ruyi o( ti|ht i\u \\oi unitCi (o at io tmm th$ lmtg« 
of (tie objrAi till tiuty get Inryoml th($ rtiimt fl« ii the i^ftif 
wUh moft old iieoplifi then • conmt^m cm)v«4( Uni of i pro* 
per form will mftke them convei|^e iboner, Atid (o form (to 
iiiMge upon the tethm ^ therefore loogi^figbted people mtift 
uie convex gldflei i end Aiort-flgbted people coneeve onei* 

The rey of light V ^^f flowing from the poini of the ohjeA 
Ft end the ny K i, flowing from the point Ry eroA muih 
other it Ot end ptoceeding in tlie feme ftreight Uneff fniiit 
the imege of ttie otijtft V R on ttie retinif in m inverted 
pofitioni id p r« 

N^fo Though the rayi of lighe ere in tlie 0gure repre* 
ienttd by fin|»le lineit, yet it muft he oh&rved tbet every 
vlfibte point of the object ieiidi forth a /imil rfr4^t% wbkli 
crofff eAcb other et O, end peint the im»ge of the objeift on 
the retine* 

There ere mnny expift imenti mede by pbiloibpberf to de* 
monfti'ttte the tiutb of thii theory of viium \ theipofteom* 
nion of which i« tlie following i-^gfce e biilloek'i eye, irbUc 
it if freflif ixm\ u newly i^illed bead, end hevingeuf of ttM 
three awt<> Um\ the b«ck p«rt, <iMite to ilic vltreoiw bummir, 
pill 4 pir-i^ iA |Mj/«:r \it\\\\M\ ihm part, mA hold iLc honi of 
iht ryr U^w^kU any hii^lii n\,\rt\^ M\i\ ibac will U: siii in- 
vtriicil iu»;ii^r f>^ ihd ohjc/l up'iit iIm: white jmpcrj whidi in 
tl)U tttic Id vi:j» u:» a it'lliia to ihf fyc, ' 

Tlwiiij^li llic iii»«j^<:nj ihiwihjc^i i« ihvrMcd in the iKittom 
of the i^ycf ytt wc \iu\yL'. U lu lie cn./l, hciiig ftlway* uiicd ti> 
rimt jioliiion ui t|»c olijr/.i. JJy an ttiifijiivu iiciiWhI of rfie 
%ire, the pMiiioii o/ the olije^t, with it' j^nnj to thai of the 
iihiii^r, in«y br; f;t(i)y aruniiitcd lor, 'iUuk, Ut view thit 
|ioi(tL ol the o\(jta I', the |iiij/|j of tJM' rye 4t O inuft tM 

iiiihtd upwui«U lowttnU A, in oi tier tiiat lUti my Pp m»y 
Irtll on ihc «yJK ol ihccyc, oppolite C, whnc uhine diftiiwa 
viiitiu io |>c<loni»ei|. And to view that |ioinlof the olijeft 
Kf the pupil oi the eye mull be turned tlownwardt, lo teke 

4 is 



OF OPTICS. 417 

in the rtiyi of light R \\ ib that r may fall on the axu of the 
eye at C» 

The diameter! of object are proportioned to t)\c diamcteri 
of the image* at the bottom of the eye : thu«i the anglo 
P O R is equal to the angle p O r. 

Sonne of the mod common properties of the eye ai'o the 
following:-^ 

I, The eye cl^ only fee a very fmall jmrt of an objeft 
diflinf^ly at once 1 therefoi^ the eye mull be turned fuccef- 
tively to the feveial parts of the objevt, that each part may 
fall in or near the axii of the eye. 

t. When an object is fccn di(\in<^tly with both eyei, the 
axis of both eyei are diit^ed to that point j thui the objci^^ 
appears Hngle, thougl) it be feaw by both eyei at once : but 
if the Ai« of both eyes are not dire^cd to the fan\e jM)int of 
the object it will appear double. 

3« Few eyei can dil>inguilh a particle of matter^ that fub* 
tendii at the eye, an angle ltf« than half a minute i and very 
few can diftinguiQ) it when it fubtendi a minute. If the 
diftance of two Aara in the heavens be not greater than thii| 
they will appear ua one. 

4. The eyeii of young people ai^ mort? convex than thofo 
«f old people ) and this ia the rcafon the former can fee au 
objeA nigbcr than the latter. 

5, The eyei of fl^ort-lighted people arc too convex to 
admit of diftinft vitiun, when the objeft is placed at the 
diftance of fix or eight inches, which is the common diftance 
of an objea for diftintft villon. And the eyes of long-fighted 
people are not convex ent^ugh to admit of diftin^t vifion at 
that diftance. In the former cafe, the rayi of light converg* 
ing from an objedt thi:ough the humours of the eye, unite 
too foon, and before they reach the retina i to remedy which 
concave glafles are ufcd, which i^cndcr the rays more diverg- 
ing. And in the latter cafe the rays of light do not unite foou 
enoughi in their pafllige through the eye, to paint the imago 
un the retina : the vea^cdy of which ii the convex glafles. 

3 Q t 6. Whatever 



41 a ^^ otTtrs. 



14. Tht Ri&¥i.itCTioN of ruyt i« their reigiTi't» ur rcium* 
ing frcMU tilt lurface (4; Aich hoUiot* lon which they f«Ut Ami 
cannot enttr : ihuii the rtiya A B fliUiog on the fnrliiev 
C D, it refliiCled or turi^d heck ug«in in the direAion E. 
(Fig, 6,) 

!{• Mi«to«t, or Specuhimi, ere thofo bodies whofe 
farieceiere fo very fmoutht et to be impervious to the raya 
of light which toll on them 1 and which> therelbret they 
itfle^t fo at to reprefent the in\aget of the objcAs expofed 
to them: they ai^ generally made ot metal^ highly poliihed* 
or of glafi poliflieii ou one lidei and iilvered uo the other i 
And are either plain, convex* or contavetf 

i6« P1.AIN Mtaaoai are thofe whofe furficea are perfeA 
planea, and whofe fecllon it a right linci at CO (dg,6)| 
the(e are vulgarly called looking^glailct. 

I7« CoMVkx MiaaoRt are thole whofe furfacea do every 
way equally rife above the plane of their bafct s the lirftion 
of thefe fort of mirit)ri i« a cur\'e» and is either circular* 
elipticali paraltuIicaU or hyperbulicaU AUU (£gi4«) it a 
circular ft{\\w i and the mirror it the iegiuent of a glohe^ 
or fpherici^l furtacc» which is that moiWy ulcd. 

iH. CoNCAVii MiHROHA uic thulc w hotc Surfaces fuik 
down with au unii'oint hollowi^eiii below the up^ker {Mit^ s 
wholip fffition alio is a cm ve, as vaiioua »^ ihe con\ex ; but 
the cuvular lorm h tiie moi\ t oiumon, 

19. R^fKAi HON 01 r»\>'ji is their l>eing bent, or turned 
out oi ihcir iomiv', in puling out ot" one n\cdiiNU intv> ano« 
thcr: as the ia> li (.: (ti)i. vj), in jviiliug into the dcufe mr« 
dium A1H1\ is M'jVaOt..*<l, or tujueii out of itt natural 
couiicCK, in the dir».Oliv>u CU^ w\\\d\ is called the re* 
iu:ted ray, 

uvj. The iNriOKNTUAY it that which comes trom any 
objr*^, and talis ot\ tiio lot^aoling 01 lotkctin^ furtaoe, at 
BC\<ig,t), or All viig'^O- 



i!. 



OF OPTICS. 419 

the fpice within two miles of it, every way, with JuminoiH 
rayi of lighti before the tenth part of a grain of its matter ii 
jconfumed. 

The velocity with which the rays of light proceed from 
the furface of a body is furpriling. The method by which 
the fwiftnefs of the rays of light was determined firft, was by 
an olbfcrvation on the eclipies of Jupiter's fatellitcs. Thcfe 
eciipfes appear to us about fcven minutes fooncr than the 
precife time, when the earth is fituated in that part ot its 
orbits between i\\c fun and Jupiter ; and the cclipfe ap))eara 
about fcven minutes later, when the fun is between him and 
\\% I from which it is plain, that the rnys of light require 
about fevcn minutes to pafs through a fpacc equal to the 
diAance between the fun and us ; that is, about ninety-five 
million of miles. 

The rays of li«;ht proceeding from a vifibic body, as they 
proci^ed in all dircAions, and extend thcmfclves upwards and 
downwards, as well as fulewnys, muft neceifanly become 
thinner and thinner ; and that they do, in proportion to ihe 
fquares of their diameters from the luminous body ; that is^ 
^t the diftancc of twice a certain fpacc they arc four times 
thinner than at the diilancc of one fucli fpace ; nnd ut the 
4iftance of three times fuch a fpacc, nine times thinner ; an4 

foon« 

Of RvfvaHwn. 

All light proceeding from any luminous body, withmit 
being rette£\ed from any opaque fubftance, or inllc^^ed by 
pairing very near one, is always found to proceed in ftraight 
lines. But if the rays pais oblicpicly from one medium to 
Another, they always leave the dircdHon they had before, and 
aiTume a new one ; and this change of diret^ion is called their 
rsfraSiion: and after having fuffcrcd this rcfradlion, they 
again proceed ifi ftraight lines, till they meet with a different 
medium, when they arc again turned out of their courle. 

The phenomena of refraction arc occalioncd by an attrac- 
tive power in the medium, through which the light paiTet* 

Wlurn 





J 


^B WhM nnyaf Hfbi pain out 0/ ■ r*ttr Into ■ dmto^H 
^B «Mi (If tW bnn lM« ■ rntn^ >nrtA>>v fotn tM^H 

^V «iri<im« Uit ihi <l«nf*r n* 4»if<i. <*in U-gIn M W MtnAtf 
^H MrtM^* W , iiol iliu Mtfflum mA\ cotillnve u» lA cfOBlbc 
^B r«r •'I l^'M >'•■>' "Avr II tin mxittrA the (ncilHMR. WhM 
• nf farm )|w ilml^i mnliuni ntrf>(|HHv, lu dlicAiM viH 
•»»W~Miwtd*«l4lv<'iailMfurf>tK at ib< mtd;Mij ..J 
^_ •pyfOMtiiMonr »v 1 pcij-mikiiUr, dnnn lltfa«(Uih(fcr- 
^^ L.««llt»f>M>)(.iin. 

^1 HwrilMm mU«|h. (y, !•* dlii^on will be mi^ nmc vUlfl^ 
^H M tlw AiffWc of rbe ram mMlluni tai tkp«t l^^^^l 
■ fnm t prri«mM(ulH ik'on ihr.>u|h the (urh» of cbt^^H 



Th'ii (In Hi; It '. 1 rr ' ,- . T.v r,f light p»ffl.i};t>ir-n;('i 
I'lr .lit m'o ilir .1 nfr-i ir.r .'■..,». A I> II I ; at fntrring th* 
.■ "Vi n>. .1.11.11 Ml rli,. jK ■. r I '. it ^i ,1! hei;iti to be Jllwrtf J 
t.i'A ,t,\i ihit nir.liiiin, uli'li I'M.'ii'.n >m!1 cbtngr ill coiicfe 
(,-inilu.liir.'t..-nrK v,th:< .,t CI- I.u FG be » per- 
l-c.^.liMihi <lr.i»ii !li...'i^1i rh '>'nlrr ,ur,li,ini i then L will 
)>riliri;iir <A rlit an,;lr .,( ri-'iVn.xi, :'»d M N rhe fincol 
thr ..ii,:lrr)l .,iuiU<i.'<-. N..W rill- n:.<'..r lU in^le of iiiLi- 
I'tn, r i> :il«.i)t |ii.ij-i:ii.>r. /, I., I lit l,:n; uf the »ngle of re- 



li.m III), j.n.[H,ry,| ,, t. .i.'r,;!;; r ,> ( .,f lighl inftl ll« 
i,.i;;i,i;nii^ [xHiri (,1 cl.-- ;;...!itl-> uIl.I in o^ti.al iiidfu- 
i.Miij. li.rilii- ijj'.dl li; l.r pill •ti'jiij; (null any objtj 
,ic 1.1.1 .lini;;in-; >., .ilii,.! .,! .'.iii ,-i .ilion at i Icfi difljiice 
li.iti(..,'i. 6ii.i;,..!,,s ; ii, ili.iri,. ,-, 'ly imn(>onogajlift 
fti. I.tiu.t.. ilic ry: .iiul i;i.- .il.|f.t, the oLjcfl citi be 
;.«(.! :ir .1 lil> i!,l!.iiii., ti.r i.)i .if light, proreeditij 
irjii I In- iil'j. .'I, ni;i l)t ni..''f ii> (ui.v(i|;e (o » |K)inl fooocr, 
itnl l.y i!;.ii nitJiij (Lt iiljvii Hitl be Iccii uiider a lirgrt 
I. ),\. 

ThuJ, 



OF orrics. 421 



ycz O ;ag^ lO/ be a^n tA^jd: to be %ic\4rt4 bf the 
c. * a: F ; whicb oo'cO, to be viewed br :hc aiked eve, vau& 
be rcfloovcd to tac d^ace of £ji inches at leail trom the 
ere. B:it bj us:cr|M>£og a iecs^ whole tccai dtdonce is ut 
ioch and aa luir, !hc cje wiil have cKiltDd v:6^^n oi the ob* 
ject a: tbe difijcce F O ; cocfeqnecc^ the obtecl wiil appear 
nxigni&ed lovr ticses in dLifnecer^ to what t: would do to 
the naked ejc And the objed appears iisder ckc aog!e 
IFM. 

It as €b«eft AB (i«:.9) be placed to one fbcms of tbe 

lau D £, aod the ere ia tbe other focus F» the eye mill fee 

juu 10 cucli of the object as b eqnal to the diaoicter ot the 

less : Ux the rajs A D and B £, which, go from the extre- 

maks Of tbe objcA to the eztrefnitics of the lens D £» aod 

are uoucd at the feocos F» m'zd necednly proceed frorr. the 

cbjod to the ieos» pftraUcI to the axis FC, and to each other ; 

thfrtxorc, the pa/t of the cbjcd AB, f'sen bf the nrrs D F, 

£ Fy wiil be equal to the (iiameter of the Jens. If onl j one 

part Jt of the lens be open» then onlj io nmch of the 

objcd AB as b eq^al thereto, win be feen by the eye. Now 

as A B is equal to D E, or ii ^ t^ 4/r .* the ang^e D F £, or 

dtt^ is the optic ?jn^te ; tbst is, the angle under which ths 

pm Off the objed A B, or ah^ appesrs to the eye at F ; and 

as G F is iVi-^po^cd hu: half the diftaoce of C F ; the ang^e 

D F E, ot JY €y 15 double to that under which the paa A B, 

Of tf ^, would anrcir 10 the njVcd eve at the diibncc F C ; 

tLuj the tyc ices tbe object lu see as large in diameter through 

the Icr?, 2s it would do iiuhou: it. 

it it be required to f^re a par: of sn ob;cA brger thai; ti.e 
len», the eye mufi be place J nearer the lens than its to: us. 
Let tbe lens be D (fig. 8) i:i two foci F and C. In the focus 
C, let there be an o\'\t£i AB brger tnan the leni : iV-jip/c 
the rays A D aod B proceed from the extremities cf the ol- 
jc£t to thofe of the lens, then by the \t\.\ ihey ui!! be co;.- 
verj;ktl 13:0 rhe pokr K, be! v?en th. \y.i ir: ! -ti iKus f • 



421 OV OPTICS. 



then, if the CYC be plocttl «t K» it wiU f<« aU the ob)cd A B. 
wbkh it Urxer tlian the letu. 

But if the c)*c be placed further from the lens than its real 
focui, it cao never fee any objev^\» or part of an objeA. at 
oncei near fo large as the leDs» but always fmaller. Let the 
eye be placed at 1, beyond the focus F ; it will then only fee 
the part of the objetS^ G H» which is lefs than the lens. 

Thus it is evident that the nature of a convex lens is fuch» 
as will render an objeA diftin^ly vifible to the eye at the 
diftance of its focus. The reafoti why thefe lenfes are ufed 
as microfcopes is exceeding plain ; for if the ditanee F I 
(fig. lo) be fix inches, which is the leaft difianee an objeft 
can be feen by the naked eye, and the focal dilance of the 
lens c F two inches* then the objeA O will appear three times 
n^agnified in length, as I M ; and if it were the furfiice, it 
would be magnified nine times; and the iolkfityor bulk 
twenty*feven times. 

If the focal dithince F c of the Jens be one fourth parr of 
an incht then will that be but one twent^«feiirth part of fix 
inches, the diAaiice of naked Gght : and fo the length of an 
objeA fccn thmugh fwch a lens will be magnificvl twenty^ 
tour limes ; the I'm facr five lunxlreii and lcvcnty-fi\ times ; 
auvl cUc i'oliilicy th'utctrn thout.uui kven huudiird and twenty- 
lour lur.cs; K»v tUoic arc the Itpuuc and cube numbeu o: 
iwentv-t'our. 

To/tml the prifuipttf Focu^ ^if ^f^fff Lrns, 

Holvl the lens jKTpenvlicularly aj;a>nrt the rays of the I'un, 
or a oandlc ; hoKI a white ^Ki|>cr l>ehind it, to receive the 
rtfraCtcvl rav;?, which will nuke a i\)\uui white r|x>t up<>n 
the pa^>er ; move the p^qnrr IvackwanU or forwavd», till thi* 
f}H)i, which is the ima^c ot the fun or caiwllc, be the leatl 
pofliUle> there fix the \^\>cv ; then the dilunce of the |>aper 
from the leus i* lUc focal dillaucc rciinircJ, oi the burning 
point. 

o.. 



OP OPTICS. 423 



Or, fecondly. Cover the tide of a lens with a paper, having 
feveral fmall holes made in it with a pin ; and placing the 
lens dirediiy againft the beams of the fun, or a catKile, and 
the light pafting through the holes will form fo many white 
ipoti upon the paper held behind it. Move the paper back- 
wards and forwards, till all the fpots coincide in one. That 
point is the focus ; and the diilance of the paper from the 
glafs is the focal di (lance, 

I fliall here give fome of the mod general propotitions and 
properties in ' the fcieiKe of optics, leaving the proceis a»d 
demoaftration for the cxercife of the reader. 

2. Wherever the rays, which come from ail the points of 
an object, meet again in fo many other points, to which they 
converge by refra^ion, there they will make a pidlure of the 
objeft upon any white body on which they fail. 

ft* Rays Sowing from all pcMnts of an object, and pailing 
through a lens, paint the image of the obje£t iji the real 
focus of the lens, and may be feen there upon a white paper: 
or without the paper, the image may be feen hanging pen- 
dulous in the air, by an eye placed fix or eight inches behind 
tbe locus, 

3. The objeA, and its image made by a lens, fubtend 
equal angles at the lens. 

4. The length of an ohjci^ is to the length of the image 
made by a lens, as the diftatKx of the object from the centre 
of the lens is to the dillancc of the image from it. 

5. A convex lens magnifies an object, when it is nearer 
than twice the principal focal didance ; but if further oW^ it 
lelTens it. ' 

6. A concave lens always diminiflies an obje^^. 

7. . The apparent mugniiude of an object is tbe angle 
under which the objed appears to the eye* 

8. If the obje6> and its image be both on the fame tide of « 
the leos,^ the image will be cvcf\ \ but if thL7 ^ ^" different 
iiJes, the image will be inverted, 

3 H 9. Whca 



4^4 ^^v OfTio^ 



lwi» %n^ ihf ohjt?ft wov^ tow^r^a the It^Rii iht Imag^ i^lfe 
iDQv^ towAi^» ih^ Wnii ) %f\i if th<? obi<^^ movMfr^)) t?^ i^p 
imnnf «K<i nmv^ ft'oi^^ it* 

1 1« In A eonvf ii Wnit if ihf> ohj^v^ b^ (V^rtbtr ot^han tbv 
piinvip^i fiM^ui« ill im^tfte wiU b^on th^ otb^rfid^ of Ibo 
gi^ft, invf rt^« Qnt if ih^ obj^ bf o§Kr«r tb^n tb« |^io(i)>9l 
fbc\U| ih^ in)?ige will b^ 00 ib^ (km^ fldo of tb« i^i^a^ 

19, lo 9 eoocAv^ Wo»A tbe Imag^ nod obj«A «rf A)w$^y« on 
uM Mp of iho l^n«, 

\^. If iko obj^ be pliieed io tb<) pi iodpi^l feeoi of ^ \^^^ 
III Appiii^ol nnagoitudo M ^oy pltK^o wbi^l^vt^fa b^yood ib^ 
kn«i will bo iov9ri»b)y ih^ fin>o r^od «^M«I to \h» i^pfiitot 
i)>»goii\)d«>9 when f^^n from the p«oir« of ib« \mh wiih i)«o 
OAk^ »yf . 

14, The appart'nt magnitudi^ of a body» p\a?ed in the 
piihi ijidl t\v\»>, will always cohiu^je the famr, i^uwrvti Ou 
rye U mowil haAvwu*! v>i UMwani, tioin the leiu, 

15. *ri><? luau I ihi^ ry\^ u tv> the Irn*, the nuMrs t^t ilu 
(\h}U\ a|>pv*aiji , anvi ihe tcinhei off the r\e u Irtim the Itus^ 
the IcU ol ihf objtv'l ia Ircn, 

i6. It iht; ol'irct he ^\eaier than ih^? prineij^l t\Hvia» Ui 
«tpj>aieut h.^^nihble IricMtna Uis, iu going tVtMt\ the ^l.\t- 
lUa if ihe tih)i'»t he Jnrihir than the faiua, the aj>|vrtjcnt 
magnituile will inneaUs \\\ giving fioiu i|, 

17. M iht- e>r he tlved in the puncipal hw\ia, the ,ip|vavi nt 
n»agniln(h' ot an obitOt will he invaiiihly the fau\r, \v\ku\u 
the ohje^ id p^avrvl hehu t the glaia. 

iH, It the eye ami ohjti\ he fuetl, anJ a \Ouvrx Ua-. 
be moved tu»n» the ubjr* t 10 the vyc^ the apinumi \m)!^- 



OP OPTICS. 435 






nitudQ of the objed incit»lts« to the mivKile, utu) then de« 
crenfea to the eye. When it coineM into fuch a polition thAt 
tile «)*« And obje^ are conjugate ibci^ the objed\ ia iafiuicely 
confuted. 

' tg. If theeyeand objeA be fixed« and a concave lent bo 
moved fixnn either of them to the other \ the api^^arent mag» 
nitude of the objedt will decrtafe to the middle, and then in* 
treafe again. The apparent diflance )i reciprocally at tho 
apparent magnitude { audi in gtncrnl, we judge the apparent 
djftan(^e of an ohje»f\ to be tho very fame', at we fuppofe tho 
real diftance of an objev\ to bci from which the rayi como to 
our eyei| with the fame degi^e of confufion. 

io. Converging rayi are made more converging by n 
convex km : and diverging rays aiHs made more diverging by 
It oot^avt. 

»i. Parallel rayt falling on one fule of a conveic len& will 
be refirafted to the tbcua on the other fide. But parallel raya 
fillKni oii a concave lent WilL by retVaftioui diverge from tho 
focui on tho fame flde. 

»t. In a convex lent, rayt diverging from the focua will 
emerge parallel on the other fide. 

ij. In a.eoncave lcni| raj t converging to the focua will 
emerge parallel, tH^^^Sl t^tit of the lent on the fame Gde. 

»4« In a double convex lent of equal radii, the |xincipal 
focot it diftaht from the lent, the radiut of the Ipheroi of 
whicl) the lent it a fegment. 

•S« When the lent it a ]>erfedt fphere, tho principal focua 
i» diftant from the lent half the radiiii. 

»6. When the lent it an hemifphere, the principal focui 
it diftant four thirdt of the radiut, when the convex tide it 
«xpofed to the rayt { and twice the radiut, when the piano 
fide it expofed. 

•7. When th^ lent it a plano*convex, the di (lance of the 
focua it equal "to tho diameter, or twice the radiut of the 
fphere when the pinto fide it expofed to the rayt. But when 

3 H • the 



426 or orrics. 



tht convex fide ii cxpofcd to the rayi, the 6)cui ii dtftant 
twice the radius, except two fifths of the thickn«(ii. 

a8. In double concaves of equal rtdu, the prinoipal fioais 
Is dtftant the radius of the fphcrc ; and it is virtual. 

•9* In a pUno'Concave, the principal focus n dilfaitit twice 
the radius ; and is virtual. 

30* If the radiant point and the focus be eqvkliftant from 
a lensi they will each of them be didant twice the priiKlpal 
focal difiance. 

31* H the radiant point be nearer the lens than Uie prin- 
cipal focus the rays after retraction will diverge ; but if the 
radiant point be in the principal locus^ they will after refrac- 
tion emerge parallel 1 and if the point be farther off tlian the 
fotttSi the rays will converge after reA-aCtion* 

3t. The dilhnce ol the radiant point and its fbaiS| nvado 
\ry a convex lens, is the leaU polTible, when they are e^ui* 
liiAant from the lens. 

33. If a convex Icoa be hcM dirr^ly to the rays of the fun, 
and a combunil>le body be held in the principal fbcosi the 
heat of the rays of the fun, converging to a point in the focus, 
will fct the body on fire. 

34. The hcHt of the focus of the lens i«, lo the fun's dircA 
ticiir, as the area of the glafs to the area of the image in the 
focus. 

3$. The i]rj;rccs of heat iu the foci of different lenfes »rf 
as the r<iu:ircs ot the diameter t!ircv.^^ly : and the fquaies of 
the focal dillaiiceH in:iproc:ilIy. 

The forcf;oiuj; propolitioni contain all the phenomena of 
rcfr.u*hng Icnfcs ; and may be proved for the moft part by 
aotual cxiKrimrntf . 

It is ncc.cllary jiifl to obicrvc, for the fake of thofe wlie 
may ufe lenfcs of a different meilium, that difT'erent mcdiumt 
have different refratHiag powers : I (hall, therefore, give a 
tabic of the rcfra^ing power, as given by Sir Ifjiac Newton, 
and proved by many later experiments* • 

I« 



ov opncs.' 



MMM 



4?? 



In the fud cohiinn nre the names ot' thcUKlics; m blie 
fi*coiut colunin, the fmos of iiiciclcmc and rctV.iOtion j in the 
third colnmni the rclViu'ting power ; in the t'oucih colunui, 
their deutity, or fpccific graviry ; in the (ilth ci^lumn, the 
ratio. 



lioJUs. 






Ptcudo topax 

Air 

Glafs Antimony 

A felenitis 

(ilali 

Rock cryftnl 

I {land cry Hal 

Sal gemma 

rMum 

I^orax 

Nitre 

Vitriol 

Oil vitriol 

Raiti water 

Gum Arabic 

Spirit wine 

(Samphire 

Oil olive 

Lini'ecd oil 

Spirit turpentine 

Amber 

Diamond 






RffLtfiinp 



I 



3201 

n 
61 

3« 

*S 
S 

>7 

10 

51 1) 

3« 
too 

:\ 

100 



:4!i.69() 

320010. CooOi 5 

9,4. 568 

4 1 ' t • 2 1 3 

fto t.^oa; 

li) I.44.J; 

3 »•/?» 

S4I1. 1267 
1511. 1511 

2CO l.2()J 

7|i.04t 

3t/>o./7«4 5 

21 I. 179 



73 

a? 
17 

41 



o«87()5 

1.2? 
!• 1^1 t 
1. 1048 
I. 1626 
I. 42 
4.049 



4.17 

0.0012 

2.2^2 

1. sH 

2. Oi; 
2. ;» 
flt. 143 
i.7»4 
t.714 
r.9 
1.715 

'•7 
t. 

j'^7'; 

o. 8()6 
o. 996 
0.913 

o. 93* 
0.874 

1.04. 

3-4 



;o« 39 

I -5* 

.48 

•54 
•54 

: I] 

.64 

.70 

• 75 

.78 

UOI 

i.2«; 
r.26 
1.2B 
1.32 
[.3(1 

I. 4s 



From this Table it appears, that thofc bodies which con- 
tain oily fnlphurous particles diAcr I'lom the* conftant rauo, 
juul have .n greater refnidif e power. 



SECT. 



42S or oPTTCff; 

ggsaaggggyf^sg^j', ,,r,'.' i.^ 



SECT. IL 



or SllfOU AND COMPOUND MICROSCOPES* 



StNOLE iillcrofcopei are fttcb that have but otit Icnif wi 
may be coufiruAed in an inflnite variety of wayf* I (hall 
give the forma of a femr of the moft uieful. 

A (fig. 1O9 plate 5) il a crrcular piece of woody metalt ct 
hrory, in the middle of which ii a fmidl hole» c* Upon tbia 
hole ti 6xedt by means of a wirci a glafi fphericjrf leiify of one 
tenth of an inch radiuf ^ whoTe focul diftance it c D« At tbe 
focus D It « pair of plyert D E» fixed upcm a flidiog icrew Bp 
and which openi by meani (ff the two ftudf %f ^ i thcie plyeri 
ierve to liold any fmill obje^ O, which if to be viewed through 
the leni by the eyot placed in the other focus F : and accord- 
ing to the focal diftance of the ieni, the objcA will be more 
or lefi mn^^nificd^ as before dcfcribcd : thuf, in a lens of this 
radiui : viz. one tenth of an inch, the focal diftance of which 
if a radius and an half from the centre thereof, a« defcribed 
su the fr>regoing proprjfitions ; the length of an ohjcCt^ by 
fuch a Ictts, will he magnified forty timet ; the furfaccy cue 
thoufand fix hundred; and folidity, Hxty-four thoufand timcf. 
For a radium and an half of fuch a fphcrc, or ^^ ^^ 3^ uichy 
ift only the fortieth part of fix inches* (tlie Icaft didafKe of 
naked vifion ;) the fquare of 40 is 1600, and the cube of 40 
64000. This inOriimcnt, from its fixe and portabiliry, if very 
convenient* The heft lenfes for their (ingle microfcopcs arCf 
however^ thofie wliofc focal diftance rt three teothi, or foui 
tenths of an inch. 

Again, when the diameter of a fpherical lens is only one 
twentieth of an inchy tlie ob'jcQ, wiU (ubtcnd an angle at the 

• eye 



09 omps. 429 

mm^tmmm 1 1 111 — ^ 



^ye as great as if it were only-three eightieths of an inch, 
^which it the one hundred and iixtietb part of fix inches) 
llifiant: therefore, the length of an object feen through fuch 
^ lens will be magnified one hundred and fixty tifpes ; the 
furfacc, twenty*five thoufand fix hundred times; and>the 
folidity, four n>iliion and nine(y-fix thoufand times ; which 
i$ fo great a magnifying power as to furpafs conception* 

Bu^ fpherule len{es,of fo fmall a diameter as the latter, are 
of no ufe but in viewing tranfparent objects ; for if an opake 
pbjtSt were to be viewed by fqch a lens> the eye mud be ap« 
plied almoft clolic to the furface of the lens, by which the 
Ifma and objedt would be fo over«ihadowed| as to render an 
opake obje6l too obTcure to be viewed. 

Thcfe fpherule lenfcs were ufed by the famous Mr. Leeu- 
vvenhock| by which he made fuch wonderful difcoveries ia 
the minuter parts of nature. And it muft be by a proper 
f rrai^geipent of thefe, that \he particles ot matter are to be 
difcovered, if ever they can, which Sir Ifaac Newton thou|;bt 
l^as poffible. 

But there are great difficulties attending the ufe of thcie 
irery fmaU fpherules: firft, the difficulty of making very 
- good ones, of a very fmall diameter. Secondly, the preju- 
fdice done to thp eyes in ufing them. Thirdly, the trouble 
of placing objects at the proper focus. And laftly, the very 
fmall part of the pbjc<5t, which can be feen at one time. 
Thcfe inconveniences render this fort of microfcopes of very 
little fervice for commoq ufe ; ihey have therefore been 
fuperfeded by others, particularly by the following; in which 
)>oth tranfparent and opake ol)je4!:'ts may be viewed with left 
trouble. 

In tfiis inftrumeot (fig. i-i) F is ^ piece of hrafs turning 
round in a focket, at the end of which is a fmall fprlug tube 
fnoving upon a rivet, through wliich there runs a fleel wire, 
terminated at one end by a fliarp point, G, and the other 
«nd hath a pair of plyers, H. The point and plyers are tq 
ibruft intO| or take up any obJetSt. Either of them may be 

A turned 



OF OPTICS. 



43» 



M (%. 15) is a raaad objed pIsiCy biack 00 one fidt, and 
vbiie oa diecMlBer. N, a ftecl fpriog, Ouniog cioira cm each 
fiiky to hold aoj 6b;ed £uL A dark coioored obieS is to 
br plaoeid <» the white fide ; and a light coioored ob^ on 
fhe black Ede, to render tfaem more difeisd. This plate 
aJ£> has a imaU pipe to fcrew on ibe needle G (ig. 11). 

Titts Bicrolbope is of late inremjoo : and brmeaof of the 
^■ilbti wakrw^^aj opake ofcged anj be nevcd viih a veiy 
£bb!1 ■nigpifw. Tranfpatent objeds may aUb be Tiered 
bf it: but 10 this caie, it will not be proper to dmnr on the 
0biea afl the li^ reioded from the fpecninm; left the b^ 
rwfwin r i d dwoogh d>e objed, meeting the lefleded fi^. 



pradnot f0o great a g^bre. For tius purpotficy a bit of p^Kr 
inar be iumpo ^ Ld b c inc e u the ob jed and iboae part of the 2 
^pecoimn. A hitie pradice wili exzabSe a periba to know 
how to fi^^idale die Hgfat. 

As cpske obieds are more rsnjerocs than others, very 
g reat dtfcoveiics maj be niadc in foch obieas . 



A yCcrcfape cm a Standi uJiuh uUl crtfuer <Li tJie 
Kr*ds tf tht large DotdU R*rfitct'ing MUrofcKfe. 

2 (fig. 17) is a roond frame of wood, on whkii U tirtd 
^x bffai icTGil A for the pcrpcnc of boldng rhe mkroiccpe 
fieadr. C is a bmk icrcw that pa&i tliroogh a bole in the 
icroU, iaU) the mkioicope D, aod icrves to ic«w it fa^ t3 
cheicroH. 

E ii a coTxave looking-ghiE, or zpccv.'. -m, of metal, iJet in a 
hrzfs box, azxi hzngiag in tb^ trcb G br two iicaC icrrws ; 
at the bcttcmx; of iL:s arrh is 2 im-ilJ brzis pin b, which gc**5 
tbrtragb tbt fiaod of the irrb ;d:o tbe wooden frame B, tn- 
•rhicfa TDtALii the aicii h t-ratd roand 12 an h^.»r:zoctaJ dirrt - 
tjon ; and tijc zx.irror iwizp iz a tctdcs] dircSion. Bj tbeie 
two morbriS tht «p^ci2lrrm it2T be ib adjured 2$ a> reflet 
t!H fT!-: drrtSiy jpwirds, djTJ»cgb the bodj of tiie aacro- 
D, wii3ch 1: £icd perpend': ulzr'y over it. 

2 I Tbe 



432 or orrici. 



The body ot the intcrofcopc may alfo be fixed in an taon- 
tontal dirt^ion, and objedi viewed either by the light of % 
candlct or the common day •light. 

To life thii mtcroii:opr,tl)c ol>jccl it fixed in a Aider, which 
ii thruft in between the plaici. through a Ait on one fide of 
the microfcope. 

This microfcope may be iifcd in a variety of ways. One 
method 1 ihall mention :-^Take a flip of glaU, place one end 
through the flit of the microfcope where the llidert go; and 
nn the piher end, which extends to fome diflaiice, any objcA 
may be |daced that cannot be placed in the flidert ; then 
place over the objcA, upon the flip of glaft, a magnifying 
kns, fcrewcd into a braft ring, (having (everal lenfes fixed 
in braft ringi for iliat purpofe, and in fuch a manner that 
the ring of braft may extend as far as tlie focal diflance o( 
the lens,) and bring the fpeculum to refleA the light up to 
the objc«!l. 

Microfcopts of this fore are the moft cafy and pleafiinl f6t 
tife, of any extant ; and will ferve to view vtry minute ob- 
jcAs ; fm'h as the animalcules and fults in fluids, the farina in 
vegetables (he rircuUtuMi ot' the blood in fnuU inftfts, &r. 
It the ob'ri*t lia\r jj»v il. vMic c! tianit>:iiriK V. tMi miciolc(*i r 
!. !ik(!y to niAr uhkc ii.l.u>cnr» la ii than any othrr. 

(if ncuflf or {'iitnpoufitl Mi.rtt/loprs. 

DouMc oi iOinpiMiitd iniLioA (tpr*. Mr thoK* \% li.i li li iW 
l\w» ^I.ilU-->, tti Irnlr* : lli.it lusl lUr i^UwC'i is r allcil thr o^-cx'l 
j-'.ali ; ;mil l\\M iir\t t!;c rv*-, ilir i vr yi\\-. 

1*\uo\'i\'\ aU (!s;', i(»> I-. pi.ufil .ii .1 liiilr ;.;:ra;r: »': i 
iMUc lii'iii tlii- i»!»|rrt y\.\*', tlian iI- t.n'Ui ; li» :!»al ll»r t \- 
tlnwinj; fa ni l!ir ilir»cic:ii piiinii nt the ol>jr;t, i»i»il ju:. : 
t!.iOUv)i ihr i»l»'.it I' ;Uii . ./, u lil iiin\cii»r Ici / .tiui , \\\.vi • 

' ■ m S 1 ■ 

♦•;rv ItMMi thr ui:..!;r it t!u ».. 'i^t. 'i'ln. iin;i;:r m MfU nl 1 , 
:lirrM-.'.t I, tin . uiji ihr « w* |, il • .' '. w l»u h is lo pl.iic*. 
•Ii.: ttir \i\...yr y > i ■ ill .' !t», u- , u:i 1 \W rVr m '!lC U • ' . 



I 



OK OPTICS. 433 

«lfO| but on the other (idc ; thtis, the rnys of each pencil 
viiil converge at the eye k^ wher^Jiey croi'i each uther» and 
after pafllng through the humours ui the eye^ they will form 
the large inverted image A B on the retina. 

This image, fccn by iuch a microfcope, will be inverted 

^ith regard to dircft vidon : for the object a h lies in the 

fame dire^ion as the image A B on the retina, as fecn in the 

figU|p I which is not the cafe when the objedl is feen by the 

naked eye, or by n finglc microfcope. 

To calculate the magnifying power of thefe double micro- 
fco(>eS| we reckon how many times the objedt is magnified by 
the object glafs, and then how many times the image of this 
objeft is magnified by the eye glafs : thus, if the object 0^ be 
nMgniiied fix times in length by the object glafs ri/, as it will 

■ 

ivhen the image ^^h is fix times the diflance from the objeft 
glafs, as the object ab \%\ and if the eye glafs #/ be only 
of half an inch focua, the image ff h can be viewed at half 
an inch dilbmce, which as it is only the twelfth part of (Ix 
inches, the image j^/^ will be magnified twelve times in length 
to what it will ap|)ear to the naked eye without the eye glafs: 
and the image ^ b being fix times the length of the objeA a h^ 
the obje^ ah \^ therefore magnified in length feventy-two 
times, and the fuperficics and folidity in proportion. 

The field of view is very fmall in a microfcope of this fort ; 
therefore, there are generally two eye glaflcs ufed, which arc 
placed fometimes clofc together, and fometiiiics an inch or 
more afunder : by which means the vifible area is much en- 
larged, and a larger field of view is obtained, though the 
objcdt appears fomewhat Icfs magnified. 

A Coynpotmd Microfcope. 
A (fig. 1 8) is the body of the microfcope, which is move- 
abk up or down in the external cafe C D, which is fixed on 
the foot of the inftrument 1, by three pillars, F is a plate 
fixed horizontally to the three pillars, and is called th« ftage. 
In tlie centre of which ia a hole, on which a piece of glafa> 

3 I » ""' 




43^ Of opttcs. 

«n angle, from the perpendkulit* to the furface of the mlr-* 
ror, M they fall upon \t, wiih regard to the perpendicular, 
but on the other fide thereof* Thui» let C be the centre of 
the mirror*! concavity. Draw the linci C/Ap Cm^ and 
C ^ r, ftxHn the centre C to the mirror* Thefe linet will be 
each perpendicular to the mirrori at they proceed therefrom 
like fo many radii. Make the angle C A h equal to the angle 
i/AC» and draw the line ^m A, which will be tiMidlreaioii 
of the ray #// A after refloEHon i fo that the angle of Incidence 
</AC \h equal to the angle of reflexion Cmhi the Incident 
and rcftedted rays making equal angles with the perpendicular 
C^ A. 

fin the fame manner the angle of rede^km mtC ma/ be 
proved equal to the angle of incidence Ctt, The ray C m / 
paffing through the centre of the mirror's concavltyi and 
tailing upon it at If is therefore reftefted back from It In the 
Jhme line. All thefe rcfle^d rays meet ki the point 1*1 and 
there piiint the image of (he body^ from which tiie parallel 
rays proceed. 

Tliis pointi as before obferved, is half the dlftance of 
/C. 

T'hc rnys wliivh proceed from any cclcftinl object may al- 
\\"Ay^ Uc. cllccnuMl parnllcl : anJ ihcrefore the images of fncli 
ol>ici'b. on a icllct'Uil Ipccnlun), will be formed at half the 
ill (lane ol I lie ccnlic ot the minor's concavity. 

llm ihc rays which proceed from any dillant terrcHrial 

«)i)jr<'t do not coiuc (piiie paiallcl to the mirror ; but come 

diver^ini* to it in Icparatc pcnv ils ; ihcrefore they will not be 

conveif;cd to a point at tiic iliflance of half the radius of thr 

concavity oi the mirror, but at a little greater ditlancc from 

the mnror, atul in Icparate poin^« And the nearer the objed 

i^ to the miiror, the farthci thcle points will be lemovcd 

from it ; and an inverted image ol the objei^t will there be 

fornu d, which will fccm to hang i>endulous in the air^ by 

an eye placed beyond if. 

Let 



OF orTici. 437 

Lit AB bo II mirror» whofo centra of concMvity ii C 
(^•3)1 D£ ia «n upiight ohjoA pUccd beyond thoc^nttoGi 
Ar^m tho uppor end D, of which flows « pencil of diverging 
ngpa (0 ovtry point of the concAve fm face of the mirror A B. 
From the centre C^ drew C A, C v« C B, touching tho 
mirror in the fame pointi where the pencili of raya touch it, 
ivhich flow from D« Thcfc three line* drawn fix^m C to the 
mirror will be perpendicular to the furface of the mirror* 
M«ke the angle C A ^ equal to the angle D A C ) and draw 
the right line A A for the reflection of the ray D A. Make 
the angle C B 1^ equal to the angle D B C| and draw the right 
line cA for the courfe of the incident ray Di\ Make tho 
«ngle C B J equal to the angle D W C» and draw the right 
line Bi^i for the courfo of the incident ray UBi all thcfe 
reflcAed rayi will meet in the point W9 where they will form 
the extremity U of the image U U, 

If the penciU of rays be drawn fron; the other point of 
the object K| in the dlit^^ion E/» E^i £/>i and be conti« 
nued to the furfaco of the mlnx>r» they will be reflefted 
back from the mirror to the other end of the objet^t «/) and 
their angles of reflexion will be equal to their incident an- 
gles : thus, they form an inverted in^age of the ol>jeA| at 
the point A% 

Though I h«ve only drawn three line» in the figvwi to 
Tcprefent rnys flowing ft'ow the point D \ yet it nuift be ob* 
ferved, ihnt tl)is point, as well as every other point in the 
objei^ fends forth a ftttiH #/ m\^ to every part of the rair* 
rori and the rays of each |H:ncil are reflci^ed b(W'k» v\^ 
ineet in all the intermediate |)oints of the objei^t 4^ ^^ hal 
^n fltown* with i^gnrtl to tho (>olnt D» 

When the objet^ is* farther from the mirror than its ceturii 
Ci the image will be lefs than the ohjeft, ami will be boiween 
the objeA and the mirror j but when the objctt is nearer 
than the centre of concavity, the Imnge \vill be further oft* \ 
l»nd biiiger than the obje^^t 

M 



438 or orrxc^. 

If the rndini of the iniri ot'h cnncavity, and rhe diftanre of 
the (>l)jrA from the mirror be known, the diihnce of the 
ima^r from the mirror may he foiiiul by this rule :•*«• 

Divide thr |)roclu^ of the dillance, mulciplied bythera* 
dins, by tluuble the dlilunce made leU by tlie nidiui ; and 
the quotient is the diftance reqnhcd. 

If a man place himfclf dircYlty before t concave mirror, 
but iU a further dillance from ir thni^ the centre, he will fee 
an inverted imaf;c of himfelf in the air, between him and 
the mirror, and Icfs than himfelf in fiae. And when he 
liolds l)is h:itid our townrdi the mirror, the hand of tht 
ima^e will ulfo approach towardv hli hand ; and if his hand 
be ill the centre of liie mirror, the hand of the image will 
coincnfe with his hand ; and an inexperienced obferver will 
fancy that he mny Ihnke hands with hit own image. If he 
extend hii hand ft irw^itrd further towards the mirror, the 
hand of the imnge will pals by his band, and come between 
bis hand and hib body : if he move his hand to either /ide. 
the hand of the imagrt will move the contrar)' way. But a 
peifon (landing at a diihnce, and on one (ide of the mirror, 
will f(pe noihinfj; of the imH/V, bff aufc none of the rcftefi^cd 
rays iMiifr his tryc. 

It la nrccfliiry that the l<.^'l(l(*l jifiKrAly un«l«!rfbnd whnt is 
here dcrmoMllralcd coin t:iniii|>; niltV lion, that he m:iy pcr- 
ceivtt how tlu* ima^r is foiim-il in tin: lar^^r cnnravr inirroi- 
of llic rrfift'tinp, lflrfi*i)|)«\ 

Aj;ain, if a romavr mirror l)i» j.l.tcrd ai;.iinlV a wall op- 
pilitit a fire in a cluuiihtrr, uml a ni.;lj();;:iny t:iMc hin;ljly po- 
lidicd, placed in the for 111 ol ih- minor; a pnlon flaiidiuj; 
farin^j the minor, bnt not *iirc-c'lly hrtvvccn that and the 
in-f, will fee a lar^jr, l>i»|.;lif, ticA in).j)M- n< the fire upon 
the tal)lt! ; and to a calnal filifci vcr, jnll cnteiing the room, 
ii uill appear in all riMpcilu like a rial fire. lUil the rount 
<lii)n!(l he made (piitc dark for tliiu p\n-j)pie, that die iiic may 
n]»|f ar inoir lui[;lit. lUil to a perlon who llundt* un oi.r 
4 iidc 



OP oi>TXcs. 439 



■*¥ 



fide the table, nothing will appear but a long beaoi of 
light. 

I^ inftead of a lire, a large candle be plac«l oppofite the 
mirror, a perfon (landing by the candle will foe the appear* ] 
ance of a large bright fiar over the table : thuii by fixing • 
large candle in a frame, with a fmall wax taper to turn round 
it, in a circle, an appearance will be made in the ibcui of the 
gUfi, reprefenting a bright planet, and its fatellite { the lii* 
tpliite performing a revolution round the planet. 

The Itefra&lng Teleft^vpe^ 

The firft form of refra^ing telefcopei, that I ihall men- 
(ion, it that which confifti of two lenfet only. The objedk 
glafi muft be convex; but the eye glafa.may be either convex 
or concave* 

Let r if (fig. 4) be a convex object glaft, in a long tube, 
and have itt focui at.E. A B it a remote objeft : from the 
extremity A ilows a pencil of rays gH^ which will be f^ 
refraAed by paQing through the glafs e /, ai to meet in the 
point/s ami the pencil of rays iim% flowing from the other 
point of the objeft B, by pafiing through the lens will be^ 
refracted fo aa to unite ia the point # ; thus the pointt A and 
B of the objcdt will be forined by refradion in the points /#•* 
and all the intermediate points of the objeA fend forth pen- 
cils of rays, which forox corresponding points in the fmall 
figui*e /<*, the inverted image of the objedt. But as this 
image is fmall, a concave glafs n c is placed at the end next j 
the eye, fo that its virtual focus may be at F« Then as the 
rayt of the pencils come to the concave glafs converging, 
they will converge lefs after pafiing through it, as hath becu 
demonftrated : and they will proceed to i and a before they 
unitci whiiph is on the retina, and there form the large image 

The only inconvenience attending the ufe of this telefcope 
189 that the field of view is very fmall, by reafon of the rays. 

3 K divcrj;ing 




at o^^l^^. 



dirtt|tng (b miKhy afor paflin^; through the concave 

flaft. 

For, from a ticw of tha dgun^ it if evident that whan the 
ft Icfeope lici direftly tnwardi the objcA^ none of the my% 
which txm fhmi the extremtttei A and B oin enter the puiTil 
of the eye ; but fall upon the irif| above and below thr popi!. 
So that| to view the diflPercnt pnrtu of an objeOi the trlrfropc 
oiuft be moved upwardi or downward!, unlcft the ohjc^ be 
a very remote one ; and then it \n but tndtftindly fe^n. 

Thcreforcy to remedy thii inronveniencc, a amvcx eye 
glafi ii ufed inftead of a conrave, af «^ ^fig. {), which in 
placed ib| that its focus may be coincident with the focui of 
the objeA glafi c y, whofe fncns is at E« Then the rays of 
the pencils flowing from the ohjcA A B, and paffing through 
fhc objeft glaft r ^, will meet in its focviy and form the fmall 
inverted image mf. And as the image ii formed in the focuft 
d the eye glafi s t, the niyl of each peiArilt after paffing 
through this glafs, will be paralteli but the pencift fhcmMvn 
will converge to each other, and crofs cKh other in the focua 
of the glafi at /.* the pupil of fhc eye being in thii focus 
the hnage will be viewed through the eye glaff» under the 
angle DeC. 

This telcfrope alfo hd«j aft inronvcnirnce, which it, that it 
ini^rta the objc^ with rffpn'^ to it, when feen by thr nalc'l 
eye: that ip, the imai^f in painted in the eye in tlir fimc 
pofition in which the tth\zft Ur% ; we thercftrt-c iudgc it t^ 
be inverted. This tclcrropf is, thcicforr, only fit for view- 
ing ccleAial hodif«, in mnny of which their pofition if imma- 
terial. But it mild be obfcrved, in the ufr of thi* tclcfcopr, 
thit whatever way the (A^jt^/eemi to move, the tefrfrr pr murt 
be moved the contrary way ; for as the objeft is in vet ted, fo 
will be the motion. 

The magnifying power in thiii telrfcnpf, is as the foc.il 
diOancc of the objedl glafi is to the f(Kal (liHancc of the r\r 
gfafs. Therefore, if the former be divided by the latter, »hf 
r]UOtient wdi exprcfg the magnifying power. 

Thcrefuif, 



or orxics. 441 



■■— ■ ■ ■ " W ^ l IP 



Tfaertforti this telefoope can be conllruAed fo, «i to mag* 
Dtfy la ai^ proportion, provided it be of a fufficitnt Itugth ! 
for th« greater the focal diftance of the objeA glafi ii| the Itfii 
may the focal dil^ance of the eye glafi be. Thui; an objeA 
glafii of ten feet focal diftance will admit of an ejra giaftf 
vrhofe focal diftance is little above two inches and a half,, 
which willmngnify the length of an object near forty-eight 
tlmesi and its fui face and foUdity will be magnified in pro* 
portion t as in the microfcope. 

Tkoii if the focal dilbnoe of the obje6b gtaft be equal 
to the focal diftance of the eye glafs, the telefcope would npl 
nii^gnify the obje^^ in the leaft. 

AgaiUi if the focal diftance of the obje^ gladi be twenty 

hiches> and the focal diftance of the eye gtafs one inch| tkt 

, length of an objcd feen by foch a telefcope will be magnifiai 

twenty timeii its furfr^e four hundred timeit and its folidity 

eight thott{und times. 

To remedy the inconveniences of both the former kinds 
of telefcopeSf tiie following one is generally uled fot; terraf*> 
trial objeAs, which gives a larger field of view than that with 
the concave eye glafs, and fliows the obje^ in its natunt 
pofturei as feen by the nakc^d eye. In this telefcope thei^ 
11 one object glals cd (fig. 6)1 and three eye glalTesi if^ 
^^ ii» They are fo placed, that the diftance between 
every two glallesi which are next each btheri may be equal 
to the (urn of their fbcul diftauces: thusi the focuit of on* 
glafii is coincident with the focus of the next gkfs. Tht 
foci of the two glaft'es r// and #/, meet at F; thofe of 
the two glafles r/^ gh^ meet at /; and thofe of gh and il, 
at«t and that of ik atx, where the puptl of the eyt ii 
fttuated. Then it is evident, from the figure, that the pen* 
rils of rays which flow from the objeft A B will pals through 
the object glafs c ^, where they crofs each oth^r, and meet, and 
form an inx-ertcd image, in the focus of the glaff at C F D | 
this image being nllb in the focus of the next gla(^ r/, tha 
rays of the pencils, which fiow from the image C F P, will 

3 K a be^oma 




OF orrtcs. 



become parallel after pafiing through tbii glafti aod croft 
cMh otlier at /» which U the focus of the next ghft gSi 
iherebrci the ny% proccctiing from thh fecut and paffing 
through the next gUfs ^ ^ are converged to the focoi of thia 
g|afi» where they form the ercd image E F of the objefl 
A B ; and at thb image it in the focut of the ejre giaft ik^ 
and the ejre on the oppofite fide of the ghdt in the other fo* 
cut, the image it viewed through the e]re glaft in thn tele- 
feope» in the fame manner ai in the former ooe» but hi a 
contrary pofition ; that it, in the iame pofition at when feen 
bX the oriitd cjt. The objea alfo appeart under the angle 

The tbret tjf€ glaflb have generally all their fecal dMancet 
«fuaL The magnifying power of thit telefcope te found in 
dia finnt mannca at that of the laft : via. by dividmg the 
fecal diAanee of the objeft glafi bjr the focal diAanct of wy 
ana of the e/e ftlaflfet, at the three tatter are all equal* 

ObjeAa feen through fuch a telefcope appear coloured 
about the edget, the reafon of which it, tluu the rayt of 
l^t coodng from the objeA are unequally refrafted thnnigh 
the glafi tent, and particularly thofe ra)rt which pafs thmuv;h 
a convex gUfs near its cilgei. Thcfe rays lacing unequally 
rcfni<f\ed» do not all meet again in the fame points ex- 
aiflly* Thcrelxirci in this ttlclcopc, there muft be a plate 
with a fmall round hole in the niidillc, fixed at *», parallel to 
the glatfes. By this pUitc, the w.mdcring rays about the 
edges of the glall'cs will be intercepted, and prevented froni 
coming to the eye ; and none admitted, but thole whkU 
cofne through the n iddle of the ginil'cs, or, at lead, at a 
good dillance from the edges. But this I'omewhat lelTens the 
field of view, which would be much l.iigei if the plate could 
be dii'iKnfcd with. 

The binocular, or double tclckope, is only two tdefcopct 
•f an equal magnifying powcr^ fi^cd m a t'r.unc, parallel to 

cacti 



OF omcs, 443 



each ochery and adjuiled by the cnenns of fcrcww, i*o an to h« 
at the ikine diftancc from each other i\% the pupiU ol the two 
eyct. Then by looking through them U^th at once, ihi'OM|{h 
one with each eye, the object will befet-n by bnth ryrn, nnii 
appear bnghtefy and more dillin^ than thro\)gh a (iiigU 
teicfcope* 

The RefleSling Tele/cope. 

Refrading telefcopes require to be of a confide rable Uf\giUt 
to magnify to any great degree, and the gi'eat Irrigtti uf 
ibme of tbcm hat rendered them very incoiiventtnt. Hk 
l£uc Ncwtooy therefore, invented the fir (I tcUffopc at ittf 
rcflediog kind, and which has received conHderiiblf \m* 
proMrcmeots fince his time* Since the invenci/in of %\wUf 
reffading teleicopes are very little ofed ior cetefliiil objr/tf % 
fer a fcflediDg telefcope, of only fix feet in fcngfh^ r^ii \m 
Iwimg^r to magnify the objed as mtjch aj one iA tbc iM^f 
iJKtafabBBdrcd feet in length* 

Tker are gtmenl^ cooflmded now io the tMmm^ mm^ 
merz TTTT (i^;) if a large tube, at tbe fiKiUbt^ 4if 
vtalb m pbocd a large coocare murrm^^ DWf^ ^invh 

■mni kdc f, rpyoiffr «ik«db ib j;[l2f(4:<f ctvr ;l«t4^l ^tiif^iMr 1, 

if- vitellB lit flCiit Ir ibupo^il DCirc: ^tt;/ l&it j;^? t^ft* wwn • v*v 44r 

askiQlgi^1Mrra■9^I^{)p0kiie2»^t^ h .v 



iUe^l: irttfat lli&Rr jHiiK^ litm V*m*i?:lw^^^tri'r»};fH«i 

Si, aR^ iSbhi^ rttmsaf ^^^M^i«^ ^ fits: («#i^^;,««M^ JW, 



J*' 



444 nr omen. 



Ntid by rmlUtiK Nt I« the |;Hiiiit of ronvfrg«tice» umi the 
t>ilncipfil fttriii of the inirrnr, they form the upper ettrf* 
tiiiiv U (if the imn^e IK, flniiliirtothe lower tittreiiiitjr 8, 
vl the ohjf^ A W \ nm) then thrv pAf<i on to the fmall ton-< 
c^vc mirrori whnfr fnvun U At m. They full upon thii (hmtl 
r\»m'.ivr minor iit j^, ami ,irr from thcnrr reflei*kd» 4?o«verg» 
i\y^ in the ilirci'liun ^N» hcrttnfr j^ "^ !• longer than jf * | 
nnJ p.ilTtnit thitnigh thr hotc 1', in the Urge mlrtori thcjr 
Mouhl pnli on to r* brfore they meet, iinti ihcrt forto the 
Itiwcr f ?itrf mitv ,/ of the rrr^ litittge (i^9if rmitlar to the lower 
rxtirmity B, of the nhjcfl A R. Hitt paffing throtigh the 
plfltic convex gUfn K, thry form that extremity of the tmxfo 
At A. Tn thr f(imc mntmer tlie ravi G» which come from the 
ehirrmity o( the t)h)i«^> A, nnil frtll pArxltcl Upon th« great 
iniupt nt F, rtir from thtrncc i^flr^led to tti fecyi, where 
thry tnim thr lower rxtromity K| on the Image I K| flmllAr 
r»» the nppci rMttrmity A| of the nhjcft ABj ami from 
thciKc thrv puis on tn the I'mnll mifrnr Ii» and fall upoh H 
at /») fiimi whenre thvy arc trflc^lctl, eonvtrglng In the 
thiortion /-O, rtml paffuig thrtntjjh the hole V of the gfeat 
tiiiiioi, thrv wniiM lurri t\\ ,/. aiul fniin thr upper cxtrc- 
n ity r, ol lh«' injn^;;r »• ./, finnl u l«» fhr rjitrrmity A, ot* thi* 
rblfi't A U , l»nf jnllnu; (lunu;.;h thr ctMUTX J-^lrtf'" U, thry 
inrit. nn.l OM'i-j Innnri, .1= it .», uhnr tlmt point of th<« 
iiiia^;r n jofn-cJ. In ihr l.noiMn.inMrr prnriU of" rny^ flww 
liutn iviiv Inl- imc'liilr pf^rt «»f {\\r n|»jr(M A M, \n thr piT^t 
fuiti'i Pr V l'\ i\\u\ Hir IVdin thfi^'r irtUiMnl \n thr fm'it« 
rl thr iuM«>i ''4^ \\hr\i \\]^ y (mmii nil itwrilrti ini.1|fr tif thf 
rl»!''iM. All'! ImIUv. thr inyc pMlilf^: in^m thr inirtK''**^* 
tlimn^Ji tbr ryr j/Udfl ^i, ami thio\i^;h n fulfill hoir r, in thr 
rml «»f ilir \(\hr Inlr^^ iluv rntri thr rvr /* whrir thry 
tii'h r;i' h i»thri in the piipil, nn«l pninl thr nnnjtjo of lh«» 
f'l'jr/^ nil thr K tiiia ill itP iMititrtl ppntion, nml the image ii 
Irrii In- thr ryo ninK 1 the Is^f^.^ ariKlr 1 #7. 

To linl thr ll^^|rnifyln^J puwrr t»l (hi.^ trlrfoopr, fhr rnle 
IS, to mtihij'ly thr kni{\ iliil^inir of the great mirroi, I7 the 

dill a mo 



or oPTici. 445 



■I ■ ' < ■ 



diftancc of the fmall mirror from the image which in next 
,the eye ) «nd multiply the focal diftancc of the fmali mirror, 
by tile focal diftance of the eye glafi { then divide the pro« 
4uA of the former muhiplicatioo, by the product of the 
latteri and the quotient will be the magnifying power. 

When the firft image I K is forme<l a little funhe r from 
the great mirror than iti principal focui, at at « i the fo* 
cui of the great mirror ii never coincident with that of tha 
fmall one ; therefore the rays of the pencila reflet^ct) from 
the fmall mirror will not \\e |)aralWl, but rather converging, 
fo at to meet in the pointi ^ #r, where they would form a 
, larger creA image than « t^ if the glafy R wai not in the 
way. This image might then be viewed by means of a Hogle 
rye glafs, properly placed) btit in thnt cafe, th^ Field of 
view would be left} therefore, the glafs K is ufed to enlarge 

t\\9 vi^w. 

The adjufting fcrew, to which the fmall mirror L is fixed, 
fenders this telefcope applicable to every fight, as the fmall 
mirror may be brouf^ht either nearer to the eye, or reuK>ved 
farther from it i by which means the rays may be made to 
divtrge a little, fAr fliort-fighted eyes i or to converge, for 
serfons of a long fight. 

In the ufe of this telefcope, it mud be obferved, that the 
nearer an objcft is, the more the pencils of rays will diverfjo 
before they fall upon the great mirror j Und coufequcntly 
they will be the longer before they meet after retloolion j 
therefore, the firft image J K will be formed at a greater 
diAanre from the large mirror. But this image mufl always he 
formed further from the fmall mirror than us principal focui 
fi) therefore, the fmall mirrpr muft be fet at a greater dif« 
tance from the large one in viewing a near obje<^\ than when 
viewing an objedt more i*emote ; this is eafily performed by 
turning the adjufting fcrew* 

The i^fleAing telefcope will admit of an eye glafs, of a 
fnuch Qiorter focal diftAt\ce (and confequeotly of a grtater 

nuignifying 



.44^ ^^ OPTICS. 



>•• •■.*M 



magnify ing power) than a refra^tng tclcfcope will ; there- 
forC| thofe telefcopes magnify to a greater power. And the 
rays of light are not coloured by the rcfledions of the concave 
uiirror, if it be ground to a true iigure« at they are by pa if* 
ing through a convex glaU« though it be ground ever fo 
true. 

Jn thefe reflcAing telcfcopeSi the obferver never feet the 
objc^ itfclf* but only the in^age of it, which is fv)rmed next 
the eye. This will be dcmonftrated by the following expe- 
riment : 

If the obfervcr 6x a ((ick acn)rt the mouth of the teIeico|)c 
before the objcd glafs^ it will not hide any part of the object 
from his view, unlrfs it covert the whole mouth of the tele* 
fcope ; but it will only make the objei^ appear dimmer, by 
intercepting part of the rayt. But if he place only a piece of 
wire acrufs the infule of the tube, between the eye glaft and 
liis eye, it will hide part of the obje^, which he thinks he 
jcrs ; which proves, that it it not the real object but the 
image which i6 perceived. This it evident, from the fmaH 
mirror !«, which it made of opake metal, and Aandt direAljr 
between the i ye and the objcv% and would hide the whole 
objvCt liom tl'.c nc, it the two j^l.fU's R and S were taUc^ 



'V'w:. ;oi..i i< \'*" opr i.s the nioll uroful infbumcnt for \ic\;% 
w^i; :: r Wu^: nt tii.- tvin ol any hithcito invented. It is foinied 
oi .1 iVi i|iti;»: full and fockct, which is laliened a^ainft a 
hole n\ ilit* window-lluittcr ot a daikencvi room; in the 
^ \ liiuhlral hole of which is j>lared the end oi a coqhuou 
utVavtinrj toltlVopc, which is to be drawn oni ti) ii< proper 
i,r2tl:; ;hen li.e b.iil .md lelclVopc arc uioxuvi ahcni 'ill the 

l.iVS 






tty% of the f\iii fall p«riKnd(eulArly on th« objtft gh(k^ thrdugh 
thf hole of tho bttll i th« tnb« which tontaini the tyt glafi it 
then to be adjuftcd, by drawing It In, or b\if| till th« imagt 
of the fun bt formed oti a white paperi in the focui of the 
telefcope, very dlfthu^ly and large. 

ny thli teleftHipei the fare of the Atn may be repreftnted 
In almoft dny fiKe» which afordi the mathematician an op* 
portunlty of viewing all the phenomena to be ften in that 

planet! f^t^'l^ ^* ^^^ ^>^^t ^^ ^^^ f^>n*> dlfci which are feldom 
fcen when viewed through fmall tclc(bopei| in the common 
way* But they may here be feen in all their dtferent appear* 
aneei i ai their Incrrafft dtvlfloni unloni beginning and end» 
lire, alftt the folar ectlpfa may bo feen to a great advantage. 
And the tranflti of Mercury, and Venui over the fiice of the 
fun are moft deilglnfiilty exhibited by thii inftrument i ai 
the plancti here appear truly roundi and very black \ their 
comparative diameten h) that of the Am may be talten. with 
tho true dtreAlon of their motionii theii ingrefti egreft« Uq. 
The circle of the Am*i dife may be divided by linei and cir« 
del, that the quantity and time of the eclipfe may be exaAly 
determined. 

The Ar/;#/rtM wn« the invention of Dr. Ornvcfand \ by this 
excellent invcntlnui the motion of the telefcope, In viewing the 
folar light, Is giratly taken off. It confifti of two parti * 
firft, a plain n\etallle fpeeulumi Aipported on a ftand i and 
a eloeki whieh dircAi the ())eeulum according to the motion 
of the earth, and thereby preleivei the image of the Am in 
the fame point of view. 

Tlw ArufMatic Tvhjiopc. 

Thii tckfoope hai a double, and fometlmei treble obj<?ft 
glaft, to coMta the aberration of the rayi of light i for all 
rayi of li^ht pairnig iluoutth n fingle leni will be Vomewhai 
ilccompoundcd, and divUleil ioto fepdiratc colouri, which 
nindcri the ohjea coloured t to rcnird) which, ihc double 



448 o» MTtCt. 

obiitA ghCi h vM* Tk\$ oMi&fti of t doiibit «oiicivt Imi 
of whim Aint gKli md f d^MMt ccMvtK of crown gtaftt The 
two |Mirt» of tht knfo, which vt on flit ftmM fide of tht 
eetiU'e, h«vo the ftme tCiQ on the rett of light M IWo trU 
anguUr prifmii which refinA the rey« of light in t coiitrtry 
^iieCitioo t^ Cich other i therefoie, if the e^ictftof refm^ioii 
ia the crown glefi <lcftroy tht divergency of coloun octit^ 
fiflxird by the 4int gleTcs the incident rey will be refinAed 
without ifgr foreign coloOrt thut| the image formed in the 
tfi^ui^ «r thin compound objeA gl|di» will be of the fkmt co« 
tour ei the objed. For the nqrt tfowing upon thefir gluflei 
fkom difiani radiant ol^e^b will pt& thioiq^ them In fech e 
manner, th|t the aberretioni ceufi^ Iqr the firft giafii i« fo 
l^r Gorreded by the fecond| that ibe raya emerging Aom it 
ere nearly perelleli end eoneergad to one feeui* Tbia tele« 
fcope mayt thereforei l^ve e much larger eperturei end e 
fffoter megnifyiiv poweri then the common refolding tele* 
foitpe cen. And if the telefoope be fliorti the lenftt fliouM 
be vory eoneett end it fliould then have three lenfte for tlie 
objeA gleft t e eoncen one of white lint> between two eon* 
vex ones of crown gi^rs. 

The Camna 0//r;/r<T, 

Tbe camera obrcuu is only a convex gUOi C D ('^({•p) 
JfLXci in a hole of a window-diiitter. In tbc fvKus of thit 
glaU will be fccn, on a flieet of white |)apcr placed parallel 
to the glnff, as at G H, the imnp;r!^ f>f all the objcrts outfide 
of the window, as tree*, men, cnttlo, Scr, which affonli a 
inotl beautiful piece of landlcape, or peifpei^hsT, partloulaily 
it the fun (liine« upon the obje*^;^ : but the in^^j^e* appear 
iiwertcd. The room for thit purpofe rt\o\i!d Ik fo ikiVened, 
x\ux no light can enter, but what conus ihrouvjh the lent. 

To reprcfent the image ht^ntoiually, the convex glaft 
C I) mull be placed in a tulns in the luie of a ftpmrc N>k, 
Within which in the plane mirror lih\ leaning backward! 

in 



OP omet* . 449 

smmmmmmmmmmmmmmmmmmmmmammmmmmmmmImB 



in HI Migle of forty-five degreti from tW perpendicular Ijf i 
then the penoils of rnyt Mowing frotn the outwmi obje^>9« 
and paffing through the convex glaft ta the plane mirrori 
will be reiieAed from it ttpwardi, and meet in poimtf» and 
form tlie image I K, of the object A B» which it at the fiime 
dtftance from the minor BF, at the image OH« which 
image they woiald havi; fo'rmed if no mirror had been in the 
way. Thii image. IK will be formed on an oiled pfeper* 
ftretched horisontally in the diredion I Kt On tbii paper 
the outlines of the imagee may be drawn with a bhick lead 
pencili and then copied on a elean flieet i but it it ufuril to 
place a plain unpoliilied glafi in the direftion IK to receive 
the images of (he outer objedb ; and their ouilines may be 
traced Upon thisi at on the papef. 

The tube in which the glafs C D is fixed muft be move* 
M»t tbat it may be drawn out to adjuft the difance of the 
gidt lens, from the plane mirror, in proportion to the dif^ 
cance of the focus. For this purpofe, the tube muft be moved 
backward or forward| till the imagat appear diftlnAly on tho 
hori^Bontal glafs I K* 

If the mirror E F be reclined in the oppofite dire^on i 
that iS| leaning forwards towards the lens, in an an^e of 
forty-five degrees, the images of the objeAs will then appear 
in an horizotital pofition, but below the box i and inverted 
with refpedl to the image I Kt 

To form an horizontal imagCf as I K of an upright objeft 
A By it it necefliiry that the mil ror be reclined from a per* 
pendicularf in an angle of forty-five degrees. Then the 
rays of the pencils stc flowing from the point A of the 
object A B, will fall upon the mirror at the points i/^, 
and from thence will be refle£ted in the lines i /, f I, g I, 
and form the point A of the objeA A B, at the pointi in the 
image I K. And the rays of the pencils qrs^ flowing from 
the point B, und palling through the convex lens C D, will 
M upon the mirror at the point mik, from whence they 
will be refle£led to the point K, where they form the image 

3 L * oi 



4<;0 OF OPTU'fi, 



ol ttie |ioint of the olije^^ H. Tho fame niAy be (lemon* 
llrntcd (if the peiicili of myii which Mow from every inter* 
iticdinte point of the objeA A 19. Thii lioriasnntAl reflexion 
(IcpcncU upon the lAyi of incidence, (which full upon %\v$ 
mirrori nftcr pnfllng iln'0U](h ttic convex lent C Df) mukinff 
angles, with n perprndicttiiir drawn to tho fnrfacr of the 
miihif , rfpMl to die anglci furmed l>y the rcfle^kd rftySy ntid 
flic iiiid pcr|)f OilictdAr i thufi if wc fuppofe ii |ierpcndicul»r 
(iMwn to tiic furfiice of tlie mirror nt the point kf where the 
jr$y A tf C/ fulls upon itf thnt my will be rcHc^ted iipwiirdi 
in the line k //I, which will make iin iingle with the Aforefatd 
pcrpendicninr, nnd on the otiicr fide thcreofi equil to the 
vnpjf formed by the per|N;n<lirtdArf and tho incident ray C k : 
:iiid t( II |Kr|>cndi('iitiir be drawn to the point /of the plane 
ntirmri where the rny A^/ fatli n|ion it, that ray will lie 
uHr^hd upwnrdi in the dire^ion//' 1. which will alfo make 
iiii nn^lr with thr lafl pr rprtuliciilar, equal to the angle formed 
by thu Inridcnt rrty Af/*, and tlie fHmr |)erpendicidar« TJio 
iunie inity be demonArnted of every other pencil of rayi 
which flow I mm the ol)jc^ A H. 

The fl.if pliino-cofivrK pjAfn, viiljruily rnllfd the nnilh 
j»lv in;; y)i\i*j i'. uird td multiply .in objc<*t. If i* forinrd ni 
:i plMtio-(-(Mivrx }(1.)i'f;. thr rotivrx (idr of whit h iK}rtnnn<l into 
irvriiil Hnt fitrfHcr!). An ob|r('t kvw thiougji fnrh ii ghdi will 
:ipp< :u inuhiphid into tin niMiiy ditlcimt ohjrt'.tii ni the ylxin 
roMf iin«« |)hinc Itirriirrq. IrtAP (lif;. tt) b«: Inch n j;liils 
the flat liiil.icrnnf which nrr l/f^ /////, ///■.• tlirn tiir i»)4 
whirh (low iioiu the ohjcrt (! to nil p.ittn of thr }\\t\i'% will he 
If fi.it ird hy thr phinr liitlntrD fo lh( rye nt II. 'J'hiiii, tlin 
I. IV I'll fiilliii)'. prt))rtidi( \il:irly on thiMiiiddlr fiiifntr, will 
p.il. thM>n);h thr yJnU wiihont iiny icfituiion, ;ind lliow ilic 
ol>M«'l (' In itn tf'tir phur j but thr lay ft A, flowing; tiotn thr 
i.inir objri^t, :iiid hilling; i>l}lir|ti(ly on thr phinr iiiHiur///', 
will hr ii h.i^lfd in thr (IJH (^tion < II : bywhidi thr obji/t 
will »p))r;it n^ at i.. Ami thr liiy t //, flowing liotn thr ohjri t 
i'f iincl l.illini; ohlupirly on the ihit luiiaitf/l| will br le- 
ft ai'trd 



OF OPTIOI. 4)1 



fmAed in the dlreAioii fH i by which th« objtA will Apptfur 
in th« llne/w» ni if it wtr« «t D. If tbo gUfi Imb tun««ii 
abound tho axil H/je^, the objeA C will r«mMiu in tho fnnte 
plucoi but (he other objoAs D and K will nppcAr tg go round 
C I becaufe the plnnei on which the oblique rayi &IU will 
Im turned round by the motion of the glofii 

From wh«t hni been fuid of the properties of diflefent 
lenfet, the intelligent render mny l)e able to fonn » combi* 
inition of themi for eny ordinary optical purpofe i but it rn^y 
be neeeflkry to fay a few words morei concerning the relie(.^t« 
ing telefoope. 

The great mirror of the refleAIng telerco|)e» at Invented by 
SirliAAG Na WTONf wai truly fpherlcali and which telefco|Ki 
Are of eflbntial fervice at thli day, particularly in the miii«/i> 
of tftronomy, when ftiiall aperturei and long foci are ufed. 
lk%Hfr/ibiU ulbi a refleAor of thii fornii in hla^yen feet 
reflei^ing telcfcope. And the hIgheU jpower that a tclefcopc 
jof a i)>herU:al metal will bear with perfeA diftinAnefn, may 
be founds by multiplying the diameter of the great mirror 
by feven|y«four. Thuii in Dr. Hcrfchcll*i I'even feet re* 
ileAori the aperture or diameter of the grent luirror ii 6.i j 
incheif which, multiplied by 741 gives 46a the nmgiiitying 
power I and the focal diilance of the fingle eye glufn \\\\\y i^c 
foundi by dividing the focul diftiu^co of x\\t greut ntirror I7 
tho nuignlfying power t thusf 7 f^^rt, the ftK'al dilUncci nniU 
tiplied by Ui and divided by 4611 (|uotci o.iBa ol an luch| 
the focal diAance of the eye giufi. 

But the concave furlace of the gi^»t mirrori in coininon 
reflcAing telefcopeii in of a puiubuiic form i which fortu Sir 
Ifiiac Newton wai unuble to give to hit mctul, though ho 
recommended It 1 and imagined it might be eilV<!;ted l)y nus 
dianical devicei, 



A TAin.K 



««1 



A TAni.K 

UF (Hi; 
N8\YT0NtAN RErt.BCTORS. 



If 


!! 
II 


jl 


Pi 




r.<f. 


l» It.'. 




f* fthr. 




1 


0.86 


I6d 


e>iAi 


& 


1 
• 


t>44 


iM 


«,«Ai 


n 


.*;!» 


1 


>,t< 


4 


4.10 


o.t8i 


>)> 


( 


*.^ 


6.HIJ 


•M 


A 


\- k1 


*>. 1 1 1 


• 11 


J 


ll\ 




i>. )•! 


tM> 


fi. H,> 


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.», 


4 


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.1'4 




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yjf- 


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f'. mi 




in 


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A TABLE 

or THK 

Dimen/ioiu anJ *i*fg»'ifl/i*g Powers tif Ike Grrgorim 









A> 


«itftrufle4 hr 








M>, SHORT. 




jj 
8 


1 


ll 


i 


1 


i 


1 
ij 

i 

■v 


1 
I 




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1 


1 


1! 


1* 


1 


1 

■a 




u[>^< 


f, n.. 


/..*),■.■ 


{>• lift 


U.D^- 


;o.i^v 


t-.JlH 


U.On 


IV 


1.61 


.ti. 


•'4- 


U. (4 


• V 


1. 10 


".(+ 


(.«( 






1.04 


■i. r 


^^.l 


•^( 


I. (0 


•■10 


.,.«o 




..6: 


1,^1 




•l.Vi 


:S 


1. >< 


I' 51 


!(.(. 


• b. 


1-41 


i-Tl 


?. 11 


4i< lb 


!■♦ 


6.>l <t.w 


>4i 


.t!» 


•:i? 


^•t* 


.».., 


^«> 


-l-« 


,..,«..«. 



Since tl» mwmlon of thcfo reSeftinn ttlefcopc*, tbc rc- 
fniAingonei ar« very llitio ufed for celcftU) obrcrvittlom. 
I^or B refraf\ln| telefbope, even of « ihotirnnd fcti fbcnt, 
(ruppoflng it poffibla to be ufedi) could nnt be madatn 
magnify more thun one ihoufRnd time* t whertni k refleAlns 
telelcope, not exceeding ten frci, mll.niagnliy ineh'e hun* 
'Ircd timet. 



454 ^ or orrtcs* 

^:. _J_.. ' ^L . JU-AnsaaammeL — l^mw^^**** 

Mr. Shorri of Kdinburghy wai the firfl who brmigbt the 
Ctrcgoriuti rcflcdtori to yttkf\\ot)f by giving tbem the tnie 
IMrabolic fornix whereby thry will admit of a much larger 
'i{>crtiirc. 

To the fame iiigeniotm f^entlcman we nre atfo indebted 
for that excellent rofitiivnncei the etjitatorial telefco}7et or, 
di he himfcif callii it, n portable off/ervai»rf \ by which moii 
of the ftars of the ftrft and fccond mognitttdet ai alfe the plA- 
net» Mercury, Vcmi^ and Jupitefi mny be feen at mid-day^ 
even while the fun fliinct bright, fly thi» inflrument, celeflial 
objedli mny be viewed with vtry little trouble. It confifli of 
a piece of mac htnery, by the help of which the mounted tele« 
fcopc mny Itc turned in ajiy dircAiou, and dircAed to any 
degree of right afccnfiriny or declination. And any obje^ 
may be cufily kept in view, or recovered when loft from fight, 
without moving the eye from iti fituation. The particular 
cffc^ of thift telefcopc depetidi upon iti exclttditig almoft all 
the light, except 11 hat cornel from the objeA Itfelf. But any 
other tc(efoope of the fame magnifying power^ and In tlie 
fame Atnationy will have the fame effect. From a fimilar 
r«iiife, the ft?ir9 are vifibic in dny^tiinci from the bottom oi 
a (Irrp pit. 

Mr. kHfiiidcn hjis ^lU^ l;itcly invented a portable obfr rv;i- 
tory, which, it is cxpr^Jcd, will cxcci Mr. Short's. 

To rciidrr the fixed ftnrs vifible in day-time, it is only ne^ 
rcflary to exclude the cxtrnncous lif/ht ai; much a» pr»ffiblr. 

A romrf, or any (;tlier heavenly body, may l>c fecn through 
this fclcfcopc; its tniichincry dire^ing it to the projxr pliwc 
in the heavens. 

The prin* ipal advantaj/rs of microrc<;pcs and tclcfcopc* 
depend— fnft, upon tlicir pioperty of ma^nilying the mi- 
iMifc paits of rljt obje^f, fo that they can be fecn more dif- 
*t\^^■\\y tha/) by U;t ii.iNrd eye ; and, fccoftdly, upon their 
tliKmin:; more ljgl,t into the pHj)il of the eye than what 
woiii J flow ffon» ']■•'.- objc't ilitlf, Tl»c n)ai;nilying powrf 

of 



OP OPTICS. 45 s 



of the glafs would be of little fervice, if thU latter propertjr 
of tranfmitttng the light be wanting ; for the fame quantity 
of light, fpread over a larger furfiicei becomes proportiooabl/ 
diminiHied in force ; and though the objedti may appear big- 
ger, they would appear proportionably dimmeri without an 
iucreafe of Hght, ai well as magnitude. Thus, tliough a glad 
fliould magnify the furface of an o\}}^& an huodrod timet^ 
yet if the focal didance of the glafs were only eight inches 
(if this be poiTible), and its diameter only the fise of the pupil 
of the eye, the obje<fl will appear an hundred times more dim 
through the gtafs, than to the naked eye ; even though the 
glafs tranfmittcd all the light which tell upon it, which no 
glafs can do. But if the focal dirtancc of the glafs be four 
inches, and the diameter the fame as before i the objeft will 
appear far more' bright^ becaufe the glafs could be placed 
twice as near the obje<5t, as before, and confequently would 
receive four times as many rays of light from the objeAi u 
in the former cafe. Thus, dimlnifliing the focal diftance of 
the glafsi and keeping its dimeter as large as poffiUei we 
ihould perceive the objeA more and more magniAedi and a( 
the fame time very diftia£t and bright. 

With regard to the comparative merit of telefcopet, for 
lerreftrial obje£ks,thofe of the refraAing kind have evidently 
the advantage of all others, where the aperture is equal, and 
the aberrations of the rays are corrected according to Mr« 
Dolloiid's method : becaufe the image ia more perfod t and a 
greater quantity of light is tranfmitted, than can be refleded 
from the beft materials hitherto known. And a telefcope for 
terrtftrial obje^s (hould never magnify above an hundred 
times ; if it do, the vapours arifiog ftt>m the earth will be fa 
magnified, lit to render vifion very obfcure and imperfoj^. 

However, the imperfSedions in every kind of glafsi vety 
much retard the improvement of thefe tttlefcopesi in which 
th<src arc five eye glafles } fo that they cannot be made above 
three feet and an half long. 

Upon the wholti therefore, the refle£Ung telefcopet are the 

3M bed 



^•Ailfo. 



\ 



.s 



.v« 



•I 'I 



¥' 



OF omci. 457 

Mtfcope muA be kept condantly dircAed to the fame point 
of the objeA t for if the telefcope be moved gently f(om iti 
pofitl^n, the objeA will fcem to move in the ffime, or in tho 
oppoflte direAioni iccordlng ai the telefcope (howt the image 
Invertedi orereA. 

If the Inftrume nt Ihnke ever fo littlei It makes the objeft 
Ainee befoix our ej'et i and caufei an indillinAnefii in the vU 
flon* In tho Gi^gorian telefcopei it is hni^ly pofflblo to pre* 
vent this quivering motion of tho fmall fpeculum» as it ia 
flxed to the tube by one arm only. And though the tube of 
the inftrument be fixed ever fo motionlef^ this fpeculum will 
retain a tremulous motion, particularly if the te1efcoi)e haa 

^ i great magnifying power. This motion Is an imperceptible 
tremor, like that of nn harpfichord wire, while it is foundingi 
•lid produces a limilar effbft to the fight« A perfon walking 
In the room, where the inftrument is fixed, prevents us fi^m 
fteing the objeA diftlnAly \ or even the pulfation in the body 
of the obferver agitates the ground enough to produce thia 
•IRiiA. The more rapid this motion is, the greater is the 
optical IndiftinAnefs i or the obJeA appears' more confufed. 
Therefore, the more firm, elaftici and well bound togetheri» 
the A'ame work and apertures of the telefcope are, the mor« 
hurtful will be the confequences. Juft as it is to a rider ou 
« wheel carriage-«the more firmly the carriage is fixed on tho 
wheels, the more violent will be the motion to the lidcr. A 
telefcope, therefore, mounted with lead (if it were praAica- 
ble), would be pit;ferable to one mounted on either woodt 
iron, 01 biafa. This is the principal caufe of that indiftinA* 
nefs of vlfion in the very beft rtfleAing tclcfcupts. Kefia>!i\ing 
telefcopes have not this inconvenience. 

Froii) hence we may ealily judge of the nterits of any 
particular apparstus, for the fupport of a telefcope : and in 
general, all fornts whet^ the t\)be is fupported only in or near 

. the middlci or where it remotely depends upon one juli\t| 
are very dcAruAive of difllnAnefs of vifion. 

•i M • The 



4 



OP OPTICA. 463 

To uje the Solar MUrofcopey fPig 4.) 
Make a round hote in the wiudow-fliutter, a little larger 
than the circular plate «f^r; pafi the mirror O N P through 
this hole, and apply the ff)\iare plate tcf the (liutter, Icrewlng 
it thereto by the two milled rcrewi</#.* the fcrewiareto 
pafs through the lluitter into their nuti in the microfcope, 
and thci*cby to hold the body of the microfcopc firm. Screw 
the conical tube A B C D to the circular plate <i ^ r j and tUtn 
Aide the tube O of the opakc box into the cylindrical 
plate fcDEF, if opake object are to be viewed; but if 
tranfparent ohje<5l8 are to be viewed, place the tube Y, 
(fig. 5,) in thb cylindrical tubc^ (fig. 4. ) The room 
f))ould be made at dark ai pofllblei and no light fuffcred to 
enter, but what comes through the body of the microfcope ; 
for, on this circumdancei together with the brighcncft of the 
ftm»fl)ine, the di(lini5tneft of the object, in a great meafure, 
depends. The mirror NO Pis to be then fo adjufted by 
Aieans of the two fcrewi Qjind R, as to reflect all the fun'a 
light through the lens, at A ^, in the body of the micro- 
fcope ; the mirror is to be fo adjufted, till you have formed a 
clear tt)Und fpot of light uponafcreen, or flieetof whito 
paper, placed at Ibme diftance. 

In viewing an opake obje^i place the objei^t between the 
plates at H ; open the door ik of the opake box, and adjuft 
the fmall mirror M, till the object is Urongly illuminated. 
If this cannot be effcAed by the Icrew S, you muft move the 
two fcrcws Ciand R, in order to get light rcfle£Ved drongly 
from the great mirror NOP, to the imall one M. The 
oW}t^ being ftrongly illuminated, (liut the door i k^ and a 
di(lin«5t image of the object will foon be obtained on tho 
fcrecn, by ndjulling the tubes V and X. In the northern 
latitudes a clear large fpot of light cannot always be obtainedi 
nor when the fun is perpendicular to the frant of the room ; 
ni the light then falls upon the back of the mirror. 

And Note, As the fun is continually changing its place, 
it will be nccelTary to change the pofitioA of the mirrori by 

3 N tb« 



A. 



I tifilMFli . • . 



flu rtw Ijitstt mik'i«(i*tw f flg, !,) Ill tite «>liinliiv*) ml-* 
XVi (fe* 4 i) [>"' ''^^ '''^"'' CK' ^) '"'** <<* H*^'* ■' ■ 
(ll|t It) .iih) the (IhUi with tlw vIvtA liclwwii ih« iw« I 
iDttM « Oh aihl dtljiill lilt laruv iitittxtc N O l\ (flg, ^^) ■ 
Mbn dtr«{t«0 lit a{uke ottJiiAs «hJ i«k"I»<» tlM fui'tntf 1 
tftn fltl|ltili«r i>t' ihf lln^lv mkrof<ope, (Ajj. (,) l>y th*l'~'*W / 
Oi ^c in<3ft pIcoUiu iHByiti^era fw ituiuiipn tili, »n i)w(k j 
' awHtld uunttwT 4 am) i In itw flidcr, (()£< h.) The fite of j 
m ^tt\ inny Im titvt-Mfnl or diiiiiniOtctl, hy uliviinit th* j 
Mian ol III* It-rven tVoi» the inlvrokflfw. Thm tllftAiK* 
ivMoh fticvv* the ubjcA moil ilifliiiA, U «l)itti( fiv* it( flit l«(t. 

9Vfn»)iMf>f»MMj^rirfHf OtJ*^iiu/u h'srr Sit* ^ lk» 

T^uut ih« flkdn. (t)|A) ri^'in in iiUpo, In Ig. i, wI 
tartw *( btttMv, (Bk j,^ liiM tl"^ h.ik M V, (ftfi. 1 1) itMk 1 
itmm e the gUfn whivli W un«tM' ibe |»)u« ai m. attd rtjptlMl 

Al ilw cod of thf tutie Q, (tig, 4O itifw )i a )<ih far )«• 
cwfitig ihe dwfltjr ef ttw raji i whloh f«fv« w t>ur« my , 
KflRtbuAibU iuhA«nu> uf entit any hiftkle dm. In wl«| ' 
tttli mkrc)f<»{M!, thtt Wi mufl tl^ner^ bo tnkta mm Mk 
lb* ubj«£t Qteulil be burnt by lb* IntcnSty of tbf tiMt. 

Thii ffikirolcftpe aAohla lh« amlett •nnrMtnntwt of tiq^ 
an aiwaunt of 111 wuntlerltil <H||nUyn)g pamr, wd tt« 
Hfenilbwhtah Imr^l perfoMinay vl«iNMah£i))|k etuH^ 
itt ih« flwid tlnioi It wufomwrly uftdoitly IW trARQtfMM 
oAJtdii hut In itifl ywr )7T4, tAr% S, Marttn ixnfKvmtt 
thli iRtlrtiRwm ft) far, ai ta remler )i tipiilkcsblf M ainto ' 
«l^(iC)i. H« ftwakiof litbMi *• Wlib ibU InArmnmuR 
^|Mki al4J*Ai| whtt^rdf thtulmiil, vtjiciabli, wmlnani 



' % 



t'.' 0» OWICi. 46J 

„;.;_ j i ir ii H ii i j u Ji j i iui. i .^^ ■ ■■■■ ^[ M . 

'{.'*: '^t^nftlom, m^ bt enhiliiitd in great |)wftAion, in rH lh«ic 
/"Jji.'; l»Mrt« bciftityi iho Mghu luid Ihadei, lh« prominencei tnd 
f;'*^'''''';^'ti<"i aivd itt the varieiiet of riifftient bi)c«, (inii, and 

^..-^ti^a^nr heigtitened by the reAcAioQ of the folu.i'«>i eon* 

; i^k',',. TTwOj)t(;rnnl microfcope il repieretited, (fig. i,) whenr 
■■■t'^Ji frp V-^ '' ^ '""K" niihogsny pyranudical box, which h 
W£'.S''i1*c boiiy of ilio microfcope i and fupported on ihc brafi 
"^ *iiUlar ftG, by the focVet H| and th« curved piece. IK 
.\/'.'' ilM:^ aiij two mbci, one within the other : to the inner tube 
*V^ ■. h.^'fikbt the vei Lical piece M !« w.hit^h ii n guide to the eyOt 
1^ '• W 'i''*^ it '" ihe.axii of the inftrument. Thii piece may 
•bX * '^|)e raided, ordriireflcd, pulled further out, or pudied funher 

pVt- - - - 



■*, * *C< ^° "'''j"'^ 't '" 1^^ '^^"' '^^ '^^ glitlleit >"d make it coiacida 
*•. " . ^li\i ihe centre of the field of view. The tubci M N are 
^£„^^cd 16 the box in a domailed piece of brafi. pp it a 
t ^rvJftwll lube which cnrrtc* the magnifien ; O is one of the 
; y.-i^a^iifieii fcrrwed into the end of the tube. QJISTVX 
f ^ . ,'i^fi ^iig ri|i)Hie bar, palling through the focbeii V, Z, and 
||'.Vc^-'T«tv<^ tn hold the flags for the objeAi: thiibarmaybe 
\.^y, -ni^Al tm^wanl or forward, by meani of the pinion «, and 
* ••^.''■'ilMhaj.i'Jtlqi <-, iq oidcrtoadjullthellDgetothcibcm. Jt, 
^ u! i»^t)rAb,1ur to fupportthe curved piece I K, uid keep tho 

^f.'^* '(({iMMtlie iljdi;^i with tho opalte object i it flideiupon tlie 
It « ' baf Q^ Sby incaiu of the focktt^i, by which, mrani itia 
■f^.y^- p/ifiljiilf. nearer to, or removed farther from, the magnifylnj; 
''iT't: ■' ^^^-^^^ "''j'^'^* ■■* l*'""^ '" '■'^ ^™"' fidcof the ftagc, 
,' J^ !" ijeit* the tube uf the microlcope, bctffcen four fmall braft ■' . 
"iS jlairt, (which cannot he fliewn in the figure,) Iheetlgeiof ')'*'•■_ 

'.I'Bvo^if the plates are feeo ati/j tho tho upper plateiacd-.v;""; 

Ajtjwytibt^ and are preffed together by a fpral fprinft-.to ■ ; ■ 



* 'r./'utt^eiilie 'nider with the objeAi : thcfe two platei may be - 



;**:■:.■ 



'•|$'I;.*-i.-. 



466 or orTic$. 

raifcti higher, or moved lowcri hy ihc fmall nut m* The ' * - 
upper p;irt of the llage/^ri, m»y t>e ukeii out, and the * **' 
tiAfu^ for trntifparent nhjctMa (fi^, 3O infcrted in \\% plact**. ^ • ' 
At the lower part of the rtap,C| thercii a femieimilar glaft ^ .' 
lamp at n. to receive the light from the lighted lamp, and* '%/ 
throw it upon the concave mirrar /, from whence If^t rt<^ • - 
(Ic^ed on \\\c ohjeA. • \ ' ^^ , 

Fig. \% \% tlie iUge for tranfparcnt ohjc(5tt : the twol^^ $^*** .v. 
and6| fit into the top of the under part of theAagt ta '4 Vt 

(^g >*) h (^tf* 3») ** ^^^c P''^ *^^^ ^^*l<l* *()c nidbra/ sf ^. ^ 
and tO| the tube that holda the magnifiers : within thjl tubi% • ^ ' \ 
therr ii another, which may be placed at any diftance frpAiV^. / 
the ttbjc^ hy the pin 1 1. When this ftagcii ufrd b^itufff, ;\.. « 
an a fingir minolcopci the magnifier*: mull lie fcrcwed into « ^ 
the hole ta, and to \yc adjudcd to the focun, by the nut 13. . '•• 
At the end ot' the wooden box ARC, (ftg. 1,) it a llider ^^ 
A, rcprclrntrd n< partly drawn out : when this Aider i» takcrt * --^^ 
out, there will Ik pcucivcd three gronvrii, one of which *. '^ 
contains the boAid that forms the cntl of the bo^t ; the next; • ,7, 
containi a frame, with a p^ray glnfn ; the third, ortheiii^*!' ^% 
nrrnioll, rpntain'» two I.11 jri- « nnvcx Irnlrs. , * * ^ 



To traPinfir ofijkr OA/rr/^, lt/fhi\ Mh *iij,f>f^r. 



.« 



4 



•*. 



Tl^r inftiMtnrnf, ^H};. t.) ii rr^tlv nmnnfcil, tOr tUi« uir- 
|M»ir. T»ivC<Mir fl»r u'fvxlrn lluiri A, .md hit o\\t tli<*ravii« 
.uul thr };i?y k''^^'^ tniin ihM! >.;it)nMi, untlri tlir Mulri'fV. 
atul \\\r jMi'«l«" I'T \\\c rvr I. M N l»rjMj» put iruo tt% |5Ia0C^ 
nml tlir U\\,r{ At t\\c hottoin i>( thr np,»Vr il.ipr oil tlic lur ^ 
<i^X r, 1«> I'.it \\u' voiu'.UT i^IhiM /, m:»y br lu xt the ttui ^ 
1^ V. »»f ihr \ViM»i|rn hp.ly. S« trw thr tu'r I* < 1 info \\\^ f.n<i 



i 



n I', With tl'.r tin^»nifirr'», ntui thr h.ubllr /•, 01 n.-llrtj qui, 
^fj;. fl.'i I l.u r«l on thr rn<l ot the pinion ,i; pi. u < th< h>;htcijl 
l.inp hrfoir thr I'.hilj l.iirp nf at, niul thr oIm«.« t to hr cm- 
itnnrd I rtwrrn thr Ipiinj; p-Alrn o| the ll.>^;c : .nul thq HiUiu*. J ' j 
:nrn» i-; ic,i U f.ii ufr. 






«•• 



:. ": • 



• 



f 









OP OPTICS. 46y 



To examine tranfparent Otjv6ls. 

For thii purpofe« the upper |>ttrt of the opakc ^^V^fgrt^ 
w' (fig. I,) mttft be removed j ami the lU^jc Ibr tranfparent ob- 
jects, (fig. 3,) inferted in iti plncc, with the end 9 and xo 
neitt the lamp. Place the grny glai't in iti groove at the cud 
AB| (fig* &i) ttnd the.objet^h to be viewed in the ilider- 
' holder at the iVontof the (Inge; then trnnfmlt at ftrong a 
\ light ai poflible on the objc6l, by railing or h)wcring the 

• lamp } And the objedt will be benutit ully dcpi^^ured on the 
\ K^^y 8^!*i '^''^K I'egulatcd to the focui of the nmgnilicr by 
^ turning the pinion «r. 

I^the gray glais be taken out of the microfcope, the image 

• fof the objed may be received on a paper (krccn. 

There it no inftrumcnt invented by the art of man c npa- 
*ble of affording fo great entertainment ai the microfco)>c. 

By thii Inftrument we can pry into the minutcfl rcivltci of 
^ . Oiturei and difcover truthi which have lain hidden from the 

eieation of the world. It ii from the ufc of this inlh iimcnt 
• that we can confidently aflcrt, that there ii hardly any part, 

f feature which ii not the abode of animal cxifUncc. Dy 
4- k Ye difcover thoufands of living cnnturcs in a fingic drop 
^ of water ; and whole natiuni) of animated bcing« in the bloom 

^rtiH^h fnrrounds a plum, u pear, and moll other fruit ; not 

'. to 'mention numbcrlefs infc<5li in cviry part of nature, fo 

^ finiUi. ihat a thoufand of them might be crufiicd by a llngle 

gn^jii of fand. 
1. From the difcovevy of ihcfc truths, the pluiofophic 
^ intnd II led to make llill further improvements ; thui, in the 
1^ formation of a mite» we can fee the lame proportion and 
U fymmetry in the (liiu'Uirc of his limbs, as in thole of any of the 
'• .Urgcr quadrupeds J as frecn rirculation of blood in the one as 

• ;ju the other i n« m.\ny members adapted to djlTevent pur- 
^ |X»iei*; as numerous veinji, mufrlcs, arteries, fincws, ^'c. 6:c. 

t.^ jl^lh a probofcis to take in its food, like that of the elephant. 
;'' ' ^ And 



\ 



*/ • • • 



46S OF OPTICS, 



jW ■ ir — — ^ 

#««i«>^<^^'V«Wt^^ "V •*• " I - — 



i«nMWHi«MMMnH 



And if wc drlccnd to infers, of a yet fi^aller fize, we Aiall 
ftlwaya find in each, all the properties and uttribiuei eirential 
to animal life : if we dcfc end to thi^fe infedii, wliofe bulk, 
pomparrd to that of a mite, ii asi that of the n>|to to U^e 
elephant* 

Other* are of fo fmall a fixe, at to he beyond the reach of 
any magnifyitii? power ; and whofe whole vxiflrnce ia circun>« 
fcrlbed within the fpneeof a few hours, or a fun>mer*» day at 
lhen)oft. Myriads therc'^urc in the vegetable world, to whom 
the Dooming gives birth, and who expire with the letting 
fan, befidcit nnmberkfs others who have iheir habiiations ui^ 
the bodies of otht r anin^nls fuih as the ichneuiiHHi| whofo 
iieculiar hubitationia on tlie body of the caterpilbr. 

In lliort, there is ro p^ut of nature which does not ^fH^vA 
to the m'rcroicopical obfcrver an abundant fonrcc of wonder 
lind i|dmiration • and ^itplay the attributes of that Supremo 
Being, whofe wifdom is as confpicuoiia in the conArudion of 
the fn^^lcft atom, to b« djfcovrred by our adSfted fight, at 
}t\$ power h evident in the formation of the planetary fyftema« 
But there are fome objects which l^ave noore immediately 
engage*! the atuniiv^n or the cuiious obl'erver : inch as, what 
ia called the liKu tiei' ; ami the ri> ll.j|li/.\tion i»t lalts. The 
iilvcr tree is forn)t'«l bv vljiU>ivii\g a lililc tilvor in ulnjall ijnan- 
lity of aqua tortis ; aiul then avlviinc, \o it xwhv the t^uantity 
of ronn^\OM wairr. T>rv>p a lllile ot ihi:^ upon a pie^c ol plain 
glab, aiul put ujm')i\ it a fmall piece ot brals wire ; and iuune- 
diaicly thr Mire u put \ipon the mixture, tuts will apjwar to 
grow, and Jilplny tlu'n br.uuhcs whiih will l»t exiijuletl, as 
far us the liipjor txiiiuia on theglais; an*! haw all the ap- 
pearance o! le.il titt's but of a filvtr caO. To obfcrve the 
i tyllalli/alion ot" lahs, thllo've a little lal-ammoni.ic in com- 
n\on water, ihop a liulc of thin n^ixturr on a piece ot glafs, ^ 
as in the tiunur calc, and when viewing ir thiough the mi- 
nofcopc, hold an hot iron i ear it, to n^aVe \i evaporate the 
quicker. As loon as the ^evaporation takes | lace, it will 

ritt 



• 



OF OPTICS« 469 



rife up in a round cyliudrical forai like the trunks of treesi 
and divide and fubdivide, fo as to reprefent branchei and 
iiougii9 : and has a truly wonderful and beautiful appearancot 
And every difPercnt kind of fait forms a different figure. 

There are feveral other objeds, which I mud recommend 
to tlie attentbn of the young obferver ; as, i. The common 
F!y^ the vibration of whofe wings is repeated feveral hundred 
times in a iecorid of time. The great quantity of eyes with 
which this aoimui is favoured renders it worthy of notice, 
each having a diftindt optic nerve, a* The Loujlt. 3. MiHs 
in cheefe* 4. The cuticular Ports in the human Hcin, fo 
clofe nnd numerousi that n iingle grain of fand will cover 
hundreds of them, 5. Tlie condrui'lion of the Scales of 
Fi/bts. 6. T\\t jHimaLuUs in feveml forts of infufions and 
liquids. 7. The conUrui^ion of common Feathers^ 8. Hair** 
^. The Siii^ of a Bto^ with the form of its barbs. 10. The 
ConfigHration of M'ood* 11. The common Mlliievj^ which 
di (plays a numerous group of vegetable fubdances. it. Small 
n^ti^isfhU Srrds, And fever.il other articles. 

I fliali clofe this chapter with a few words concerning tlie 
method of making fmall fpherule icnfes fo^ microfcopesi aa 
recommended by the late celebrated Mr. Georgt Adams. And 
alfo the method of mixing the metals for the great fpeculum 
in the refledting telefcope. 

To make the fmall fpherule lenfcs, a piece of window glafs 
is to be cut into ilips, about an eighth of an inch in breadth. 
Then, holding one of thefe (lips of glafs at each end in the 
flame of a lamp, as the glafk begins to melt| it i«to be drawn 
by each hand into a line thread, and at length it will break. 
Then one end of this thread being held in the flame of the 
lamp, it will run up into a fmall globule, which is to betaken 
off; and is a Imail fpherule lens. Several of thefe Icnfes are 
to be made, and examined ; and thofe that are the bed, are 
to be prefcrved for nfc. For feme will always prose faulty, 
though every precuuiion be taken. 

Jn 



4)0 nt nptiGA* 



tmmmmmmmmmmmmmmmmmmmmmmmttm 



U\ tIfU phnrlfl, the lattip )Mo bd fup|il)eH witlH^iMfti ctf 
wiitn ihltrnit of nll| fiiMl tlti* flrtruft Ij4 to tie Ittnwti iti rtd hrtt-f^ 
AMiitfll iDiciHUm by n Nnw«ptf)«i m a |irt^r t^l bcllMwti f^t tbfit 
pui puie ) Atul tho ^ln(<t Ittbl In the ^hltcft p^H nf the Urtttte^ 
left the rtt;oke iully the i^Uh. 

The uietrtl fnr thr fjtrfuhirti (»f th»< wfl^^lhg frl#»rrri|ie, Is 
grhrhflly hiMiu'd iif{o\i\ier mul grrtlh thi| »hfl )h th(? phtpor^ 
lum r»t tW(» p« Minds of Hwedifli ii:>ppeff tn foMflr^en Mtiiitr^ 
iihd nil hftif rtf ^ft^bi tl»| rttid thh ttilNttifi U tO be tnelterf 
lw)(c itvpt'^ ktore It be vt\^ iritn the itimihl* 

AVhfii the titetfil \» r»ft hifn rt rdti£#ve tiit^HM't if l<i 
ghtutid tlpMhi Whfit Is rrtltcili the rmigb gMnitrfy nl f'Vcm it 
eominiMi ^Hinbltniir, f>f the Ihttie n*fllu« «» fhr r-onrrtvlty itf 
the mrtrti, to tttke nff the rnugh frtce. Then If h grfMind rm 
A btMlo t MhveN ^ilMtlet'i tn ^)vo h tnie Iphet-k'rtl Of^Mfe i nt\A 
UiWyi tipMtj (t rmivek bed ol hritie#« which U \o \mM) thttt 
llfinie, tiiul give the metnl rt flMi< ^fimtflt frt( ei Then tl»« 
«oit<:ftve (fife oF the metrd I9 tr> bt pditlted by ti ('ntiveK t»nl| 
(ovned with pitch. Aml^ Irtttlyf It i» tn Ite bimi^ht httr^ tite 
}mr(tbolic fntm by a merely m»hiitiit!Al method *if ^thtditig 
it «n fhr pollfhrr In rt ihffptuMl ilhr^lnh. 

Jlu» \])r ImH Mirtfd Inr lprrnliMno« jp tJMl pinp»»f«d by tl»< 
Rrv. IVli-. /' ffiiffttf/if siihI wliii h vvhp pr< vpiI hy hh i\f'^flnt\tir, 
h» »H'')i h» I'Mi^Jifn* |ij Mini »1i(Imp'Im' h n| \\w Iihijn, iv«>y 

ntio I ll» hll ilir-ll lttl*i«VM. It • 'iMllllq m( | h*! > V I "/«> f 'llllf ' () ot 
t '>|i|ir I, NVIlli till' en "I (1 'If ( II fiiMK rq ni ^tMilt |Mi (M'M|(t. 
iii^ t'l tilt pMiity nl ill' I 'i|i|>i t ), willi fMHMMMM ^ el l>if>rQ, 
MIU KMMro III (|lv«l, mihI n»'»' fiiiiji r nf miImiH. I 'iln i* <Vrt«i 
pM l» fit nl tllf » ilUillf.' nl I l|»' • nlllttl 'll flljq Ml* ImI ; MH'I, wIkH 
Dflilli^'l^ It i((lf''i'<l Mi«>i>> li^lil tlinll niiy (|M'rt|h)iti I ll4Vr. 
ivri !• • II. 



B I. ll ♦»! I tIR t I I« 5 I VIM l'r.t>- 



ItMl** UMff»ll .^li">l« HmIK'hii 



'midif 



Dir$(HoH$ to thi Wndgrfor placing ih Plata. 



VOL.!. 

I* Copiei» No* L to face •— «^ 69 

•• Short-hand — — — • ^j 

3. Menfuration of SvperRciet •-* — 311 

4.. ArcWttftore •- — , ^ 407 

5* Mlcrofbopei •- — — 4ir* 

6. Tclcfcopet — — •« 43J 

7* Dr« Herfehel'i T^efcope — > — 457 

9. Improved Stlar and Lvoernal Microfcopci ^ 469 



^«p 



VOL, U» 

9* Trigonometry «i^ •*« «« tf 

10. The World flk &. ~ t#f 

11. Europe ^ •— ijt 
!•• Ada *- I— i ij^y 

13. Africa. — ^ «« _ 18} 

14. North America -ip. — .^ ig^ 
«(• Soui^ 4<>vurica «-«. «« •— aiff 

16. The Solar Syfteiin — — — . 199 

17, Proporiioni of the Planet! and EcUp&i -^ tM 
xV. Ecllpfet ^ — ^ •« Ajj 

19. Mechanica — — — > t69 

•o» E^eArieitjf *« »» .^ .^ tSj 

•I* Mediqal Eledrlcity •- •— 307 

at* Pneumatici «-• mm *^ S*S 

03% H(xdh)iUtici — .«• « 34^ 

04. Hydraulic! -«» fm «» 367 

ft jt Netdt vif Dfvwing ib» •■■> S9f 

#6^ Raman Pigurea fior dkto ^ ^ S91^ 



8. OomiLL, Prlnttft 
tktlt QuMA 8trt€t| Holboro. 



,* 



* 



#■ ■ 



•y.^ ' 'Q/ftykiHjf Prte Oirs SiiaLUiro, •.• M 



-(I .1: t. ■'• 



r: NATURAL HiSTgJJiyr 



. .r . 



#<9Prut«^raati9n« •iid:df/iViqpUbl(t^ Miiw»lf« tec. 

By J. S. BXIER^ Esq. 

• ,;Tli» wliolt «r tut WMitlfnl dltlmiWIiorroir Wng loft prinUi eC In 

>,M Mttmri in 6% MiiMlNrft Prist lit MMb, msf Iw Milf K riw C^bm 
dif FtMlUfcrft kf mmrm man m rTirnty «r ii|'tWViliiim»iteiiW in 
fM MM* ittVHl, rri^MI^ SI.I or In HMi, '<^mIIjI(>P«9 

I'' "NATURA-L HISTORY 

C" ' ' • or- 

^KRDS. REPTILES; i^^ISH, ahd INSECTS. 

,V*^ This very valiMbU A44iU<Nt to Bvrf PV Mnif juft finifhad off' In tli£ 
Milter 'i be'ft>l4iiiierf- In only V^M'<^t>'^> *>^*f be bad hjr one or mote u a 
y'iflKf Pricftjf. eachi or in Five Vaa|iiiet» buuiMi in Ctlf ami lecteicJi Prii^ 
ft?, II. ( ui in BiHirtiif Pries only i/. itr* (</# 

fit ** ■ V • 

Tiie whole of thii valuabU Work, formfngi beyond ComparKbn, tht imA 
49mf^eu: 4nd«tei];ant Natural Uiito&v in tlie KoKlilht or any oclicr k«n- 
lUjI^flf beautifully prinreil, and nukini Fifteen Voluntiy in 8va. which con- 
nMrtiie4r 5000 l*4Ke* of iKatiririil Lettrr-pref«, bedds tht cii|«ic and numenitifr 
^ffCpf ofl^mA C<i|>per.pUtM» taken from Uk, may be had 

, io. Boardk, Hiice ^* — ^5 * ^ 

Botind in Culfi and lettered — -~ 6 4 • 

V • . Stf|antly bound hi Calff |Ut and ietterad • 6 %f 6 

lM[HDoirr Printed^'fuDm the (TraiiiUtiimt^ Alr.BARRtafor 
the Proprietor; and (old bv H. D. Symondi* No. to. 
Pf ternofter Row t and m»y ne had of all Bookfellen ana 
Ncwfmen in Town and Countryi on the above Tensit 



.' .■.'.. 



1.1 



|.;. 



( 



TU* liMuk i* wMlar 

talian fruH ifca 



M««v k «< *• Mh|» 1 K. iMlar «• iIm U^m iw'ifl 
^ *• «««^ A « 1 w^ lUii iti«y l»4i Ml I* iIm fa 

<«■« ff^-rrtir, »W/. I.. Mt >• It ■ Tlwy htl W|iM 4 



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0mf I, «r ilM •Ai'A A n. ttai fMAnf Aravgh *r 



plMC4«»ffl|VAIt, r^) ' 

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cat 'jE 'm ^«srt mtriit^ ti irf.v^n ^w<iivro<t4«' vhii iim «> lu- 

Tbu ItTBigt tSiigU- tuf:# U^M.vVi.t UP ♦u«iii.i O: . 1. •*,•• 



Tnriuljuftifig kw:*', ic vviifci. l.: itii-i *...»***• . I..»ir' 



diverge S» Itttk. Brt AM/fl'Lr^iUi.! *.>«... ^ t: i.^i*fcvtg. iwi 
It tiK Ut of ti:». i^ttkiry l u>tlj u OjUi«L< t.,^; tj^i 

irdmt til*:; ial! iff>^i. t.** i^'^^a Hiti*^! ait< ■. ..i.^^^...'., 

tilC* wil. Ue til* iO .j^^:' *»ii.^K. l^s .i*ci' dlvc* .i'!. \:... 
QtrUlUt*: tlUff. tl4« stfli^' Ui'titf* i>i« till ; tui^g' ... :i a....i. ^ 



a? zvrrocSm 4rTa 



7T& on -11 1 riund j^'iouncai tiicii liiis :iie tnniics at tn 
ami div'dE: aad VJXHfnv'dcy. vj is ii reprs^oit (znncixes sni 
^Mty : sui iiss a T:iiy x/imtctui ant Jiamirai JuprTraniT, 

Tben: ir^r tir^cni z^TLcr ii:ied:a» xaici E ixnnL csnomxend 
IE ae xreaion cf :ne 7cmi;r abiervcr :.!£».:. The .-jmman. 
Fu'y dm rihonon ir i:i7icLe x-.uip "s rsajcatea itr/emt tiniarot 
Times ia a isLinfi ^if dmc- Tjc g^^ir .-.Tiaiinr? u: £r**a. ^ua. 

nrh ixa^'-.nn i diEiiicr sttc serve, s^ Tie Lau/d. z. JfCtex 
in t^Hg^*^- ^ The rirtmttr Pjt^ in rie hmnao. ikin^ rt» 
cfoUr uni tmnier^iiE* i^lit i io^ii: zTrrn ;ar dn&i wLI cavor 
iDimircis zr :idin. r. Tbc a:c h~nT:t:a re rx Slu^ ^tt 
F^h&m 0* Tile J;iiimui.ji^i .n liiv^ini* iira cf jir;uonH anil 
Jif|aiiUk 7> The 'iiir:JrUirr:i:ii or amsmm. ^Tur.-r**:. i*. ££/.>• 
i}» The ^/TJKg- .^' 1 ^-av "^'.ri ;:ni: /astox ar m iismu* r i. The 
C^H^k^ratran ci ^imiu :c. The ^.tTtr.nart J£M£n:sy wjii:!! 
itiipiari i mimer'iUB ^arp af ^cersczbie ■'icir.ini'ri. uu ScuJ. 
^s^ j ^ udi ii Tastti. Aiiu ik^xerui iicter -STtiLicfa. 

£ fioiL coie nns liuoter trrc: 3 ai^v v-zriii^ asncs^nxixnc '^» 
aaeduut or ixaii.n'^ acail ipneriie Vt:;!:^ !br oiicinnbspisv m 
TwnmmrwAed by rne uue crlc'inred ^Ii-*. &*>ff-/v Ji^nu. Acd 
aiiii die asechad if xi^c^ n-x :i»:*Xd Xf ±c ^reat tpecuum 
iacSie rfflfef^ing adeiirnpe. 

Ta Kafte ±e thniJ: .pi:en:e er :cr% 3 ciers cr wiciicw j^unn 
ib K iae cue ^nisu :i.. :k. ibi:nr i.t ii'r^ni 'rr iz incii u: .^nuttdlw 
Then, iiC44sin^ ':r.e -ft ruitJi ±^ J ^-xii ir cac-i cia :s.ac 
fane oc x Jzicp* ik r :«• ^irr* -e^Tia ca xc. '. i:: !» r-i be irwra 
fco e:idt ixacii mc: a. i.:ii rrr-iid. i.-l! ir .: ■•r:!i it w:iL br««*4- 
Thea ane eaii -f -1 i rr-r-iat: an .:^ -cc n :iB iar.e oc -3e 

ctf ; anil !s i lt:.i.* : : ...;:'.L»i .e?:s- i^i-yif-i^ jc" liieie jirrlti irr 
^ ^^ Hr*"i*^*»-*^ -'-1- ■ T« ^ T ''.^i- V . ., • ■ -^ * -*.■■ --- 



IMrpAi aodibc gfUt htUladw «lkuttt put ttJ ilMldne, 
M ihc £b<A< i«0y itM (Ufc. 

TImj^aI ^ Ihr fpenhm a( the Rll«Ai»f t^tkoft, m 
|n«j|Jr lommlnltafiftr •ndgnintifi] md !■• ilvpn^M- 
OM* Cf IMP poMOdl of Iwcubli COffMt M fa w Ttaa tMHM 

mdmbdt^ pdn tiai od lUi nlMratoMbrMM 
Mto wtTf b*fa(v « bs cat iMo iht moaM. 

VIka (b> MKul M oA iniB ■ OMMMfc oiitMir, tt n 
|tnnd up«^ #faM b caltid, the tiragb (riadrr, nr r«co ■ 
•MMDOM |tim4-iaM, of the IJBM nduH » the cuaortiy al 
the awiil, to iiLt off ibe rofl|h bee. TVn it it ptumd m 
_ J bait MAKi ^Bdtr, to f rwv ■ iru* ff^Mf letl fif urt : nA 
URIf, U(ax) 1 rof»ei brd uf l.:<oci. ui!iicb it ii> !«<{(/) thu 

fif;.,..'. a.,.i L:..r Ihe .lulJ .1 li'.c f.i.rKlh f^. r. Ti.Ui llw 
t..ii'.nr r .. <■ it idc iiid.il i>«> lie |H)lillird l>y .1 O.inrx too', 

|>.p.i'..l I l.,:rii Ipv .1 ii,rir'v ii.*»hjniial nirltvKi of ^1 liuling 

r >l,. |.-ill.. I M 4.1 tt;i,tii .)ura>'m. 

11 .1 i:.r \..H iT.rr.ill r Ijh. iihiii j, is thi[ |iroi«if..d bj ihe 
k.,, M,. ; «...■.,-,;,, .1 ..! «1,! h H.1-. prued l>>- It... !/.;/:,;-,«, 



11 .-.r.y l|HCiiluin I liave 



Ittltl 



' f«r tUaf Oi Htui. 



. QgM^StfcLtt&ce 



'T 



t. l i|ii 1 1 r i l I »< L«n»il l l«w fc if« _ 









aih. Tie Swr Srftea! — _ 






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- »«» 

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S "^-Trii I . Nmh, 



BARR'i Kew artfl bealVul Edtt'ioa of 
BUFFON'i NATURAL HISTOICY, 



BVFFOJVS 

JKATURAL HISTORY: 

i, .-. C9BT«IFIIiO 

pMoiy^lhcLulht 1 G«omi ifHbry of Mao, gt li'C 
^^PtvwCraaout miaS VefcuUtrs Miutnl*. kc 

Bi J. S. BARR. Em. 



NATURAL HISTORY 

niRIJS. RKPTII.KS, KISir, AND INSECTS. 



■J.*. 


• »,^^- 


'1. ui !■ r..(Vmumri, t.-uoJ jei Cil( inj lt:;ttr;, Pn.; 


' r - 
»•'>■■ 

>i'i'..r 


1::::, 


■„. ..;.,iMr U'™k. rormln-, V^vo-.! C«iipiif.,n, irwrril 
■M«*IL'.A1. M<.I.,«V ....,„ Ki-^MK, 0. ». „.s-: U-- 

)< {I'M, r.kr.ifiomljk, miyhc h«J 






n IM(, .nj l^t,„d - -64. 



^«^:.<)•T I'linitd, from (be Traiiflalion gf Mr. BARR, im 
Ilic Troprietor; and fold by H. D. Symondi, No. 10, 
I'aternolliT Row ; and may he had of all Bookfellm ajJ 
N*-" (incri In Tywn and Country, on tbc above Tcnns. 



"""iV-ss^iSi.^ 




