IMPROV” D; 


1 55 The Whole Az T Perform d, 
a 1. Geomerrically : By Scale and Comp: ſſes, by 


2 Een the Sphere upon the Plain, whereby the * | J 


eaſons of the Operations are demonſtrated. 


II Arichmetically : By Sines and Tang 


. AS Wo 
| How to deſeribe all neceſſery Faruitare for S un.. 

| | Dr a xs, as the Sun's FIT and Declination; with 
= the # Babyloniſh," Italiet, Jewiſh Hours, and the 2 

Point of the Compaſs the; ap iS upoꝶ at any Ti me | 4-2 
aof the Day; 3 to make Dials to give the Time | FA 
4 the w . at 8 Ehe propoled, 2 80 x Part af 


: Egge Dialling = Sue b 7 A to: i LI. 
Dial chat ſhall. * the true Hour of the N 1 


Where the Sun cannot ſhine. 55 
> * , e which 18 now 


Poems Dialling « By the Lines of E 44 


with the Manner of ordering and Car far: 14 3 
2 Painting 8 un-DiatLs:.- 1-4 

5 ce with Tables mede calculated: for an SY WW + 
| | titudes and Declinations, for the more sup SO] E 
— They fines upon any Fl. — 1: 


+ of 25182 Es 111 0 N, corre | 1 inge EY 1 
Do Eh 8 LES 1 * D BET 3 


1 1 


Bir or N. ec. VI 17 U Us. _ S 4 


3 x © 


3 s 1 
1 4E 
+1 


And Inclination upon the Stales, and likewiſe Mes. Fa 
| | :chanirk Dialing, whereby any Perſon may, with-+ 
J-: 3 out Matbematiels, make à Dial 2 any Plain; 


9 — Ed, 90 FS TY ' 
, "EE 27 wow 


* 8 
1 1 
& mY * * 
4 0 3 a . * 
# F % 
2 * 
P 
* 
. os. 8 \ 
* 
8 * 
* * F 
N 
o . . 
% . 3 , BE. 
v * 
* 
+ p 
: * A 4 
3 Y F 
. * . * » 
« — * 
5 
17 * 
. 1 8 
© * 4 
. bs we : a 
60 4 * > " 4 o 
- » . 
7 * * 4 
* 
* ' 9 er 
* 
- 
* 7 . 
7 5 « Lala F 
% 
— 7 - - 
+ ths . 
— 
4 1 . 4 * A 
: $ 
# bl 4 > ; 1 ; * * 
2 at 
I < 
j p 5 , p 
1 * N 
i 
4 . 


- 
4 t ”- 4 hor! 
7 * x - U 4 % 2 { 4 2-2 * 
1 ; . 7 * z * - 2 0 * - - 4 
2 s l * 4 w 
1 4 s 2 5 ; ; ö 1 = 
* * ” * * 0 1 5 * 1 1 * 
= ” > — q 
* ; y * 4 Fg & a 
k A 3 © 2 5 > 8 
* 7 . * * = 
a 4 ; a * 4 1 . 4 4 1 
* - * * 4 - * — W * : 8 2 5 * 
- py « t N # 2 5 . 7 4 IS 
F i 
& +4 2 - * 1 5 7 1 1 1 a 
Mi 4 ö 7 * 8K - x 
** 1 * F 


* 
2p 
2 


N 

* 

* 

5 

2 

£ 

| 

— 

* 

Bs 

& 

- ww 
3 
. * 
6 
r 

. 


2 
> 
ö 1 uy 1 8 1 „ has 2 : 
3 , g | * ** * * J 
* ; 4 Y 8 * 8 8 * 9 N 4 
£ ; 46 8 4% bags * N * * my 4 
8 z * . * 1 4 % 
6 5 1 G 2 P 1 8 £ * * 5 * * * % : 93 1 "ec * = 
$6.5 þ * * 0 A * > „ ö wo EN 7 7 I & N 
W ; * + P 7 % 2 0 : 2 9 £8 + +. 8 * „ + % 4 . 2 
+ . 1 * Wi 1 . % U * * Ks * N ” 4 ; : kg 
+4 3) . * : ® ne * 4 » * : LEES — * oy * 4 p Y | 
C ; * : * ry * > N * (4 , I 
5 : — * ' : 9 * 2 __ * 
98 4 "I 25 2 I 3 x ty 1 * y . * v + 99 * 7 
* 4 A 1 2 : —-. ; 3 . ſ 
4 * » 4 PS PR 9 * 1 N q . . Doty 4 k 12 4 * x 3 
8 | 24. £ $ x0 5 I $44 5 ; a N 3 1 * 1 * 8 ; 
4 «dis P. is TK 0 + p £4 x N 4 8 — 
— 1 1 1 1 = - Ts RE 12 77 5 $5 » & £4 ; : 1 Ec 4 7 * 2 = y 
P ; a 8 bas . : FF * 5 * , s 
O 85 1 2 1 7 e . ** 5 18 4 $i Gets. He aa bed Py en ae #4 Lis * 8 
* a 2 i 1 a F 5+ T FLAY FEI PR A * 2 2 ed ' ah HO : * 4 
an 4 . 4 4 v4 Ws Lk nn } . : 3 4 - 
1 a o RT n 2 - l 2 
. * PPP * 8 57 a 
5 x „ . d a 


0 Cy 
«8 
—x * 


W 
3 


; 
4 
* 
4 4 8 IS 1 v 1 q b 1 © of * 
wars Wee eee ee 3 1 
T&F 25 | 1 


Wee . +4 


6 ** 4 5 . ; FP y +. 

ma 4 2 * * S 1 J 4 ye 

: ; 2 : 4 : , * F — * #%% wx N # 
PEE 7 8 . * ee 5 ener 2 2 Ne, \ 2 ee 27 8 * 2 1 
r . „ P?T rn OE e bod hgh 2 N 2 e +" 1 F * i 
| * 2 , : 36 Gal) 4 8 / 3 ** 5 uy 2 at hs r n - . 8 VE 
: LY 4 c . 23 —_— * 4 ; * ** 2 * $ * 2 * 1 : 4 * > 8 1 * 2 * < * 1 4 5 4 F x 4 5 FC * | 
3 e CW ; * e PN 8 IEF Gale 8 


i ME bor 
ad 7 is $00 


> 5 rs 


_—y * , * * 1 x f 
5 " 3 # , : ' ] . 1 £ ; * q 0 < - 5 & 2 : 
[ F 8 1 "= + 4 21 4 A 13 > # 15 4 
7 * * K > 3 2 - I * 
. . 1 7 * 5 
n # ob © oy - ” 
* * 5 P # — a * © "8" 2. *. by * S 1 4 * + 2 4 S; F 
f 7 5 Q : ad 1 . 1 A 
F\ £4 £D * > 7 * f D ien 12 
T7 CLE 35S %% TI SER Ms CC gS # we) n 4A, 
ö : 7 + 55 1 
+ : * 7 £ — 
; 4 0 F i #% of = * |} 
"PT ©. * . 1 * 


s i ; 
7 d. - > ＋ * * : - F 
* by 8 Ly e $ L 7 4 £ 
7 4 N |: : . s 
SE. . 4 E 
* 


bi 5d! 10 11811 1 
Tes 7050 ain 8 Y 
$45"; 96-6 Þ 3 


N. 1 1 8 1 
Il known, o univers 1 5 DE - 
A, uſe. ful | 19 7 0 Nice, we we J 
e 125 gau 1d . 1 
ter qhlige elbe W With oy Ne 
roving w 15 rin 0 : 
2 100 ge it uſe Eon 


[ AE rr, bed 


1 FertY L 5 8 in rhe. 5 


i 


<Y 
of 
* 
= ay 
„ 
7 0 
* % 


_ 4 
* 
"oo 
+» 
* 


E. I 


8 8 s Azimuth: 2. 
Dung, as performed by 
- | the _ 3 


ib +3 K. 
. 3 


* 0 : 
A 


ede Renz. 
the Lines of Hours, and Inclinations, 
Sc. upon the common Scales. 3. Me- 
| chanick Dialling, ſhewing how to make 
a Dial upon any Plain, without Mathe- 
matical Inſtruments, Trigonometrical 
Tables, or any Knowledge in the Ma- 

thematicks. 4. Theordering of Oyl and 

Colours for Painting of Dials; together 
with ſeveral Varieties, as making a Dial 
to know the Hour of the Day at any 
Part of the World, Sc. Theſe, with o- 
E therdiverting Improvements, are added 
iz this, which were never in any Im- 
© preſſion of Leybourn's Dialling before. 
III. WE have contracted the whole 
by reducing the Cuts, and engraving 
tem on (epber- plates. whereby the 
Book, (tho containing all the above- 
mwmegtioned Additions) will come chea- 


per than the former Impreſſion. | 
el I know it is a common Objection, 
& that let a Book be never ſo plain, it is 
©  impollible to learn any, Science, (he- 
| ther Nialling, or any other) fo well by | 
2 Book as with a Maſter. I anſwer, that 

may in ſome Meaſure be owing to a 
© "Want of due Order and Apptication in 
reading the Bopk; as for Inſtance, Sup 
poſe having this Book, and no Inſtruc- 
. 5 . 4 5 1 EIS} FO 42 | 5 A ks 1% tor; | 


3 —— % FO MW * 


* 


oQ © - 1 


a 


19 — 
4 


Te en v 


tor; it; it was required to bes A Hos 


ri gontal Dial in Lead;\'Braſs or Stone, 
turn to Page 37, and there you have ſuch 


plain Inſtructions, as if follow'd, yow - | 
cannot miſcarry in your deſired Succeſs. 
Likewiſe, if it be required to make a 


South Dial, or a Declining or Reclin- 
ing, or Iuclining Dial, &c. Lock in the 


Table following, it will direct vou to 


the Page, Chapter, and Section, where 
you have full Directions. 
Ax becauſe this Bock may ben 


come into the Hands of ſome Maſons, 


Carpenters, or the like, in theCountry, 
that have not attained ſo much Mathe- 


maticks, as to qualify them for under- 
ſtanding theſe Directions, I have, for 


that Reaſon, inſerted Mecbhanici Di 


ling, (Chap. 11. Page 215.) whereby a- 


ny Perfon that can but read and write, 
may (by the Directions there given) 


make any Plain Dial, and perform the 
whole as well as they that have attain- 
ed a greater Ferfection i in the | : 


matickas 1180 347 


I do not A: ani Difficulty the I 
pe in this, 3 
dur. lines, 


Learner can be under, exce 
that having deſcribed the 
5 N 225 PI 17 there is not a 


4 9 
i 15 _ 
. => 
W 
2 = 
8 2 
+4 : 1 
" oy 
* <Q 
= 
: 5 = 
'— "it 
— 


<4 * 


1 

0 2 

F * 5 : 1 + . 
4 5 2 5 * 4 . f % : 4 1 . 23 

* - - S K* „ $Þ-* a * * J 4 

8 q oy TT 

= 

: * * 1 


2 
1 
—_ > 


Ly k . 
* 4 


F vi ; 75 Te R Aan E . 
Fpunter preſent that underſtands the lay- 


ing on of Colours in Oyl, ſo as to en- 


dure the Weather, and conſequently be 
it for painting of Dianne 

Jo prevent, or rather anticipate this 
Objection alſo, T have given Directions 
for the ordering of Ovl and Colours for 


ting of Sun-dials, (Page 254.) ſo 


pain 
tat this Piece of Dialling, with all 
the above-mentioned Improvements, 


and others therein contained, and not 


a here mentioned, I think, may, with- 


out Preſumption, be recommended to 


4 is World, as the moſt: perfect Com- 
= poddibancat Dialling now extant ; and 
f be ſaid that Mr. Goods: Dialling 
B hath. acquired. the Name of à uſeful 
E Book, ir is eaſily proved, that it is in 
Fart only a Copy of this, as will ap- 


hy comparing the two laſt Plates 


. acer S Dialling, with Plate 9 and 10 
Aug; and if an impe 
5 — be of Uſe, I hope much more 
the Original, with thoſe uſeful Addi- 
FS | tne wick whichic e e gr wh 


Impreſſion of Leybourn's Dial- 


rfect Copy, or Ab- 


1 IS hne den 15 
Aim, Lover of the Mathematichs, 


© Wn 


8 * Sada an E 


8 te E- Cu urs [2A DBETTER. 


FAA eee 


——_ 


„ * @& AS” Þ»* 


| 
; 
þ 
) 


e 


4 1 


41 
| 


ys ” q 
" 
WES a * 1 8 5 
* : 3 & > - 
\ 5 A , » 9 
5 "a 5 *; "i 
* N 5 
. 9 4 2 
0 = - 
” iN 
4 
* * 
b ” . a * 
+ 
P iZ 
* 5 
y 8 
a Pe . 
4 K a 
9 
6 l * 
* E - 
© 3 
* * 
L * 
* » 3% 


# 127 


— Problems: ITAL 49 Pages 
4 Table of the Sun's Declinaion | 26. .- 
Great Britain. and Ireland. 8 3 


Foe Ae: 


Chap. 1. Of the ſeveral Sorts of Plains,” L 
which Sun-Dials are made 56% 
Chap. 2. To find the Declinzion and 'Rectination - 
1 The Reclination 

2. The Declination 


f Gap. 3 3. How to draw the Hour lines a „Ver- 


tical (Commer called a Horizontal) Ed 
Chap. 4. Of 3 or rect Plaus — 
Chap. 5. Of Erect Direct Plains, . and of f 6 

South Plain 
Chap. 6, Of aw Ered Direck Eaſt or Welt Pian W 


D 7- 07 Upright Decliving Plains, - En-? 4 


Chap 8. Of Upright Declining Plains 
Ge 9. 2 * N in General 
-& © 


| : 10. Of Dies Reclining Plains, and fr 
1 Eaft aud Welt Recliners 37 
Chap. 11. Of South Reclinerrs e 3 
= Chap. 12: Of ax Equinoctial Dia! 63 
© Chap. 13. A ſecond Variety of a Recliner - 64 
= - Chap. 14. A zhird Variety of a Recliner 68 
Ohap. 15. Of North Direct Recliners 70 
Cap. 16. How to draw the Hour-lines 2pen a Di- 
rect Polar Plain, which reclines Juſt to the 1 5 


noc! | 
Chap. 17. 074 Nor Reclining Plain, * e, 
b V. ar. iet ; 5 


© Chap. 18. The third Variety 
E Ghap.- 19. Of Declining Reclining Plains : 42 | 
=. Chap. 20. of South Recliners, the firſt Variety 
; => ant oe we 
= is. 21. The Seeand Beh 0 3 ne 
E Chap. 22. The.third Parie a 355 

1 Chap. 23. Of North Rect ners, the feſt Pariey | 


= Chap. 24. The "als! * $2 2 Hin 5 
Chap. 25. N 1 5 15 

= Chap. 26. A Propeſicion by which the whole is de- 
moemſtrates c 103 
1 Chap. 27. Of Incliaing Plains, beth Dire and | 
= Declining 110 
= Chap. 28. 4 any ef Rule | 10 une which Pole is | 
4 eee i : 113 JN 


PE 5 


| GronrnicaL, DIALLING. 


z 


8 x. "Of « South Declining Plain . 8 
Sec. 2, f « South; Node Eaſ and Wet Bed 
e — re 


x o . 3 12 * 
83 A f ; 
PE - 
V 4 . 
* + * . 


„ 


7 - oy; & þ 
S-. 3 444 * Rt N $3 
* 8 . 
8 4 t : * 
1 bs 4 
1 * 


11g rye ey? 8 


Seck. 1. Of Horizontal Plavs 450 195 bes 
Seck. 5 _ North and South Eret Dres Plat oo IF 
: *'12V 


1 


Sed. 3. Of North end South Breck beam 2 
Plains " i = * 


Sec; 4. Of South Diredt Reelining Plains 2 ve - 
Se&. 5. North Direct Reclining Plains x33 
See. 6. Of Eaſt and Weſt- NE 5 Plains 


seg. 7: Of South and North D Deen 1 | 

Plains nog 133 ̃⁵⁸ 
Sed. 8. Of the Hour Diflimeer upon the Plains 111 
Sect. 9. To find the Sun's Aim, 147 . 
A, ſperier way to find the Sun's Azimuth 1492 


A Supplemen) ro GrouerRICAL Drattaxs: 4 


Sr * 7 
4. 4 1 ' A 4 "30 
n 


| Chap. 1. Of ſuch 888 of hs Sphere, as are *. 
ſeribed %* Sun-Dials- e 

Chap. 2. Of the EquinoQtial Tropick, and Paral- 
| TO 151 


Chap. 3. Of the Babyloniſh awd Italian rs 152 
Chap. 4. Of the Jewiſh or Planetary Howrs - 1 38 


Chap. 5. Hot to deſeribe the Azimuths F 4 3 
plains I 64. 
| Se: 1.0» 4 Horizontal-plain -, | -- ibi 1 


Seck. $. Os an Erect Direct Eaſt or Welt Plain 5 
Vene -7 2p" 4 
Seck. 3. 05 an » Eveet Dire Sdoth-plaln „166 
Sect. 4. On 4 South Declining Plain 187 
Chap. 6. Ho 0 b 68 *he Sn Altitude 1b. 4 4 
E one u. 18 
pl. J. m_ v projet haute, pen I 
Plains. * TY 42 1855 41 „ 1 My 


at © * > adn ate bs G G * 9 1 0 " 
_ IN "IL 7 © +. nk - 


1 100 Wirk W T I. 

Chap. 8. To make 4 Reflective . 

| | Chap. 9. To make a Dial 70 fg 7 = 5 
Fe afigned, as well a as London, or where 
3 _ the; Malis made for 7 AD .« S836 
I = 4 Table Latitude and Longitude 7 the _ emi- 
B e lane n 


er 


15 In s MENTAL DITA L ＋ 2 G. 


4 Gone: 10. Sect, 1. ben de hw the Hour-lines 
es any Plain, by the Help of the Lines of 
- _. - Hours, Inclinations, c. «por tbe Scale 184 
3 848. 2. Upon a Horizontal Dial 186 
& © See.:3. Upon South Dial | | 887 

Sect. 4. Upona North Dial i $1..0 ht 
. SeQ; 5. Upov a South or North Reclining Dial 


5 192 
5 ee Ef. Welte 255 
on an Eaſt er Weſt Reclining on 
197 
S Ses 8. Upon a a North or South Declining Plain | 
3 XZ . +2. 
3 : £2. 25 Don Car Declining Plains 20ð02 
3 1 0 » Declinin 8 Plains 205: 
1 Sec. 11. 4 Polar D Dial - AI 
8 12. Upon aw EquinoQtal Dial. 213. 


er Mrcnaniex DIAL LING. 


| Qhap 11. Sect. 1. Of a Horizontal Dial Pg 
Sect. 2. Of an Eredt Dire South Dial: 28 
Sec. 3, Of an Eredt Direct North Dial. 220 
=. SeQ.:4, 0f av Eret Pired Eaſt Dial. 221 
e. 5. Of an Erect Dire Weſt Dial 0 
Sed. 6. Of a Sontb or Noreb Declining Dial 46. 
1 1. 7; Of - South Dial eln Welt Na | 
1 Sea. 


229 


Direct South "of Len Icing or | 
Reclining Plains 43 


a 


- Be: 10: Of derne South Inelining, Pech, 


* : 
3 22 * * 22 2535 


Seck. 12. 1 make 4 Lige a 
Sect. 13. How to mals 6 Dial to 
er 288 e gas Gyong 


NN 3. "is to 2 the Colours for Painzing 2 
Sun-Dialss be e en,, 

849. 4. Of the Nature and Colour of ſome of the 
n ed in Painting of, 


Ses. 5. How t0 make ſore Gries Colours 
Table of the three Requiſites in 
A Table of Meridional —_ . 


_ The Uk of the aforeſaid Z. 7 ables... e edel 


bY. if . Ny 
bY ” 5 a 2 2 ü 
Y "co s 
E. : : o 
RE 0 4 . 8 : 
8 POS tas : * 5 5 2 » 
* £ 
3 
# 3 


E E Artificer's n Con- 
taining, an exact and diverting Repre- 
5 * of the Lives, Conduct, Characters, 
and various Humours of the following Profet- | 
4 fors; z as it was taken from their own Mouths, | 
in their ſeveral reſpeftive Addreſſes to Mo- 
ther ArxT. Viz. Limners, Stone-Carvers, | 
Glaſs-Blowers, Frame-work-knitters, Tay- 
lors, Hatters, Carpenters, Joyners, Brick- 
- ayers, Sawyers, Plaiſterers, Glaziers, Wea- 
vers, Wine-Coopers, Potters, Dancing-Ma- 
'Rers, Pipe-Makers, Watch-Makers, 22 By 
- Edmund Carter, Philo- Ars. Printed. for Fo 
- Wilford at the Crows near: Stationers Hall by 
3 Price One Shilling. 


n | Geometry, Aſtronomy, Geo- 
+ gray. and Navigation; the Uſe of the 

- Globes, Maps, Er. Surveying, Gauging and 
- Dialling, are carefully Taught by Charles Lead- 


- bitter at the Hand and Pen i in e 
Shore-Ditch, London. 5 


Slobes, Spheres, TEN Thermo- | 
meters, Leleſcopes and Aſtronomical Qua- 
= Adrants, Declinators for Dialling; all Sorts of 
2 | 1 Inſtruments in Siver, Braſs, 

Fyory or Wood, according to the beſt Im- 
BEE are accurately made and ſold by 
ohn Fowler, at the Globe in Sweeting's-Alley 

the Royal Sai London. Allo Ma- 


ks 
_—  Geome- | 


3 


b R 0 B L E N * 
Upou a „ Riche Line gives ro ad a 


Perpendicular” | 5 

= ae 1% x 
DEFINITION: q 
* by 1 
6 Right Line is ſaid to be N 23 
: to another Line, when it maketh the 
9 ay. Angles on either Side of the erefted 
— Line equal; that is, fo that the Line 

. inclines not either to the Right or to 

3 the Left, but Randeth upright upon the Line = 

—_ 7 which it is erected, as in Plate 1. Fig. 1. the 
f right Line A B is laid to be Nb ei to 1 
IN the Line C D, upon which it is erected, becid I 
i= WW the Angles on either Side thereof are equalyz 8 
72 namely the Angle A B C on the one Side, is o- 

7 qual to the Angle A. BD, on the other Side, 72 — 

a- either of . ce ate called. Re Ang * 

4E3TD 4 EY | 0000 1} la ME 


"$3 T1423 


8 


Bs 
* 
2 
a 

* 


i . 
4 


. * 1 
of * * 
a . 28 
\ Tt ot 
* — 5 1 
; : a SIN 2 


ical” P * N AK 


n called-qhe 


1 e Line * 0 re 


PRACTICE. 


*:. 
* R Q e 


19 C D be a [right Line given, and let. it Os. 
required to ere a Perpendicular thereupon, from 


the Point B: Open your. Compaſſes to any con- 
venient Goal! Diſtance, and ſetting one Foot in 
„the Point B, with the other, make the 
Plate 1. other two Marks E and F, on either 
* 1. Side of the Point B. 

open the Compaſſes to any other con- 


venient Diſtance greater than the former, and ſet- 


ting one Foot in the Point E, with the other draw 
the obſcure Arch & G, as near as you may gyels 
ovetthe given Point B. Agaln, (the Compaſſes 


being faut opened to the ſame Diſtance) ſet one 
Foot in the Point F, and with the other Foot de- 
ſeribe another abſcure Arch H H, croffing the for- 
3 mer in the Point A, ſo is A the Point, through 


which if you draw a right Line from the given 
Point B, that right Line A B ſo drawn, fratl be 


icular 2 the given Line C D, and Tag. 


e Point t B, as Was e 


— a a8 1483444 


b R OB II. 


| How ne (or near) the End ef a 5 ht Line = 
SOUR, erect 4 Perpendictinr. "ig | 


22 effe8t-this, there are ſeveral Ways, but 1 
will inſtance only in IO; Which are familiar 
21 my 


3 F< 
0 oy 
wo 5 E : D # 
Problems. i 3 =; 1 2 4 
Ty "a 
a 


This done, 


The p 


pe N due! Tube. 


„n . pe * gt 4 4 r 4 gz 4 55 Wie ot; * 
3 : . # 5 of "8 1 7 þ 


** 1 va þ * # 0 1 4 * PS * 1 * * 


"The Pp We 7. 


LET A B be a Tila gen, * from the Point | 
A, which is towards the End thereof, let it be re- 
quired to ere à Perpendicular A C. 

Firſt open your Compaſſes to any Plate 1. 
ſinall Diſtance, and ſetting one Foot Hg. 2. 
in the given Point A, with the other 

deſcribe the Arch F E D; then ſet one Foot of 
the Compaſſes in D, (they being open'd to the 
ſame Diſtance) eroſs tie Arch in E, and ſetting one 
Foot in E, with the other deſeribe the Arch AF 
G croſſing the firſt Arch in F.—— Again, ſet ne 
Foot in F, and with the other deſcribe the ſmall © ñ 
Arch. H H, crofling the former in the Point o 
So the Line A C being drawn, it ſhall be pern 
pendicular to the given Line A B, and from the 
n A, as was required. 


- The 4 . "8 0 3 261 a 


Ter B be the Point given, and from it-let it be. Ro 
required to draw the Line BI, perpendicular. to i 
AB. Open the Compaſſes to any ſmall Di- 
tance, and ſetting one Foot in the given Point B, 

I Pitch down the other Foot at all Adventures, as at. 3 
# K, ſo the one Foot being in K, turn the other. 
Foot about till it croſs the Sindh Line AB:nl, 3 
then through. L and, K draw the Line L K M, s. 
+ and ſet the ho thn Diſtance K L, from K to M, fo: 
„ tte Line B I drawn from B, through M, ſhall be 
5 E to A 2 7 de "—_ e n | 


ml 
. —_— 
4 
| 2 
n = : # £5 Bo : . "3% 
4 5 5 0 Is 
— 2 ns ? 
8 
p =? * 5 
9 are . - ” IL 
2 * % * 
* 4 
1 
: 
* El 
1 * 


4 1 MS % 
1 , 95 * IF 4 i * : 
5 E's 


. 


1 4 : Geometrical Problems. | 


| eorengecneeoenceeeces 


R O B. Il. 


Kew from « p ; Poing above 10 let fall a. \ Perpendicular 
to a right Line given. | 


N this there are two Caſes, Firſt, het the 
Point above is over (or near) the middle of the 

Line. And Secondly, when the Point above is 
near over the End of the Line. 


a 


12 5 1 Te Hrſt Way. 


Ter R 0 de a right Line given, and from the 
Point P, over it, let it be required to 


Plate 7 let falf the Perpendicular 1 
be. Hr. 3. Firſt, open your Compaſſes te any- Di- 


ſtance greater than P Q, and ſetting 


one — in the given Point P, with the other 
© deſcribe an Arch of a Circle, cutting the given 


Line RO, in the Points RS. Then, Secondly, 
diyide the Space between R and 8 in two equal 


85 parts in Q, (by the fourth Problem following) ſo a 


Line drawn from the given Point P to Q * | 
be Perpendicular to the wen Line R O. 8 


The Second Cafe. 


| "Jar? v dong the point given, from benen to let 
| fall a Perpexndicalar to the Line RO, —— Firſt, 
- ffom any part of the given Line R O, as from 

T, draw a right Line to the given point V, which 


Tue (dy the next Problem) divide into two equal 


Wok in the point X, with that Extent of the Com- 
8 (one Foot being placed in X) with the o- 
_ ther * the Arch or Semicirele V OT, cut- 
ting 


- 


he 


O, and towards the End thereof, as was required. 5 


one Foot in the End A, with the other "Plate, 1. A 


1 1 Problenie; - 


as given Line R O in O, a Line drawn from 
V to O ſhall be perpendicular to the given Line R 


— þ 


e 17 
Hew to divide a tight Ling given into 70 Mo parts. 


LE. T the Line A B bea Line given, to be di- 
vided into two equal parts at tight fo 

Take in your Compaſſes the length of the 

B, or (if that be too long) any other: Diſtance . 

bove half the length hecdge and ſetting _ : 


draw the Arch CD E, (then the Com- Ng. 4. I 
paſſes unaltered) ſet one Foot in B, and = 
with the other Foot croſs the former Arch (both! 25 _ 
bove and below the Line) in the Joy F and G;, 
then a Ruler laid from F to G ſhall cut the given, 

Line in H, ſo ſhall A B be divided into two e | 
parts in the point H, which was required, 


» 
I 44 . 


0 17 


auf Rd fe g an Gx A 


ROB. . 0-1 n 


4 right Line bei giver how to draw another” right 
Line, which 25 be parallel thereunto, at any | 
Diftance required, or ti rough any Point ee 1 

| DEFINITION. 1 

O F- Paralkl Lines there are princip ly. "rho. 4 
kinds, viz. Strait or Right Line! Parallels, 1 

and Circular Parallels. All Circles that are deſcri- i 
bed or drawn upon the ſame Center, whether ey 3 


N r ee Gee ds ' 
- Ps 99 * — . 5 tt 3 4 3 3 5 * 7 
. . r "30 5 5 
1 0 , Os LOS n 9 : : x 
h * £ ba R 7 * 
5 nd * N 8 * p » Sg 
a © OR” F . 

* 1 4 of C K # 
q * Pro 8 

* 4 3 v L 

2 TT” 5 \ N 
2 
3 % 
N 


be greater leſſer one 10 he 2 are ſaid 
1 or Concentricł Circles, as 


the Circle AB C D may be ſaid to be 
Fir. « 5. Aa Concentrick Circle with, or a Parallel 
ele to EF GH; becauſe both of 
them are deſeribed or drawn upon the ſame Point 
or Center O; and of both theſe Circles, the right 
Line AC is the Diameter of the greater Circle, 


C and E G of the leſſer, the point O is the Center 


of both, and all right Lines drawn from thence 
to the Periphery . Circumference, or Limb of either 


4 * of the Circles“ Fo equal, and are ſometimes cal- 


led the Semidiameters, and ſometimes the Radius 
of the Circle, as the Lines O C or O B of the 
greater, and © H and OE of the leſſer; it con- 
E  taining-6o ſuch Degrees or Parts, of which the 


E whole Circle contains 360. 


Bor Right Lined Parallels, ate ſuch right Lines, 
A chat being Lean upon the fame "Os 0p, infi- 
5 nitely extended on either | 
Side, would never con- B- — Cc 


cur or meet, but always Bo — — 


in all parts retain an e- 


an D, in the Margin. 
sx the deſcribing or drawing of parallel * 
there may fall out two-Caſes or Varieties: As, 
1. Ir may be required to draw a Right Line 
Parallel to another Right Line, at a Diſ- 
tance given. 
2. Ir may be required to draw the Parallel 
| Line through à Point affigned. © 
© Ol of this kind there may be two Caſes ; F 
. Tux given Point may be over or vnd 
5550 the given Line; Or, 
* Ir may be oblique to the * N 


® : 
os 
a7 * * 4 
"Y wo . 
3 Fe S 
. — Ws 2 1 X - * 
2 * <* 5 a - : | : pa 
E. * 4 25 
* 2 9 8 7 
7 - 7 : n 
1 * 
3 — 
8 


yrs 


qual Diſtance, and ſuch are the right Lines, B 0 | 


* id a. 


2. 
1 


„ — 92 — 2 — 


122 4 * A 9 5 T N an x Wer _ OY * * 7 T . * * * 
* 1 
» ! * 
| Ca ; 
— F 
1 
i p 


-- 


paderies, 
Of. the Fiſt Cafe. wen 


* E F de a right Line given, 5 let it be 
required to draw. another right © Line parallel there- 
unto, at the Diſtance of the Points & and H. 

TAxk in your Compaſſes the given 
Diſtance G H, then ſetting one Foot: Pla 1. 
of the Compaſſes in E, (or any other Eg. 6s. 
Poiat near the End of the given : Line) 
deſcribe a mall obſcure Arch of a Circle, as I K a. 
Then moving the Compal (5. to F, (towards the 
other End ot the given deſcribe another 
obſcure Arch as LM; 57 ay. 3 Ruler to; the 


do not croſs, but juſt touch either of them: Then! 
by the ſide of the Ruler draw the Line ok = 
ir-ſhall be” parallel to the given Line E 25 a 3 
the 'Dillarice G H. which, was required. - aeg 
e 5 


The Second C N 


lr PO be 4 right Linie given, and let it be re 135 
quired to draw another right Line parallel thereun⸗ a 
to, which ſhall paſs through the Point R. 
Fixsr, ſet one Foot of your Compaſſes in the 
given point R, and with the other taſte the near 
eſt Diſtance to the given Line PQ nern 
is done by opening or ſhutting of the Plate x. 
Compare till the moyeable, Point 93 Hg. 7. 
töurh the given” Line P Q, de. My: 
Fa ug che Arch s t. The Colmpaſes, fill xeſting, | 
at this iltance, ſet one Foot in P, (or any o- 
ther Points to the End of the given, Line}. and 
with. the other Foot deferibe the Arch u . '% - = 
| 65 . 


NEE 


. a . «ij 
: * ry 


very Top of theſe twa Arches, ſo that.the Ruler 


* >; > > INE, 5 22 125 " 2 
* 6 : 
ot aa a. 
WWW 
* e £ 


6 ” ry 8 N * WWW 9 * 
0 * r * l x E * 
» x ; If 
+ * 
* 
3 
F 1 14 
» Ss 
8 = - * ** 8 
> 
» = 


. By the very Top of this Arch Y, draw the: 1 
right Line Y R, and it ſhalt be parallel to the gi- | 


ven Line P Q, and ſhall. paſs directly through the 
1 nous . R, which was 8 0 . 


1 "The third Cast. . 
125 A Bb TE a tight Line given, id 101 it ve te- 
quired to draw another right Line parallel there- 
unto, which ſhall paſs through the Nac CREE 
Taxe i in Pr Compaſſes the D e from the 
ven point C, to the End o the given 
Plies ke? Ine B. then let one Foot in A, the o- 
Pg. 8. cer End of the given Line, and with 
the other Foot deſcribe the Arch f g. 
- Again, Take in your Compaſſes the length of the 
des Line A B, and ſetting one Foot in C, with 
other deſeribe the Arch die, crofling the for- 
mer Arch in the Point o, ſo the Line o C being 
nb, ſhall be parallel to the Line A B, and ſhall 
1225 through the given Peint C, as was requited. 


# 
# #231 


4444445 24244443 


28 n OB. vi. 4 6 


= Three Points (which are wot in a 4-0 Line) 
being given; how to find the Center of « Circle, 
.» which ſhall paſs through thoſe three given Points. 


L E T the three given Points be A B and C, 


through which it is required a. Circle ſhould 


1 be deferbed: Firſt, Set one Foot of the Compalſ- 
= Cs in one of the given Points as in A, and extend 
E- Na ak Foot to B, another of the Points, and 


draw 


4 293 a a e 


me Co 


288 


the 


Geometrical Problem, 5 © 


draw the Arch of a, Circle G E D. Sepandly, 
The Compaſſes not altered, ſet one Foot 

in B, and with the other croſs the for- Plate 1. 

mer Arch with two ſmall. Arches, in Fig. 9. 

the Points D and E, and draw the right 
Line D E. Thirdly, Set one Foot of the Com- 
paſſes in the third Point C, (they ſtill keeping the 


| ſame Diſtance) and with the other Foot croſs: the 
firſt drawn Arch G E D, in the Points B and G, 


and draw the right Line E G, croſſing the former 


right Line D E, in the point O. 80 is O the 


Center ſought for; upon which, if you deſcribe a 
Circle at the Diſtance O A, it "ſhall. paſs-through 


| all the three a Points Anden, * 
| ee ))) 4 


: ; - f I n 
4 2 T3 

- 

— 


WEISER _ 


Y% 


, " wx 3 1 . «#5 e 3 
7 7 419 : 5 411 0 1 þ i bd bt 6 
4 : 4 
* 


40 Lp p R 0 B. VII. <0 be 


70 wo Points within a Circle bing given, FLY to * 
tube Center of 'a Circle, which being deſrriled 
paſi through the tus given Points; an fall A0 
divide the Peripbery or C ircumference s 4. OF 
Circle into ergo tua Parts... E 


| HIS and the foregoing Prapofition, come in 
T continual Uſe and Prattice mie is 


Work, and wereldte ought'more SN to be 
„and the 2 i 


minded. tr enn th 35 "If 
ET the Site given 12 NG 
Ports within the fame be. ESE ? 


4-40 


915i sr, "Through eithe 
wh — 5 1 op Tin 15 58 5 


8 (as N 


0 [th 5 e e Scud | | 


""Geomerrical Problems. 


and at right Angles to BED. — Thirdly, from 
tte given Point E draw a right Line E 
Plate 1. A, and upon the End thereof A, (by the 
F 29. fecond Problem) ere the Perpen icular 
AG, croſſing the Line B D, (it being 
1 in the point &, {© ſhall & be a third 
Point, and then having the three Points E F and 
G, (by the laſt Problem) you may find a Center, 
upon which a Circle ee ſhall paſs, 
=, whoſe Center will be at without the given 
| Girl upon which point, i if ou deſcribe the Arch 
r Grele arthe Extent or Diſtance of H E, H 

Ht] of HG, it hall paſs through the two given 
Poi E and F, and divide the given Cirele into 
to equal parts in the points M and L, which was 
- _ Fequired.. And that this Arch thus drawn doth di- 
| (vide the given Circle into two equal Parts, is evi- 
* ö . Line drawn from L to M will paſs 
4 E . direcdy* rough the Center of the given Circle, 

bo and ſhall n it into two I * 


* 


195 2 2 GT * 4 * x IP 129 . qt . 8 : ko dar. LISTED A ht hb \ 
48 14S eee 
=. 3p 1 60 
34 : > | " E N | * % | — 0 
1 . TS ION „„ 
b 3 G s 5 
* 5 . ; \ * * 1 " 1 
* | Prod” VIII. 

1 


* 3 Chords 21} ban e 
e ns Gama 
Au or Radius. 4407 


. 
*x7 
© 


9 to 6 


$29 1 


„ ad ©: 95 Kill an . 
4 JOatucn as thron « ill whole Teak, ere 
1 Js contin on and Uſe made ot a5 2 


of Chords, it 18 impertinent im this x 
255 diſcover the makit ig per. for 0 5 5 = 
l imes 1 1 Ol ie = 


© Fw. 'have' the * of Mat A 
Pe Iuſtru- 


8 draw the Line A C through the Center, 8 


In 
CC 


nd AO % *» 7 


ad! Ot, -=* 


Inſtrumeut Maker, to whom theſe Due ate 


Circle great or ſmall, is divided (or fuppoſed to 
be ſo) into 360 equal parts, called Degrees, ſo 

the Semicircle contains 180, the Quadrant 9% - 
and the Radius or. Semidiameter (Which is thaʒt 


ſcribed) noted in the pda, Figure with the | 
that Circle which it eres, and therefore 50 


thereof. Thus much for the e of a 
Line of 0 now, or „ Ons ON 
5 1e 0 * 0 L VU s 10 N. 1 5 i 
2 Br 4 right Line of any" tg; 18 4 
F B D., and near the Middle thereof, vie . 
firſt or fourth Problem) erect the Pergeridien -* 
AB. arg es -. 
Second L Oven your Compaſſes to the Ra. ; 


"Geometrical Problem, wm 


COMMUN: 


DEFINITION: "3 ol 
A Lint of Chords is no other din 90 5 = 


af the Arch of any Circle, transferred from the 


Limb of :a Circle to a ſtraight Line; now 


Line, upon which the Circle or Semicircle is de- | 


n 
7 nn T_T 


* 
1 


Lettets A B, is always equal to 60 Degtees df 


F 
ere 77 27 9H 3a > WT 
” 1 


on WA 0 


Degrees of a Line of Chords is called the Rau, 5 


or length that you would have your Live of _ 
Chords to be of, which ſuppoſe A B, and with that 
Diſtance upon B, as a Center, deſtribe the Qui- = 
drant RSAD. Sh 7 

Thirdly; Divide the Arch or Quadrant A R'SD, : 
into 90 "equal parts or Degrees, which ou inay 4 
do in this Manner. (Take the LI of de 
Line * ad and kt that Diſtatice upon the N 9 
tant 


"T2 | Geometrical ' Proble Ms. „ 


. AD, from D to R, ſo is D R 60 deg. os 
"AR 30 dep. en take the Diſtance A R, 
ſet it from D to 8, ſo is the Quadrant divided * 
to three equal parts, at the points 8 and R, 
each containing 30 deg. This done, divide the 
- ſeveral Spaces between AR, RS, and 8 D, into 
three equal parts, each of which will be 10 deg. 
according as you ſee the Numbers ſet to them; 
theſe muſt be again divided into two equal parts, 
each part containing 5 deg. and every of thoſe 
into five. ſmaller, as you ſee in the Figure, and 
ſo will the whole Quadrant be divided into 


. # Ruh, The Quadrant A R S D being thus 

divided into 90 parts or degrees, ſet one Foot 

WJ of your Compaſſes in D, and open the other Foot 

to 4 and deſcribe the Arch A E F, touching the 

Line F P in F, ſo is D F upon the right Line F 

5, the Chord of 90 deg. 

— Hfiöh, Open the Compaſſes from D to 80 deg. 

_ and deſcribe the Arch 80 GH, ſo ſhall 

EE: Plate 1. 3 be the Chord of 80 deg. 

2 E. 11. Srathly, Open the Compaſſes from D 
oF to 50, and deſcribe the Arch 79 I K, fo 

E 3s DK the Chord of - 70 deg... 

1 Again, Open the Compalles from D to R. t 

© 3 or 90 deg. and deſcribe the Arch R LB 

3 foi 18 3 B the c rd of 60. deg. _ 82 the Ra- 


ms. 7 . 
© Do the like wi 50, 40, 0, 20, and 10 deg. 
80 Jhall you have the 2 F divided into 90 


_unequal parts called. Chords. 
IN this Manner may you ZR a Line of Chord, 
Four Any lcugth;. and ſet it upon a Ruler, aud it is 
t to 5 —— all the Uſes in this, Book; and it 
were convenient that upon one and the ſame u- 

b Mar you had three, four, . or five * of ſeve- 


ral 


* 


Wo 


"Y 2 — X » 


— 


e e EE nn ee A > > + apa 5 r — A San wx; M2373 1 


ber c Problems: © 


| i: Thats Radivs's, or a 1 
wers the fame End, as in Practice 8 will: 


R, © be ht _ commodions. 8 
"4 . 1 
he | : +. "$4 $$ # 
[ TE Bia , * 9 : * e + # ” A 15 4 $2 - + 
to a s 8 * g K . 7 ®, HY 3 1 » 12 * - ps 
* „ 


EY - Being Ref provided is Tine 0 

wow fhew you how #0. work tuo Concluſions 
Geometrically, which are of abſolute Uſe in 
7 ; Dialling, : ene is f0 fing the Hohn of the 
Day, aud 11 1 to find. the Axiiae h of 
the Sam at any Time, and in any Place. 
Au with W I ſhall conclude theſe Geo- 


mie Aronenice! Eleme 


— 
oO 


1 23 * 4+ i 
bot „ e eee en 
# Hy 8 08 4 . 1 
3 * 1 * X $a * 1 — 
the $ . 4 4 3. {3 031 
$ . S EE. * * 4.2% 2775 
- 7 ö i 
* 4 y * 1 Ln > 
- * # 4 2 43 0 11 EIS 4 IF | 
* * . * 
1 * * A . | EP $9.0; 
2 » p . * Ar 29 114 130 oh 


1 7 * 14 2 
itil tj ac 
g FE 1 2 1 * 5 
: i O11]. (1 36. of 
„ h LY 

ö 4 ; +£ 4 ' E ©: 4 N 

Wa 1 — 8 e 26 en 
5 Bens 
= + 4 7 1: RAJ TE 54s 


* 


* 


i 


* e * r 


e 
Sr — 4 


* 
7 
'@ 


6 ; s =, " 
140 As Lane) dard men 979%. ve: Gs nen 
82 90 Nu IDE I 2 va HD SING 


= — p = : : ; G es. ane | > 
VE W dab clit n e We 

I * 90 a 

IMS Son ld Ys wand on Wt. 


K O R the detter deen of that 
Which followeth, the Reader ough 
g oY fo be acquainted with the principal 
| Circles of the Sphere; as alſo wit 
_ ſuch other Lines and Points, as ar} 
Pp * Seſleribed and noted upon the Material Sphere of 
= Globe, in Imĩtatigm ohoſg which are imagine! 
Ang of 


many of the; 


A Gli oC 2 Body, containin 
only one — 45 Middle there is 
Point, from whence all Right Lines drawn to thiff 
- Superficies are equal. 1 

Tux principal Circles of which a Sphere q 9 
© Globe is compoſed, are in Number ten; where 
1 are great and four are ſmaller Circles. 

4 CUES it hoy os is that which divideth the Bod 
ve the"Gfbbe into two eqml Parts or Hemiſphere 
A ſmall Circle is that which divideth the Glo 
into two unequal "yp. 1 | 


- : N 3 2 I : 
N . d 15 = 
« ; hs | TRE" 1 4 
ITS IS. F vie 


nid ant] | The fr grea Circ any 91: H bs 
- of e neee | 1.3. 362/54; ne 


—_ The * 7 {* CA. The Eulipit, 


4 2. The Meridian, 0 . / 115 ori | 4 
3. The Ae | Free ry two at 5 


Ws laſſer Citdes v 1 
7. The ee Cans" 3. The Ami Circle. 


i 8 Att * 4113 15 NOTES 
2. Tbe Trepick of ce 34. „ 
run e 0 bf ee. 7 K COLNE 
+ , Rind e chene ang 2M ek L 4 
5 05 theſe in the Art af DiMiing:chere are pri 3 
cipally pax five to be taken Nice of ee pre 3 
great Circles, and two ſmaller Circle. 
. 340i 
Rin age great Cine are,” 158 An 2 
231 Wo; 1364 3859 tl iwo 39570 2 15 obs 
£5 RR 4 The Horizany 297203 Din * | 
a2 The Merian, nt F 4 
" oaly- on 3. The Ruinoctiali 1025 un. "TI 2 
5 N I 
© The leſſer on a,, . 31% *. 3 
5 3 304 £23. + ery [0 ory 
WAY WE 74 A ene, N | 0 
| 2. The Tropick of Capricors. : 115 GFA 1 1 


I. oy OPT ZN * 


lr the Figure, let the ontermoſt Circle e 
noted wich the Letters HN ON, i month IN 
repreſent a Sphere ar Globe, chem Fla r WL 
the:Horizom is a Circle) which d- 57 . 11 1 
viderh/or ſeparaterti. the viibles Part 
of yh Heavens r ge "Et fromthe) insb Y 

none” 3 


— x 


MET + 
. 

= 
Ly 

3 
A * 
3 


i 


4 ie Part which we ſee not, Hoe is repreſent- 
ed in the following Figure by the Line (which 
repreſents a Circle) H QO, ſeparatin * =_ - 
"viſible Hemildhere H2Z O., which we ſee; = - 
the inviſible Part N 1 6 O, which we ke W , 
Mot. { 92 TY 


Un. 06 the MERIDIA 95 0 


Tux Meridian is a great Circle of the Sphere 
5 ved enen by the Poles of the World, and 
1 through the Zenith and Nadir of 
1 Plate 1. the Place.” To this Circle when | 
. 22. the Sun cometh, he being above 
| Zire our Hotizon , maketh Noon or 
„ Mid-4ay, and being in the fame . Circle, » when 
3 it is under the Horizon, it is then Rlid- 
ni BY | 


= EE 8 2 „ 


ich is that Point in the Heavens which 
is direc y over your Head, in what Part of the 
World . vou be. And. | 
Tux Nadir is that Point in the Heavens which Sp 
. our Feet, directly oppoſite to the Ze- cle 
j 3 . th 
„ Meridian Circle in this Figure is noted * 
4 | the Letters HZ ON, the Point Z at the Po 
4 Fa "Th e 7K 8 k and N the Nadir 22 
| ines. 'F 


In. av IN O CTI AL. 


2 Jun gui noct᷑ial is a great Circle of the Sphere, 
HY dividing i it into-the Northern and Southern Hemi- 
ſphetes, which take their Names from the two 
/ Poles, .- that being called the Noertbern Hlemi- 
5 in which the North Pole is ſeated, and 
ti the Southern, in A the South Pole is ſeat 


ed. 


* 5 
ve £6 BY 2 


— 2 
De, D 
N * 


— * ä =. AY „ 0 ata ds ey 
_ GN; R ä ed 1 9 > I'D * A 7 C HE 
- - * * £ 1 | 

3 a 
= * > 5 
= 
A _ 
V _—— 
9 1 
- "1 

$ 

* 
* 


| ed. 'Unto. this Circle, when the - Sun in his iChat 
Motion arriveth (which is but twice in the whole 
| Year) the Days and Nights are of equal Length 7 
through the whole World. A. 3 


As; | * 2 
* 9 
* _ 
1 7 
7 


Tis Circle cutteth the Axis jay the World at = 


Right Angles; and is ſeated in the Heavens 9 
Deg. or a Quarter of a Circle, re Neef f 9 
ther of the Poles. : 
IT. is repreſented in this Fi igute but the . ar 
Circle Æ QE. The two Poles are noted with 
and 8; P being / the Nori and 8 the South Poles. 


and ſo the Hemiſphere æ PE, is the Northern, _ 3 


and ES # the Southern Hemiſphere. And the tight. 


| Line PE Q 8 is the Axis of the World. eroſſing che 4 
Aquin»tial at Right Angles in Q, the Cu r 3 


middle Point of the Sphere or Globe. 
IV. Of the two TROPL CKS.. 


2 


e 
Tas wo! \Tuprcht are ſinaller- Gireles of | 


Sphere, deſcribed parallel to the Equinadi C. 
cle, and at 23 Deg. 29 Min. diſtant thereftom -* 3 


that being the greateſt Declination that the Sun 


hath from the Æquinoctial towards eithet of h A 
Poles, Of theſe Circles one is called the . i 


7-4 of Cavcer, or Northern Tropick; the /othee* 0 
be 7ropick of Capricorn, or Southern Tropickgiſo; ' | 
enominated from the Poles which: they reſpect or 
dehold. As the Tropick of Cancer, marked witty 3 
he Character of Cancer, & & at each End "4 
hereof beholdeth P, the North Pole, and 'thes Þþ 
EI ropick of Capricorn, noted with the Characters 
of Capricamu, M W at each End _— reſpec- 
eth H. (tha South kee. Ned dee NB 


— . 
ward, pen declines not nearer to either of the 

n + Poles) than 23 Deg. 29 Min. Where- 
Plan 1. fore, when the Sun in his annual 
Fg. 12. Courſe ſhall arrive to the Tropick of 
Cancer, Which is about the 10th of 
. he maketh the Lomgeſt Days to all that in- 
habit in the Northern Hemiſphere. And when 
he arriveth to the Tropick of Capricorn, which is 


about the ꝛitk of December, he maketh the Shorteſt 
Dayt to thoſe that inhabit the Northern, and the 1 


Tages to thoſe of — ppm Hemiſphere. 


: . 5 Beſs thiſe Circles Fer ene 8 are divers 0 


e _ Uſ? in N 


KH ne uur Circles, and 1 3 
£8 8 " OF R Wd 1 «4 - 

= He U R ne are great Circles of the Sphere, 
b which meet togetbet in the Poles of the 
World, and crofs the Equinoctial at Night Au- 


gJies, of which the Meridian (or outward Circle 

in this Figure) is the Hour Circle of 12, the 
ſteeigde Line P QS, which repreſents the Axis of 
World, is alſo the Hour Circle of Six, and all 
the reſt of the Hour Circtesare drawn from Pele 
J to Pole berween them, as the Circle P A8, re- 


an Hour Circle, and fo of all the re(t, 


which are 12 jn Number, reprefenting the 24 q 
Hours of the Day and To being! taken _ N 


eee 1 „ ae 


ann FI i a LO ne 


Amur are ai one nr Gene Gp ere, 


2 hers deſcribed upon the S #0" S 2 980 ; 


12 0Q 


8272 


Ca Oo 


O NJ 


— 
- 


- ley 2. 2 


N 


meeting together in the Zenith and Nader Po nts; | 
and full upon, or interſect the | Horizon! at Right j 

Augtes; as the Hour Cireles do the quinoctial. 
Ol cheſe * n Pts Circle of this Fi- 


bu i : * of al 


fon. | 
pure” 'reprefents” the North aud South Arjijni | 
fd the Line Z N the Azimuth of East 
Weſt, and is commonly called the Prime Vertical 
e And all other Circles drawn through the 


zon t Right Algles, are eee 42. 


3 berween the Eaſt and Welt, Ws he, 10 


South Points. As in N 1 1 15 ra a 
2 B N is an Ra 10 PA bet Nach 1 


Sth li weder 10 1 — 18 7 IF | 
the Nadir 95 ſuts, ms Po 55 af. th IC, orizon, - 
they being 96 by. diſtant from O "the ot 
Point, from Q the Weſt Poipt, and from, H the 
North Point of the Hotzon. 

is | the. 25 o the Meridian Qihte H 


1 0 N i be being 90 90 , Deg. diſtant thereto i in all 


© "Kea" P lud 8. Jas North add South" Piles of 
wh W are alto the Poles 'of the FAquinoQial | 
gl 5 ey being removed therefrom. on either 
9 
Bur the Pole of the ure tele F avi a C, 


and the Pole of the Azimuth Circle Z B N is at 


D, and how to find theſe Poles, and al ſo the Poler 
of any Oblique Circles, ſhall be diſcover'd in di- 
verſe Places of the following Diſcourſe, where 


there is often Occaſion for the finding of them. i 


f 1 1 * 
2 


I 
Note, And whereas throughout this Book there i Fr, 
continual Mention made of Degrees and Minntes, 
Know that a Degree is the 360th Part of 
\ Circle, each of which Degrees is ſuppoſed to 5. 
vs divided i inte 60 Parts called e fo that 4 * 


[Zenith and Nadir Points, and cutring the ori No I 


5 


Ls 


» Mis. is three. den of a 3 30 is half 


| 2855 


48. \ 1 4 1 $2: dis. 108. 


ker are ſack e 118 as I con- 4 


ceive,. moſt hegeſſary for the angerſlanding that 
rich follows ; 

Ir reſteth now, that 1 ſhew how to perform 
two or three Aftronomical Concluſions Geometti- 
cally,” Without which the Knowledge of making 

of a Dial will ve of little Validity; for to what 
. Parpo ſe will a Dial ſerve without it be rightly 
pics ? Or ho can you make a Dial for any ap- 
ted Place, without Na 0. know the Poſition 

e thereof? And to theſe Purpoſes are 
ue following Cone! uſions ſubſervient. ; 


And becauſe it is requiſite to know at all Times of 3 


11 1 ng 72 mor, eclination the Sun bath from 
. he p either, Northward or South 
20 a, ave therefore at the _ — his In. 
e inſerted #wo Table ewing 
the Sun's Declination every. 255 in « he Tear. 


46 7 


b I 1 And the other, 4 Table _þ Prov tte 2 


1 5 214 the Principal Cities and WAS in Lag 
e Lgcland lien XY MT! 


* 1 * A > n 9: 3 (3465 the » D 41 * 4 9 
1 . * 2 24 F © 2 POO 45 > 4 # 
W544” L L et or $315 ASS ©3377 DTT ©7 WC F #95 


. =» * * oY pf 4 'S l E; 8 14 © # * 28 
. ot Hef anne gn ettgt 


"7 at ung "= x Wb : 4 . * 1 5 F a oft : 
iin r 4 t i 
Et COR" io 2 1 VWs EY | 
e Ee 2:5 
4. | 
2 | PROB 
N » 
ler CT e 5 bf * 13 A * e \ 1 ; 7 4 : 7 
0 2 3 ITY GL * 181 4 nf 3 * Bo 1 N 3 3 : 53 . 
2 3. 5 8 3 ? E . 
l 25 n 4% | ae = N * ur 8 ; % b. 
Me 4 
* o , 
*. #0 % „ * ak. tf C? * * RR 1 
Wend obe * "IL uin men 
* * * 85 os C ; * ; 4 
SY #3 24 {7% 87 e \ * 1 * 2 1 e 18 BHS v4 LO 
. 0 9 IM EVE 
7 Ir 38 W r % + E 
. 8 e 
l 8 & va 


. and 1 5 Aus one n of a | , 


„ „„ fan} * fad 


- : 4 A 
„ 22 207 
5 5 1 . JF; STM 
; 1 14 : £4 I 
{ : { l n ot; . 
q ; # N Ta ; 5 9 
Ha + 
Fr * — * 4 
- * N ww 
£03. - 5 - N 
- a LT % a 4 
1YOROM £4 * "LS * * — 
va ; 4 


2SS220424448 


PRO B. IX. 0 


Ra * Bie 'of the Plate, the Alkitade m bel 
Sun, and the Day of the Month given, to find the. E 
Hour of the Day, and Azimuth of the Sun. © | i _ 


ng E T the Place be London, whole Latitude i is 5 

"at deg. 32 min. North. Let the Sun's 1 4 

tly be 45 Deg, — And let the Day of the Month be. : 
.de x 1th of May, at which Time, by the follows, 


ing Table, the Sun's Declination is 20 Neg, 20; E 
| Min. North. 3 1 2 3 3 = 
| FirsT, Deſcribe the Circle 1 HZO Ns repr 3 


of i Ride Angles with the two. tact, H G 3 4 
"a for the Horizon, and Z N for the Prone Vers, 
b- tical Circle, or Azimath of Eaſt and Weſt... 

* SzconDLy, Take 51 Deg. 32 Min, the Lat Latitude. 

8 of the Place, out of .your Line of Chords, r 
Fo ſet it from H to P in the North, and from Qu 

es the South Pole; and draw the Line P QS the. 

* Axis of the World. And becauſe the. Zquinoc- - 


tial Circle is in all Parts diſtant from the Poles, S 
the World go Deg. take 99 Deg. of your Chord 
and ſet them fcom P to E, and from & to , 
Ty; the Line. Z.Q =. for the Aquino, 
irele. I 
TrikDLy, The Sun's: Akitude given being 4 Ne x 
Deg. Take 45. Deg.. from your Chord, and ſet. 
them from H to A, and from O to T; and lay a, 
Ruler either from H to T, or from G to A, and 
the Ruler will croſs the * Vertical Circle im 
L, through which Point the Circle. of the Sun ? 
Altitude muſt be drawn, and for the drawing of 
dnt have. three ran L and T, ; 
35 5 8 #4 


by the sth Problem — 9 you may find its 
Genrre, which will always be in the Prime Verti- 
cal Circle Z Q N extended. 
+ 8 The Sun's Declination for the Day 
pr 272. the 1 ith of May) being 20 
— hg — 3 take : _ Deg. _ 
Min. alk: of your Line of Chords, and ſet them 
I from M to C, and from æ to D, towards P the. 
North Pole, deenuſe the Declination was- North, 
-- otherwiſe it mould have been ſet towards & the 
77 0 Poe, Then 9 1 a Ruler either from E 
9 D, or from æ to it will in both Cafes cut 
- he Aris of the World in E, through which Point 
the Parallel of the Sun's Declination for that Day 
mut be deferibed, and for the drawing of it, you 
5 three Points, D E, and C, whoſe Centre 
Will always de in the Axis of the World 8 Q, 
Degel, and may, be found. by the former th 


* W 


FX 8 
OM 


3 3 Problem. 

Ih *Frerury, Obferve in your Scheme, FI the 
EE Paraltet of Altitude ALT. and the 
Fi. . Parallel of Declination B E C, do 


2 


Fiz. ccroſs each other, which will be at the 
„Point ©, and that is the Place of the 
Dun at the Time of the Queſtion. _ 
= "StxTury,” By the fore-mentioned '6th Problems 
4 2%, 8 m Hour-circle through the three Poĩms P 
Sand s, wWhoſe Centre will always de in the R- 
Y E=:: quinoctial Line extended, if Need be; alſo thro” 
: the Points Z © and N, draw an Azimuth Circle, 
Mole Centre will always be in the Horizon! er. 
. Doe when. e 5 | 
* HESE two Circles dn dran, vom! 
> 9 ed for ea 15 4 25 ws 
Hour 5nd A * ay e 


* R of * 


0 


e 
n 


Wai" Ws 


: = * > 3 
FAR 2 "of 24 „ 
8 * 45 1 1 Wo hs 12 We 4 4 1 1 3263 4 * 1 


A. 


"IS <A us 8 * i * 
N . * „ ag SAS 2-247 5 

) . : pe 4 1 LEO EET 2 aiars 4.2. 1 
1 RN © % * 8 2 * l Pe * Y Pe 2 4 Lew: >, * . 


7 * 


N a 7 * 
1 - 


6 * 4 F 
1 . 8 a Se e 


8 25 — * e — * Oe 12a ; 
1 4454 wet mY. _ 4 TT * * 1 5 4 
4.4 p . 
. 


1 


4 
N 


VCC 
% M Ob 26. 085 ee 
30 4 9 nn MU gg. 
5 | 


ry 


a. 


. 5 . 
10 46 * 7 Pa 411 * &1 * 17 þ i . F 
ie 053 21 Zn mo 


* 
[16 (PTR 


La a Ruler to P, the Pos of the World, and 
G the Point were the Mond cirele eroſſemm the 
EquinoQial;: and the Nuien mill ent the Circle 
in a, So the Diſtance from da t being me- 
ſured upon the :Litielof: Chords,- wall ohe found to 
contain 41 dege 48 min: -whichs is the Haur ; 0f˙ 
the Day, eaunted fium Noon, Much reduced in- 
to Time (by allowing 15 deg. 10 an Hout and 0 
deg. to 4 Minutes of Time) will be 2 Hours 47 
Minutes, mat 18, either Miantes afrek. 2 in the 
Afternoon, or 13 Minutes after 9 in the Forendon. 
792-45 25h. 2 2 20 nie aavig ad © 08 
I. Fund, Armut (T arr > 8 

5 r onde ant 

_ Lay 2 Ruler to Z the Zenith, and ta Mthe 
Roint where tha Azimuth Cirale (95 llethrehe Ko- : 
riaon, and the Rulen Wilk.cht . dian Git 
cle in the Points, Mithe, Diſtance & being - 
ſured upon the Line of Chords, will b 
i contain 62 Gege- 8 min. And fuch is the Suns 
, Azimuth from ithe K Part of the Metidian ññ ʒ 
Or he Diſtance: 1 being meaſured pm e 
Chords, will be found to contain. ae ͤ˖—. 
hich! is>the:Sun's:Nilkance or Mimum fra ei- 
ther: Eaſt! or Weſt}! accring t che ¶ imat 
Ithb Day U oa h Wii brig. (droht ie 
CCC 
Tnvs by one and the ſame Projection uf ue 
Fphere, yau bave fopna& both the Hour ank 
the Azimntb, and mailyopther:-Cancluſions 3 
Aſttonamical might be wrought byhhis 2 
. _ of Projection, which I have more full xf. 
une in my Geometrical Exerciſes. But _ 21 


Pg 


* 


RCs 10H. - £5 fHiw it 7 3 #1246 e 


r BY f | 
5 ſuch frequent uſe in 
5 can be done to pur. 


Diatting, 5 
at withou 

Projection, ſometimes the Centres of the 
Fa Circles will be very remote; I will here 
10 I ſſhew you another Geometrieal Way, where- 
21211 Þy:your may find the Azimuth at any Time, 

eg ie any Place, by ſtaigbt Lines, which 
0? twwill -be ſome Light and. Eaſe to the Pradi - 


| - 50 1'tioner, that ſo he may compare one Way i 


"=o . wich the other in Caſe.of any Doubt, which 
$ E : will be 2 god Confirraation of. his, Work. 


3 ö et © ee Way io foul the Azimath. 5 whit 
orie oon 
3 i the given Latitude be 51 deg. 32 min. 
Tux Declination North, 20! deg. 
Tux Sun's Altitude 40 deg. 

3 - let the Sun's Azimuth be required. 

1 * mor, Upon the Centre Q deſcribe the Se- 
E micircle H 2 O for half the Meridian, 

E Plate n. and: Sr N.. raiſe the Perpendicular 
WM "By 246 

351 „ Set · (by the Help 1 


Eine- of: * 1 deg. 32 min. the Latitude 


-of the Place. from 2 0 K. and rarer gn Q for 
1 the Equinotial. nien e: FI 

nm, Sct:20 deg. the: Sur „„ 
” from. JE towards Z, to the Point D, (being 
ba is 33 and draw the Line D T parallel 


A Q, DET. . Parallel of the Sun's. | 


* 1 TY: Sto v9 


* FoeHTAL T. Gait 40: 7 ny the Sun's Attitude | 
gien from Odo L, and: from H to M, and 
nv, the- en Sly) for the Paraltel-of Ab | 


i -- 7 25 

=. . 5 . 12211 0 

4 8 p of { + ed TO „ . | | 
Ann nne een VE FPtornlr, 5 
3 2 w * 2 ; N 8 
x X i 2 CE * 2 

_ 


720 Th that in this Way of 1 


5 5 — 
1 8 

bs] 4 
P * 


5 | 


8 L, or 8 = 
— e ee by ron 2 deſeride the inner 15 * 1 
moſt Semicircle.;.; .- 10 e 
WW $:xr8Ly, Through the point B. which is * 1 
the Parallel of Declination,. and the Parallel 
0 Altitude do interſect, erect the 8 | 
ul it touch the innermoſt nee 
= LasrLy, Lay a Ruler from 0 fete and it wh * 
cut the outermoſt Circle in E, > ſhall HEI mea- 
ſured upon the Line of Chords, be 109 d 4 "Y 
min. the en Azimuth from the North « 
| + hall 4 19. deg. 47 min. e uh 
W Eaſt or Weſt. And. a 1 
E O fhall be 1 15 min] the Aumath roms 
the South Part of the Meridian. Gel 3 
Heving nds this fair Preperative,. I will haves . 1 
ſert the two fore-mentioned e Tables ef the. Y 
. Sun's. Decſination, and Latitudes f Py Nees "i 
. them proceed to the Art of Dialling, e | l 
1 e Ati; 


329 54 


8 *-'y 4. 
= 
WY 
o 
0 


I4 


[+ 


Ow x IV H 


+ 


* 


HIS 
* 
U 


3 25 


15 


15 
* 


17 


17 
17 


42121 
121 


72 


29422 


24622 


ths 
18/22 
34122 


55 


2 os 1 ata No. 45.53. 


25 
33 
12423 
20123 
2 95122 


36.22 


41/22 


47,22. 
7422 


58 22 


ples” ll 
14 2421 37 
4623 


17 
14 
10 


A 


5 5 \ | 
591 


17 $5023 3.22 
. TH 


_— 

„ — 1 7 5 ; 
* G 

n 


* 7 32 4 2 . 4 . 
. % 


= 5 R 8 2 5 2 „ 1 
„ FS 4: Fd © 
7 * : 5 * 25 1 47. . , 


=” Ta — ee | FE 75 
7 aly; W ny Sept. 8 Nove: Se 


m. [d. m. d. 


i Bro 14 24] 7 13 


222 814 2 $ 35 38 
— + 
2 
1 
| H JL 
5 19120 13 
TO _35 


11 30 "1683; 
12 1 O 403... 


a 


4 iR + i its 1 Net . ” 
titudes of the Cities, Towns, and ' 
'*<Iſlands in and _ _ Britain and 

47 7 Ireland. | We 3 


1 \ 
3 * 0 
1 


5. M1 Egled 
„ D 3 
495-50 8 
51 27 Norwich 
52 . Nottingham 
352 12, Orford LINN 


SOT 


4 5 
Ni 


155 21855 


Radnor 


St. Davids. 


Ma 
Pembroke 


„ 
1 


n 2 
i 


Edinburgh 
Glaſ; 1 


Kinſa 


Orkney! + 


King's Town 53. | * 4 


x 93] n 32 


4 
„ 1 | 
; 3 11 1 1 8 £1 2 „ 14 5 18 . — 


3 


Fi. 11 7 * 0 


metr 


1 95 projecting the rl of the Sphere ll © 
E N 82 r 0 
e. * acc Tin it ſelf. = | 
er Le 5 
; T4 3 XX te Te a - a 
TP 10 1 se 
44 <2 "The "Firſt" PART, 44! 4 ; 
. 0 | 27 bann j 7 P met dont 
= £7. NO ATP. 1 X 4 } 
- Of the ſeveral Sores of plate As which DIALS 
are uſually made. 
——-| |. may be made upon any plain 
Superſicies, and all plain Superficies 2 
are poſited i one or other of theſe p 
three Poſitions, viz. either Parallel, * 
Perpendibalar, 2 Oblique to the Hori- 


20on of the Place wherein the Plain i is ſeated, and 4 
all_the Hour-lines drawn upon any Plain, are ; 
2 N 


88 EL]! 
— 


q "IM n „ Fe oc A YER „ _ yore . * * * 8 * — = — ä * e _ 1 
* _ 
25 7 : 

; * i 

e 1 r 2* | 
. * 
. * 
* 


>reat Circles of the'; 8 which being pro- 
bed upon a plein Sepertkates, become 1 4 
ines. - 
| Naw the Art of Dialling. confilteth chiefly: ra "i 
the finding out of theſe Lines, and their true Di- 
ſtances each from the other, Which do continuall77ßß I 


9 b vary. according as the Plains upon which they 
$ are deſcribed or ed, are firuarcchin _ 
of the Horizon of the Place. R 


Or theſe Plata there are. but three van. _ 
* VIZ. 1 
Parallel to dhe Hermon, ae i6 he Horizomtal = 
* which I call Oy Plain only. 


p 1 North & G 
” 2. Perpendicular v 
44 to the 32 83 
a weilte 
8 to the Ho- 

i xon. 7 
in No in me nie of cles Dias, which 
5 are in Number 25, I reduce them to 17, by ſupp- 
f plying the Iwchning Plains from. their 6ppolite Re- 
” | chiners, as being indeed the fame. © 1 
q AND to avoid Miſtakes, which may poſſi biy 
| ariſe by comparing my Examples with other A ö 
Authors, or others with mine. You are to take vo 4 


AQF | 
i 55 None 


1 


— 


* 


4 , 
8 3 
* . N * EM 
- 
* 
"IS * > * 
7 I F 
| } 7 1 8 


Fs 


Dialling, | 


TI denominate all m 


15. 
4 
E 


V 


In. 


take Notice, That 
ns which moſt . 


Therefore 
al 
r INE 


#. 


11 from the 
in the Hea- 


7 


their Ax 


16 
ircles of the Sphere 


ons) of 


ti 
, and not from the C 
Fhoſe Pla 


Bw 

8 

a a 

S = > 
28 2 
1 1 
SS it) 
5472. 
28 2 - 


„ 7 A. PAT TT n 


— . . ¾ 98 


* 


* n 


p North“ pak of the 
Becauſe : South | Horizon. | 
Poles WY s 
| Faſt Points df be = 
75 lie Welt Horizon, - - 
in the | 
Wo Poles of the World. 
3 Equinogia Cir 8 
5 þ.- „ #150 r >, ns 


s £4 


* "i 
8 88 __ rey a, 1 COU 
K 2 . 


= —_— 


— —— —— 


PP ²—Ä ˙—˙⁰ ⁰öw w —If ?ðr ?1r? INT As — 00 


the 


Jea- 


2 : 
Im 
, * 

5 
wo 
YL 
& 3 
L 


1 9+ Polar, Or North 


Again, all. „ Teac parc Died or 
declining, whoſe upper Faces behold the Ze- 
ith, I call Recliners ; and the nether, or under 
aces of them, which reſpe&, or look down.to - 


he Nadir, I call Inchners. 


This Diſtinction being made, the Plains 
of all which Examples On are 
thus denominated. 2 | 


TE Vertical or Horizontal. ; 3 : 1 
2. Sonth and North Direct. „ 


3. Eaſt and Weſt Direct. 


* 


E | * South and d North, cnn 2 40 i 'L 2 "i 
1 a © 
8 


r 
1 


i # - # 8 7 — * * 5 
5 ”y 8 | *4 4 2.37 5 * * - * . 
0 1 3 1 * 4 6 $4 3 
4 o 5 £ * * 7 „ 7 * £ a * „ 
” 


© S : . | 12 ; . 
5 N and 1 Die On 151 162047, | 5 
* N 4 j0 4 


« OP | 
Sg el Tnclinmg. - | . „ 


6. Equinodial, Or, South Reclining or , Ic 
ning to the Pole. Re 
7.2 South Direct Recli- $ leſd "than the” 


8. ning or Inclining d more Porr... NE - 
Le or e 9 


Norrb Direct Reeli- le Itban the K. 2 


the Equinodtial. 


18 ning or Inclining 2 more F ui 


12. Equinodtial, Or Sonth, Declining 12 or g | 1 


. Weſt Reclining to the Pole. - 
ad Soxth declining EaſtC above 1 F 
BY ot Weſt Reclining s | > = Ms 


14. J or Inclining. 


15. Polar, or Narth declining Eaft Or WP, ne. A 


. Clining or Inolining to the Equator. _, 
above the Int 


16. | 
 / North declining Ea | 
or We/t Reclining | ou {9 2 
} T3241 _ er ng Equator. x 
| 1 Thus 


nne 
. 


* 5 2 LI; having 1 Thread or Plummet hang. 


9 1. Geometrical Dialling. 


Pues are the ſeveral Plains denotninated, f 
mall now ſhew how the Situation of an Plain 
may be attained, either in reſpect of its Declinz 
You or Reclination. A | is 


0 AP. u. 


AA „ 3 25 


ne to find the Reclination and Declination 7 . 
N Plan. = 


I. Ber the Reclination. 
r e of a Plain, is the Arch a 
the Vertical Circle or Azimuth, which ö 
perpendiculae to the Reclining Plain, or that Ati | 
- muth, in Which the Pole of; the Reclining Plain 
lieth, comprebended between the Zenith of the 
Fee and'the Reclining Plain. 3 
To find which, let BCD be 2 Reclininl A 
25 903. Nfl Plan, draw firſt thereon” by the Heb 
Plate 2: of @ Ruler and Quadrant, a Line (| 
OY 1. F parallel to the Horizon of the Place 
which ſhall be the Horizontal Lin 
of the Plain, and croſs at ir right Angles wit 
- another" right Line K 8, for the Vertical Line 1 
de Flas? to this Vertical Line K 8, -apply 1 
-» ſtraight Ruler K I, and to that End of it he 
lieth clear of the "Plain I. - apply a-Quadran® 


N 


* J „ Pam fs 


| rom the Centre at I, ten ſee what Number 
BE by of the "Quadrant are contained be. 

tween O and L, for ſo moch doth the Plain re- c 
0 e N ee h Ar 8 * 


cy — 

* 9 1 , 4 k ; 4 * A a F { : 

* * p £3 * 4 a 4 —_ . 1 "i bo 

3 1 1 # 8 1 ' 5 j 

A - : 7 © 

- — * ö 4 4 43g F : 5 

1 - \ 1 * £ © 

F 7 1 5 * k » * & 5-5 : 5 

ene nne 0 II. For 

o 35 ; g 3 Py - ; . 
8 RN 5 L 


8. 8 


0 
14 
» 


omen ar Tung... 
5 et & 4 l 


N 


ö 

9 s K I 

1 5 N * * 
» * CY 
* 7 ©, Ts a . - ; 5 
„ 9218 4, xt . Ty "#28 
Hoe ee 1 22 the Declination hes 

2 4. 2 * 
F 4 4 11 r * 
n 441 


N (e 1 
Tut Declination of '# Plain, is art Arch of the 
1 [Horizon comprehended between the Poſe of 
lun, und the Meridian c the Plate. Or it s 
RE che Piſtanee of the Plain k a Rſs prüme 
Vertical Circle, or Azimuth of Ka d et. 
To find out the Decllation be 10 Plat, there 
rere required two Obſervations to Ts by ic 
IF Sun at the ſame Inſtant of Time. "The Belts = 
| the Horizontal Diſtance - of the Sum from he... 2 4 
| Pole of the Plain. And ſecondly, Of - the oh 
Altitade-” 3 9999136 eee e, | 
"Fo find de- 1 Diane; f. 9 
1 Pole of ihe Pleis Apply dne Edge of 
Quadrant to the Horizontal. Lie of vu Plath: 
fo that the other may be perpendfeulat to it, . 
the Limb of the Quadtanf may be towards th 
Fun, and hold the whole e 
hear as an eonjecture.) Then fbf 
up # Thread: and Plimimer at full” Liberty, 
that the” Shadow öf the Thread thay* 9 
trough the Center and Limb of th G | 
obſerve then the Degrees cut by the Shadow Of 
the Thread, and number then from chat Side 
of the Quadrant thi ſtatideth fquare 4 
eufat te che Plain For thoſe D 


W * 


N Diſtanee r | wy 
; Diſtatice ang the 8 1585 


Tis Horit 
Altitude being obfervecd at tine fange Time,” 

as may be) Will Help you to the PIs 1 
tion by the Rules followings!) ?: oh 

FissT, By having the Altitude, you my 

the Azimuth by the two laſt Problems of the 

"PINS | then by comparing the . 
all 


_ " Geometrical Dialling. 


and this Diltance together, you may find the 
Pais Declination in this Manner. * 

WHEN you make your Obſervations of the if | 
Sun's Horizontal Diſtance, mark whether the 
Shadow of the Thread fall between the Sozzh, and 
that Side of the Quadrant which is perpendicular 

to the P lain. - 

1. Ir the Shadow fall between them, t the A. 
zimach and Diſtance added together, do make the 
Declimation of the Plain, and in this Caſe the De- 
chination is upon the ſame Coaſt whereon the Sun's 

Hzimath is. 

2. Ir the Shadow fall not between them, then 
the Difference between the Diſtance and A⁊imuth 
E is the Plaix's Declination ; and if the Azimuth be 
the greater of the two, then the Plais declines to 
te ſame. Coaſt whereon the Sun is; but if the 

Diſtance be the greater, then the Plain declines to. 

the contrary. Coaſt. 
4 Ao hen here note, that the 8 thus found 
18 always accounted from the South, and that all 
Nec linations are counted from either South or North, 
EF towards either Eaſ or Jeſt, and muſt neyer ex- 
Feed go Degrees, 

2 5 Is therefore the Degrees of Dechuatios "A 
| the Soxeh do exceed 90, you muſt take the Refi- 
due of that Number to 180, and that ſhall be the 
ration from the, North... 1 55 
= the Degrees of Declination exc 180, 
= ay the Exceſs. above 180. Degrees gives the 
Fleiss Declination from the North towards that 


Coaſt, which is COMM: to abe Coo a 
the Sun i = 5 


ks W 
£ F | 18 * f 5 


a + 


; 


45 of Vertical Dial. 


5 


|. monly called Horizontal ) Plain. 14 


3 Of a Vertical or Horizontal Plais i in „ the 
Latitude of London, which is 51 deg,, 32 Wes 


FIRST, Dtaw a Circle E S W. N. whi 


wo Diameters, viz. S Q N, for the Meridian, 

ind Hour- ine of 12, and E 2 W fot the eine 
ertical or Hour- line of 6. 

SECONDLY, | Becauſe the Latitade of 1h Plies 
"51 deg.” 32 min. beg roy 32 min. out 6f 


our Line, of Chords and let Diftatice fig 
to a, and fr 80 0 70 5 Ge u 

Tuikprx, P39 A eons E to Anat wh 
ut the Meridian Line 8 N, in the Point P., 


rhich Point P is the Pole of the World : And a . 


hers Poi e % Gen Point end ep the 
quinockt la chi ert 
ou three 95 10 * 0 
bhi ich Jo muſt dt Re uino Circle | 
XA W, wbbſe 1 1 ml 
ill alw 33 he 7 in the Me- Aue, Eu. 
dian 8 N. 8d that you Sort Diul for the. 
ay 000 tl t, as 1 1 B 
gen ; Before "tan bt, and in IS. 32 wait 
is Männer alf aw the” Plate + 2. Fo.» 
N which aka. 8h IMG. 


— 


'Gitcle let repreſent your Vertical Pg 1 2 RO 
in the Middte pwnd at right Angles | with" us 4 


Later laid NY 3 to . cut the Meridiin 


K. add. W e 


dee Dialing, — * . 


| 2 ro o drow che ihe 5. ht Pe. 4 Vertical [Gow | 


* 


* N 7 1 + 1 0 » 
os 8383 Ks 2 
Wien FIG 


** — —  —__ — 
9 nn . 
— 2 
pu +. * 
1 
4 
1 


eee e 


1 
. 2 
EL 
. 


; " the-Semicircle EN W, in 12 other unequal Parts. 


= from 6in the Morning till 6 at Nigbt. 


| goo N raiſe the Perpendicular A C, cutting 


into 12 equal Parts at the Points © © ©, &c. be. 
ginning at the Point N, and ſetting 6 on either ſide 
thereof. The Semicircle may eaſily be divided 
into 12 Parts in this Manner; for 60 deg. of 
the Line of Chords will divide it into three e- 


Plain, and upon every of thele Points © © ©, | 
and the Ruler, Wil = the Equinoctial EA W, 
in che Points Be. e. diyiding Jt into 12 un · 


World; and the ſeveral Pc 'oints * 85 . e, upon 


ſeveral, 22 11 Sr. draw ſtraight Lines, 3 | 


true Hou 8 for ſuch a Vertical ot ie eme 


Center Q, an 


„ 


val Parts in the Point A, upon which | 


the Meridian S N, in the Point C, which is the " 
Center of che EquinoRial Cirele EE W, upon 
which Point, and the Diſtance C, you * 
deſeribe it. a 

F OVRTHLY, Divide the Semicitele EN W, 


Parts, and will divide each of them 
7855 Wi that is, Je equal Parts, and 1 Aa 
is the ba thereof, prey 5 a. Dy Part, © 
* 
FIFTHLY,, Lay a {Ruler | to O. the Cetller of the 


equal Parts. 
SixTHLY,. F; Ruler laid 1 b. 


the pole of the 


the EquinoQial, will cut the Circle repreſent. 
ing the Plain in the Points | jj, c. dividing } 


Lasrty, Front the Point Q, and through the 


Q17,Q18, Qs tc. they ſhall A e de I 
Plain. Namely, for twelve of them, that 1, J 


Bur for the Hours before and after 6, [that 5 
tor 4 and in the Morning, and for 7 and. 8 on 
Night, they are to be drawu by extending te ene 
Hour⸗ line of. 4 and 8 in the Morning 65 the he 


them on the other {1d 1 
ee the 


'39 1 


the Plain, ſo ſhall they be the Hours of 7 and 
8 at Night : ——— A\ſo the Hour-lines of 4 and 


ter Q, will become the wur mer of 4 and 5. in 


dhe Morning. 

V. Fon the Stile of this Dial, take 51 deg. 32 min. 
„e che Latitude of your place, out of your Line of 
de 1 Chords, and ſet them from N to e, upon tho 
* Circle of the Plain, ſo ſhall a Line drawn from 


through e, be the Axis or Stile of the Dial, 
which may be a thin Plate of Braſs, cut exactly 
to the Quantity of the Angle „N. 51 deg? 


of . 12, or the Meridian $S Q N, with the angulay | 
WE point at Q, and thus is your Dial fini 

Ir into this, or any of the following Diel. 
you have a Deſire to inſert the half Hours and 
Quarters, divide the Spaces between every one 
of the Points O O into two equal Parts for the 
W Half, and into 4 equal Parts for the Quarters 
9 } of Hours, and proceed with putring on.of them 
on in all Reſpegs as you did with the FINN) 5 


ent- Y 

15 „eee eee | 
1 II. of Upright or Ereat Plains. Sh 
1 1 'T 
_ H 4 . 


t is, fo | ; Pg. 3 

_ HOSE Plains are ſaid to be Erect or Up»: | 
right, which ſtand perpendicular to the Hori- 
on of the Place, whole Vertex or upper Part 
endeth to the Zenith, and their lower Part to 
he Nadir, ws Auch are the Walls of Steeples, 
þ 2-4 Mo SES Churches, 


t is, 
8 u 
4 the 
k the 
le of I 
the 


Geometrical Dialling 


5 in the Evening, being drawn through the Cen- 4 


32 min. and ſet perpendicularly upon the Line Aj 


BR 


| 3 - "oo pie. And, 


1% Ceometrical Dialling, 
* Churches, Houſes, or the like, againſt which (for 


the moſt part) Dials are made. 
OF theſe Upright or Erect Plains there are two ö 


Sorts, viz. Direct and Declinin 57 
Tnosx Ere& or Upright Plains are ſaid to be 
direct, which do directly behold either the true c 


Eaſt, Weſt, North or South Points of the Ho- 
rizon, or whoſe Poles do lie ditect in either of 


them, and theſe Plains are called Erect Direct 


Plains. ; 
TnoskE Erect or Upright Plains are ſaid to de- 
cline, which do not lie in, or directly behold any 


of theſe Points, but are ſituate under ſome other 


Azimuth, as South-Eaft, North-Weſt, North-Eaſt, © 


Sc. and theſe Plains are called Erect . 


Declining Plains. Of both which ſorts I ſhall give 


Eee eee 
I 3 1.07 Upright Or Ere&# Direct Plains 3 


CHAP. V. 


by > to EY the Hour- lines upon a Di = 
. South Plain. Bag 


Kwang, 07 4 Diredt South plain, in ab 15 j | 


titude of London, 51 deg. 32 min, 


= F. IRS T, Draw a Circle Z EW N, repreſent- 


ing an upright direct South Plain, croſs it at 
right Angles with the Diameter Z Q N for the 
Meridian, or Hour. line of 12, and W QE for 
the prime Vertical Circle, or Hoar-line of Six. 
, SECONDLY, Out of your Line of Chords take | 


| 4 5 30 deg.. 28 min. (which is zhe Complement of 


4 - 5 AY 


9 Dialing. „ 


the Latitude of the Place) and ſet that Diſtance 
upon the Dial. plain from Z to a, and from E to 
b, and from N to e. 
* Tuinply, Lay a Ruler from W to a, it will 
cut the Meridian Z N, in the Point P, the Pole 
of the World; and a Ruler alſo laid from W to 6, 
will cut the Meridian in A, fo is the Point 
through which the Equinoctial muſt paſs; and 
for the drawing ot it you have three points given, 
viz. E, E, and W, and the Center will always 
be in the Meridian Line Z N, (extended, if need 7 
be.) The Center you may find by the Geometri- 
cal Way taught at the Beginning of the Book. 
Or thus, draw the Line E and divide it into 
two equal Parts in A, upon A | 
erect the Perpendicular , Ab Ere& Dire# 4 
extending it, till that and the South TeX Pi. = 
Meridian Line concur in G, 2. 1 3. 617; 40-347 
ſo is G the Center of the * : li, _ 
quinodtial Circle E AW. +l 
_ FovurTHrLy, Divide the cemiciegle E N w SY 1 
to 12 equal Parts, at the Points © © ©, S. 
FiFTHLY, Lay a Ruler to Q, and each of theſe Þ 
Points © © ©, and the Ruler will croſs the _ 
Esinoctial Circle in the Points , Gs. di- 
viding that into 12 unequal Parts. EE 
| S1xTHLY, Lay a Ruler to P, (the Pole of the = 
| World) and every of the Marks * oc. d 
the Ruler will croſs the Circle of the Plain in 
the Points 11 1, Sc. 
| LasrtLy, If through the Center Q, and the re- 


; 
. © 
60 
— 


ſpeQive Points | | 1, Sc. you draw right Lines, 
they ſhall be the true Hour-lines of an Ered Di- 
redt South Plans. ©, 
For the Stile, take 38 deg. _ 28 min. the 
Complement of the Latitude of your Place, out 
of the 1 of Chords, and ſet them from N to e, 
C 3 | drawing 


7 


_— 
4 * * * — ” 
CE? —— — 3 — — 2 


— Dia ne 


. the Line Re for ite Alis of the Stile, 
= which muſt hang directty over the Meridian, or 
* Hour-line of 12, and muſt point downwards to- 
= wards the South Pole, becauſe the Plain beholds 
tte South Part of the Meridien. 

 ,. In making this Dial you have made two Dials, 
| for the Ere& Dire North Dial is but the back · ſide 
E . of the South, it lying in the ſame prime Vertical 
K.. > Ciccle, only as this beholdeth the South Part of 
E the: Meridian, and hath the South Pole ele- 
E-  wvated above it, the other beholdeth the North 
Patt of the Meridian, and hath the North Pole e- 
levated above it, and as the Meridian Line Z Q 
N in the South Ba repreſenteth the 12 4 Clock 
Hloour-line at Noon, the back- ſide thereof (namely 
the North; ſide) repreſenteth the Hour-line of 12 
nat Midnight, and therefore is not expreſſed, nei- 
der che Hour lines of 9, 10, 1 at Night,” or 


ver being above the Horizon at thoſe Hours: 
35 Wherefore the North Dial is only capable of re- 
3 - ceiving theſe Hours, namely, 4, 5, 6, 7 and8 
in the Morning, and of 4, J, 6, 7 and 8 at 
Migdbe, and (in this Latitude) not or all them nei. 
1 ther-3 for it win never ſhine "upon this Plain at 
3 Sin the Morning, ot at 4 in 
1 V Eredt Dired the ARernaoon, but it is beſt 
Vor Plain. Plate — put them on (as in the 
= 'a. A Figure) that thereby you may 
* know how much it is paſt 7 
= 4n the Morning, and how! pot ie wants of 5 in 


| ow! n 


* 
SI 


* 

W 

* 

F. 

$6 

* * 
* 

1 

% 


E of 1, 2, 3 in the Morning, the Sun to us ne- 


; 8 k 4 4 * 
4 84 * * N 7 by 
- 4 * F A #- -- ” 7 / 4 
* Fo a . 4 J * « £*.% * ” 7. * * n 
. 7 4 g — fs 8 4 * 2 5 9 9 
- | & 5 5 L : n 3 - . * es, : oO : 
4 . 5 | a 4 0 . > "hs; 
& * 5 4 4 TS 
* * 90 


nnn, * 3 
e 9 Sa... 1... 2 
* 4 2185 - E. 
2 
* * 


. EM n .. P 
3 — wy 4 A « 
FL. a N y by 'S Y 
\ - 5 * 3 "LM 
k . s "4 
720 vetvica _ _ 
_—_ 
& = 
| cent "i 
N - 
"as 3 fs K bs 
2 y : N 
5 , 1 A 8 5 
n 8 75 4 : = 
- 276 OW ®) 1B 3 7 14 1 
9 


* 


= Ks 


15 10 drow the ine, igel ppin en Eredt, ba q 


* 7 - x 
p bf of Fall. or We t Plaig.. © 


1 Can that an Et of Weſt Plain, witch 155 1 
the Meridian of the Place, and whoſe Poles 


lie in the Prime Vertical Circle, . or eme of 42 


Eaſt or Welt. 
Now for as much as the Prat nem m 25 vers 
| Meridian Circle, in Which 0 the t ales of 


| the World ate ſeated, the Plain muſt gecelfieits 
pals through oth theſe Poles, and FIT of 
them can have any Elevation above it; "wherefois = 
the  Hour-lines in theſe. Diabs muſt. be e a = 
to one another, and Foolbgueatiy'. 1 
Axis of che Torld:” And WO 
my 


no Center N a the Diu m 
| followeth. TY ; at 8 


Example.” 975 Faſt Dieck Did uh 107 Tor 
INF 8 2. 32 min... Co 
Las? A B 10 de a Dial- de 

yo would. draw '2 dire& Ea 
| Point D, if it be an Exit Di 17 


* 25 


Point C, if it be 4 Wed Di, eee, 9 


= 
- = 
> 


1 

mf 

A 
- 


— 


1 
— 


with the Radius (or 60 deg. 50 g oi ee 5 7 | 1 


of your Line 40 Chords, de- red Exft Di 


| ſeride an obſcure Arch of a Cir- Plate 3. Fig: 155 1 


cle E F, then from your Chord 


take 38 deg. 28.min.. the Complement of the La | A 
ritade of the Place, (which is alfo the Heigh 92 Y 


Elevation of the Equinoctial) aud ſet Ab fro 


E to F, and draw the Line D F quite” throught | 4 
the Plain. Then, we Rds you may FRY 2 oO 


K 5 4 * of 2 * uy ©» At 
Q £4248 9 2 * 
3 4 Pp 8 55 x 3 . * 
4 * * 
8 8 * 9 
1 
4 


SSS 
a4 Geometrical Dialling. 


Stile to your. Plain, ſo that you may bring on all 
the Hours from Suncrifing to 11 a Clock, aſſume 


through the Points G and H, draw the Lines 


pendicular Stile proportioned to this Plain. 
Now for. the drawing of the Hour-lines, ſet 
one Foot of the Compaſſes, (opened to 60 deg. 
of the Chord) in L, and with the other deſcribe 
the Arch of a Circle MN, betwixt the Hour- 
© line of 6, andthe Line & L, which divide into; 
= equal. Parts in the Points © © © © ©, and a 
E Ruler laid from the Point L'to each of theſe 
Points, © © ©, c. will cut the Equinoctial 
Line HD, in the Points * * * *,*, through which 
Points draw Lines parallel to 6 H 6, as the Lines 
L 7*7,8 *8, &c. and they ſhall be the true Hour- 
Goes of an Eaſt Plain, from 6 in the Morning till 
11.before Noon, but for the Hours of 4 and 5 in 
the Morning, you may put them on by ſetting the 
' ſame Diſtances upon the Equinoctial Line before 
c, as there is from 6 to 7 and 8, after 6; and 
through thoſe Points draw the Hour-line of 4 and 
J, parallel to the Hour of 6, as you ſee done in 
EE. cot is; 
E __Tavs is your Dial finiſhed, and in the making 
© of it-you have made two Dzals, namely, a Weſt Dial 
” as well as an Eaſt, for it is the ſame in all Re- 


* 


i 1 


4 
3 N 
7 . 
— 


two Points in the Line F D, one towards the 
End D (at the Point G) for the Hour- line of 11, lh * 
and another at H, for the Hour-line of 6, and 


11 G 11, and; Hes, perpendicular to the Equi- } 
npctial Line D F. This done, upon the Point 

, With 60 deg. of the Line of Chords, deſcribe ? 
an obſcure Arch of a Circle I K, and ſet thereon * 
15 deg. of your Line of Chords from I to R, and 
draw the Line G K, to cut the Line 6 H 6 in the 
Poiat L, ſo, ſhall I. H be the Height of the per- 


4 * 9 3 * - 2 E : : A 
Geometrical Dialling. . 45 "m8 
> 5 


ſpects. Only whereas the Arch A E through 
| which the Equinoctial paſſeth in the Eaſt Dial, 
was drawn on the Right-hand of the Plain, in the 
Weſt it muſt be drawn on the 

Left-hand, and the Hour-lines Az Erect, Direct | 
of 4, 5 6, 7, 8, 9, 10, and Weſt Dial. Plate 
11, in the Forenoon on the 55 Fr ig. 2. 

Eaſt Dial, muſt be 8, 7,6, 5, 

4, 35/, "and 1 in the Afternoon upon the Weſt 
Dial. 

Tue Stile of the Eaſt or Wet Dials may be ei- 
ther a ſtrait Pin of the juſt Length of the Line 
HO, which is equal to H L in the Eaſt Dial, 


and exactly perpendicular to the Plain, ſhew ing 
the Hours of the Oe of the Apex, or very | 
Top thereof. | 
OR, it may be 115 of Braſs of the fame. 
Breadth with the Diſtance between the Hour-lines. 


: of 6 and 3, which mult be ſet perpendi- 
ſe alar upon the Hour-line of 6, and ſo it will ſhew 
at he Hour by the Shadow of the upper Edge there-- 
h of, as in this Welt Dial. | 


Tazse five Dials here deſcribed, viz. the Ver- 
Fical, the South, North, Eaſt, and Weſt Erect, Di- 


ehe, which Body is called a Cube, 


„„ Hl 07 


fixed in the Point H, upon the Hour-line of 6, . 


ct, may de made upon a Stone cut ſquare in form 


 Geometyi ical Dialling. 


FF 


; How 7 to draw the Hour-lines upon 4 Seath or Nerd 


Ere& Plain, Declining either Eaſt or Welt. 


THE upright or ere Plains, that we bar 


| hitherto treated of, are ſuch as did diredh 
dehold the four Cardinal or principal Points «| 
the Horizon, namely, the Eaſt, Weſt, North nd 
South Points. All other upright Plains are ſaid to 
decline, and their Declination is counted fron 


the North or South, towards Eaſt or Weſt, aut! 


_ theſe Plains are cal led South or North Ere& Plainſ 
_ "declining Eaft or Weſt. 


- BgFORE the Hour-lines can be drawn upon a7 i 
of theſe Plains, two 1 muſt be given, and 


: er Ge Things muſt be found. 
| The Things given muſt is 


1. The Latitude of the Place. 
2. The Declination of the Plain. | 


7 he Things required are, 


The Height of the Pole (or Stile) above tel YZ 


Plain. 
2. The Diſtance of the Subſtile from the Mc} 
- ridian, or 12 a Clock Hour-line. 
3. The Plain's Difference of Longitude. 


Fon the finding of theſe, we muſt proje& upon 
the Plain ſuch Circles of the 3 (in their ol 


11. Of Upright Declining Plaine. | | 


don 


Oli- 8 
: 
i 


awith the two 


| Poſitions) 22 are ue for the finding of them, 


and thoſe Circles are, the *Horrzon, the ee 
and the Egquinoctial: Which Felt ſhew how to: 


perform by giving an ö 
E. le of a South Ereck Plain, ' decknin Weſt 
20 24 deg. 20 min. in the- Za e 
51 deg. 32 min. DO 
*. p 


Latitude of the Place 51 3 F 
| Give deinen Sort lle 4 W - | 


| d. ms 7 
. - Diſtance of 155 Subſite from | 19 
_ Y the Meridian, | + 18. 8 
| Required | Height of the Pole (or dle) „ 
A bove the Plain, 34 33 73 
N Plain? 8 Difference of Longit. zo” o 
To find Weds. 1 5 


Es, Deſcribe the Circle 2 H NO; rep 4 
ting the declining Plain, croſs it at right Angles,. 
Binney ZQN, and H Ma | 

the Point Z. reprefenting the enith, and N the 
Nadir, and the Line Z N, the vertical or per - 
pendicular Line of the Plain: (and the Hour-line: 
of 12) and the Line H 20 is the enen A 
Line thereof. ; 
| Secondly, Becauſe the Plain Seelibes 24 dex. 20 
min. from the. South Weſtwars, ſet 24 deg. 20 i 
min. from N to a, and from O toc. Then boy . 
a Ruler from Z to a, and it will cut the Horizon - 
tal Line HQ O in 8, ſo is S the South Point 
of the Horizon, through which the Meridian malt. 
be drawn, and for the drawing of it you have: 
three e viz. Z 8 and N, and the Center 
„„ Will 3 


a, 2 em © 
_—_— 1 

* 2 
1 —4 

4 48 
< 

> 
[ 


Y | 


An” Uprighe. Pla will. 4 be io, the | 


' Declining from the Soxth Horizontal Line 


Weſtward 24 d. 20 m. O, extended if Ive; be. 
Plate 3. Fig. 3. Which Center may be 
| found Geomerrically, as is 
Formerly taught. Then lay a Ruler from e A 
and it will cut the Horizon in W, the Weſt Point 1 


thereof. 


Thirdly, Having drawn the Meridian and the 
Horizon, take 51 deg. 32 min. out of your Line 
of Chords, and ſet them upon your Plain, from 1 
H to b, and from N to 4. J 
2 Faribhy, Lay a Ruler upon W, the Weſt Point 
of the Horizon, (Which is alſo the Pole of the 


Meridian) to 4, and it will cut the Meridian in 
the Point P, ſo- mall P be the Pole of the World, 
through which Point P, and Q (the Pole of the 
Plain) draw the ſtrait Line B P QD, repreſenting 


the Axis of the World, and the Subſtilar Line of 1 


the Dial. 


 Fifthly, Lay a Ruler Hom W to d, and it will 
croſs 2 Meridian in the Point E, ſo is A one 
,Foint 3 in the Meridian, through which the Equi- * 
noctial mult paſs : And the Point W in the Horiz. 3 


"non is another. So have you two Points within 
the Circle, by. which to draw the Equinoctial, 
Which you may do Geomerrically, as is before 
taught. Or you may find it thus, the Center of 
the Equinoctial will always be in the Axis of the 
World, and therefore in the Line BP QD. Now 
to find the Point, draw the Line E W, which 
divide into two equal Parts in the Point , upon, x 
ere& a Perpendicular, till it cut the Axis of the 
World, extended in m. So. is w the Center cf 


the Equinoctial, upon Which Point you may de- 


ſeribe it. And thus have you drawn upon. your 
Dome all the tbree Circles required, vi. the 


Horizon, 


- 


1 „ e e am. 


N "7 Te * © ts. ca E. 
: * 1 9 py a 224 A "FED n 9 
0 0 8 * 4 ret a LE bet ak R * 
* * r * * * 2 oe N b he” 
I SBI. y d AAS. 85 927 « * * * 4 
* * * 
0 4 | 8 4 
\ 
N 4 * a 88 ; 
1 : 8 
* 8 * 
0 * : f 
5 2 4 . % 1 
* N 5 . 


de rrizen, Meridian, and the Egsinoctia'; by:which 3 

21 33 the three Requiſites belonging to 

is 1. To ßud the Height of the Pole above the Plas, 

nt | _— to G, Where the Equizedzal cuts the 
Plain, and to P the Pole of the World, the 

1e Ruler will cut the Plain on the oppoſite Side 

1e in the Point v. So the Diſtance from B to v, 


meaſured upon the Line of Chords, will be 
found to contain 34 deg. 33 min. the Height 


nt of the Pole above the Plain 
Ie 2. To find the Diſtance of the Suſtile from the : 


Meridian, repreſented in the Scheme & the Ar _ q 


d, ches Z B, or N D. Take in your Compaſſes 

ie the Diſtance Z B, or N D, and you ſhall find 

ps | either of them equal to 18 deg. 8 min. and 

f | - ſuch is the Diſtance of the Subſtile from the 
NM Slat ts . OR 

I | 3. To find the Plain's Difference of Longitude, 

e | repreſented in the Scheme by the Angle PK. 

i- Lay a Ruler from Þ to E, it will cut the 

i-. 3 Plain in x, ſo the Diſtance between D and 

n x, meaſured upon the Line of Chords, will 

I, be 30 deg. And ſuch is the Plain's Diffe- 

re . rence of L] / ²˙·ꝗm ah 

of Laſily, Theſe Requiſites being obtain'd, we 

e come to the drawing of the Hours; to effet 

W Which, lay a Ruler to P, the Pole of the World, 

h and ZE, the Interſection of the Equinodial with 


the Meridian, and it will cut the Plain in the 3 
| Point x. =— At this Point x begin to divide tble 


f Semicirele Lx G, into 12 equal Parts, at the | 
- Points SO ©, Se. Then laying a Ruler to O, 
Ir and every of theſe Points © © ©," c. it will ; 
e 


cut the EquinoQial Circle, dividing that into Þ 
Pe | bot " 12 7 


% „ 1 


* 
* 


» 


12 e Parts in the Points , We. 3 
A A Ruler laid to P, and every of theſe un- 
equal arts * ** *, e. will MIT the Plain into 
13 unequal Parts i in the Points Se. — 

8 and every o Points 1 1 1, 
Dc. drawing Lines by the Side in and they 


Mall be the true Hour-lines proper tp ſock a dech- | 


oy: yak you finiſhed: the Hourlin, the 
2 — * Line upon which the Stile 
muſt ſtand) is the Line QD, falling (in this 
Dia) juſt upon the Hour- line of 2 in the Aﬀer- 
E noon, becauſe' the Plain declined ' Weſtward. 
TDbe Angle of the Srile is DR, containing 34 
= Aeg. 33 min. and muſt be either of Plate or Wire 
| to ſuch an Angle, and muſt ſtand perpen- 
| 8 4 the 5 and over the Saat 
Now: have you fniſhed your Diat, and in ſo 
Eng ven have | in this one made ts Dual » vic. 


18 Sourh declining Welt | 5 R 


> a . of the e of the Hours and 
the Stile reſpectively upon each Plain. For in the 
South-weſt Plazw, which we have now deſcribed, 
the $//e ſtands upon the Hour-line of 2 in the 
Afternoon ; in the South-Eaſt declining as much, 
it will ſtand upon the Hour ine 10 before 
— Aubay And ſo all the Morning Hours of. the 


© Weſt Decliner, will be the Afternoon Hours 6 


2 the Eaſt Decliner; and the Afternoon Hours of 
| the Weſt Decliner, will be the Morning Hours of 


| he Eaſt Decliner | And de the South Decliner 
; . Wi 


* 


. 


Wee dan, 


Will woke the North-weft . 42599 
Decliner; and the 'South-weſt Bee ris 
Decliner, the North-eaſt De- D Dial. 
cliner, by only extending the Plate 3: Fry. 4. 

Hon lines, Stile, and Subſtils 

quite through the Center. And that there may 
yet remain no Doubt, I have drawn all the four 
Dials in one, by which you may plainly ſee that 

there is no Difference between them, but what 
hath been already intimated. © Only before I leave 

them, I will, (becauſe theſe Dials are moſt in uſe) 
give you one other Example of an upright declin- 
ing Flaim, which by Reaſon of its great Peclina- 

tion from the Prime Vertical, or its Poles 2 

Deviation from the Meridian, cauſeth the 4 

have but ſmall Elevation, wherefore the Dial my 4 
all ſuch like) muſt be drawn W a S **Y 
the DireQions IE, 


CHAP. va. 


Huw to Si the Bel pon Upri 1 far De] 
clining Platns, which by Reaſon of the ſmall E- I 
levation, which the Pole hath over ſuch Plains, 
- Hours (if they be drawn frowa Center) cannot | 

be of any competent Diftance one from another.” : 


HOSE Plains which lie near to the Meri. | 4 
dian Cirrle, and whoſe Poles (conſequent! _ 
neat the Prime Pertical Circle, or Azimuth of Eaſt 7 
or Weſt; the Pale hath. but ſmall Elevation a- f 
dove ſuch Plains, ſo that the Honr- lines (æſpeei- 
ally thoſe of them which fall near to the Szbſtile): 
from the Cen ter, cannot be drawn at any com- f 
petent 


# 


* A 
0 Wy 
R NID 


a ; * E 8 * * R * I * I 4 
* | — " G 2 * * 288 * P NE N FO 2 * * N 
+= * : N N 0 0 47 
[ 2 — 0 o 

k N 1 ; I. a : 
F- 2 . c. 191 . 

I þ 4 S$ 7% 4s 6 3s R 3 G 8 

1 8 * 

* 

= 


petent Diſtance, without à large  Extention of 


them. To 'remedy which Inconvenience, you 


F may draw the Hour-lines for ſuch a Plain at 
a convenient Diſtance, and in a little Room, 


and the three Requiſites mentioned in. the laſt 
| Chapter, vis. 5 


x. 7he Hoighe of che Pole above the Plan. 
23. The Diſtance of the Smbſtile from the Meri- 


3. The Plat Difference of Longitude. 


ward 80 deg. in the Latitude of London 5. deg. 


F „ 22.00 . | 
To find theſe Requiſites. 


Fit, Draw the Circle Z HNO, 
= Plate 3. crofling it with the Diameters Z N, 
—_ rizontal Line of the Plain. 
= . Secondly, Becauſe the Plain declineth 80 deg. 
= * ſet 80 deg. from N to a, and from Fi 
Vir, Lay a Ruler to Z and a, it will cut 
the Horizon in 8, the South Point thereof, and a 
= Ruler laid to Z and 6, will cut the Horizon in E, 
the Eaſt Point thereof. Cs . 
Far, Having the three Points Z S and N, 
chrough them draw the Meridian Z S N, whoſe 
Center (by any of the Ways before taught) will be 
found to be at 2. e en 0d | 


* 1 
I : 
2" % 


. Fiftbly, 


— >a 6 

>. ot ene 
1 9 . ä 

< 5 2 « F 

* # * 0 1 

5 #: * 

* ” 5 

g * 5 

> , * 


without any Regard had to the Center. But be- | 
fore you proceed to draw the Dial, you muſt firſt 


| Example of aw Upright South Plain, declining Eafl- 


Oo = nod LA ACRDMNHMHHOQ We 1. old A rn A. 


Fig. 5. the Perpendicular, and H O, the Ho- 


_ 


+ NE IE. e 
f 8 x 
- 1 — ＋ 
9 Dialing... 53 3 
7. 7* 
. 


. Fifshly, Out of your Line of Chords. take 51 
deg. 32 min. the Latitude, and ſet them from O 
to c, and from N to d. Then laying a * 
from E to c, it will cut the Meridian in P 
Pole of the World; through which Point b an 
Q, the Center of the Plain, draw the right Lins: 
OB, for the Axis of 1 World. Alto the 

Ruler laid from E to d, will cut the Meridian in 
E, ſo is X one Point in the Meridian, through 
which the EquinoQial muſt. paſs, and R is anther 
Point in the Meridian (extended) . the Cit⸗ 
cle, and a third Point is E, the Eaſt Point of 5 
Horizon. Now foraſmuch as theſe three Points 
RE ,. through which the Equal uinoctial is to be 
drawn, are almoſt in a ſtrait Line, ſo that the 
Center of it will be at a very gre reat Diſtance, -we 
will forbear deſcribing of that Circle, and content 
ourſelves. that- We, 70 found the Points RE AE, 
through which, it ſpould paß; becanſe we. alf 
draw t Ep Hour-lines in this, 1 the like Caſes. by 
other , and ey, I, 160 proceed to. Mk 1 
the other Requilites. And r 10 


* To find the Heig 2 the. Palo MAY Wy Piu 
 . repreſented by P C. Take 50 deg.” of y“¹ỹk 
Line of Chords, and ſet them from c to e, a 
TINT laid to e ang Py Will cut the Plain i in 
2 ſo is 0 C the Height of. the Pole (or ile) 
| 2 the Plain, vix. 6deg. 12 min. 1 
2. To find the Diſtance of the Subſtile from the I 
WB EN e Z by B. N or 2 c,—Take - 24 3 1 
the 5 11 MM 
(Which i is equal thereto). in in = A Erect — W 
ur Compaſiey, and wen. Plain 11 
Lure it upon your Line of . 2 $0 deg. 
. ſo you ſhall find P 725. I. Wl. "6 


* 


77 2 


fare. 4. 


ae ba 


it to contain 38 deg. 4 min. Which is the 
Diſtance of the Sz4/tile from the Meridian. 

3. To find the Plain's Di TE of Longitude, re- 
bo 5 by the An 'E, 3 P. — Lay 2 

uler upon P and it will cut the Plain 
in g, the Diſtance g B , meaſured. 1 the 
Line of Chords, will contain 82 deg. 8 min. 
the Plais 7 / Difference of de | 


1 iii 5 


: : M DG 1 Sow 20 We Fo he Plain. Oy 
Fer, Draw a right Line A B, for the EY 
E 1 2 7 Line of 3 Plain, and upon A as a Cen- 
der, with" 60 A ot the Radius of your Chord, 
* an obſcute Arch * A 88 DE and 
1 thereon from C'to D, ſet 38 dey. 4 win. the Sub- 
. Diftance from | the Meridian belies b. found, 
du draw the Line A D for the Subftile, quite thro* 
| the Plain. 


a = L 


R 


de Poi above the Plajn from your bot, and 
tet them upon che fame Arch from D to E, and 
= draw the Line A E for the ile. 
Drah, Foraſmuch as the Sie A E in this 'Caſe 
js. but final Elevation, viz; but 6 deg. 12 min. 
: Draw the Line G H parallel to A E, at ſuch con- 
1 as you ſhall think 2 for your 
# r. augmented). Seile to ſtand from Your. Sab- 
1 e 


5 Aſſume any two Toints in the Sabſtile 
AD, as R aud 8, and througb 'theſe two Points 


draw two infinite eright Lines, oth of them at fight 
| 255 2 


3E (c DD ae 5 


ee aa ow» 8 VJ Fu &A 


Geometrical Dialling. "wu 
| Angles to the Sub Filer Line AD, as the Lines Z £ 


and XX. 


Fifthly, From the Point R, take with your Cant 
paſſes the leaſt Diſtance to the new augmented &ile 
G H, and ſet that Diſtance upon the Sabſtilur 
Line, from R to K: Alſo from the Point 8, take 
the leaſt Diſtance to the new Stile G H, and ſet 
3 Diſtance alſo upon the Swb/tilar Line from 5 
to 
. Sixthly, Upon the two Points K and L (as upon 
two Centers) with 60 deg. or the Radius of the 
Line of Chords, deſeribe the Portions of Circles, 
and in either of them ſer off 82 deg. 8 min. the 
Plains Difference of Longitude, as from & to M, 
and from R to M, both on the ſame Side of the 
Subſtilar Line, on "which the EE Line of 

the Plain & B was drawn. 


, N r a Ruler ks Point 1 ik every. - 
of the Diviſions © © ©, Sc. and the Ruler Wil! 
cut the Contingent or Eęuinoctial Line X X, in 
the Points * * * e. Alſo a Ruler laid to K, "and 
each of the Points © © ©,. Sc. will cut the o- 0 
ther 3 Z Z, in the Points * G.. 
_ Laſtly, Lines drawn from the Point * in one 
Contingent Line, to the Point * in the other con- I 
tingent Line, each to his Correſpondent 8 4 
the Szbſtilar Line will direct you how to do) tho 
Lines ſhall be the true Hour-lines belonging to ſuch 
a Declining Plain, and be drawn as in the Figure 
you ſee done, at a competent Diſtance ' one "from - 
another, without any Relation at all bad to the | 
Center of the 1 5 


* 


<A 
2 
: 
x « 1 
« o : — 5 2 
* 2 * W 
5 * W _ 
, 7 x 
H 8 
* 
* 2 
bee 3 
9 
x 


— ————— 
7 * 


A eo > \ a * 
g — * * IL 
As * 
bl * 8 
1 N 
3 : 
, of — 
Y 
— — 
* N as 


— 
13 


ova 1 Didlias: 


Tuvs h have vou finiſhed your Dial, and in the 
kk of this, you have made a South declin- 
ing Welt 8o deg. alſo ; for if you turn the Paper, 
and look. through it, it will on the Backſide be a 
South declining Weſt 80 deg. only the Forenoon 
Hours in this, muſt be the Afternoon Hours in 
that: Nay, rather, you have in this one Dial made 
four, vis. a North declining either Eaſt or Welt, 
if you well obſerve what was ſaid and done in the 


4 Chapter. 
Aup thus have I done with all. Uprigh or Exec 


* 


5 Plaim, either Direct or Declining. I ſhall 


no proceed to ſhew you how to inſcribe 
© Hour-lines upon ſuch Plains as are not upright 
but reclize from the Zenith, and of them 
there are ſuch as are Ne, and ſach as do 
ane. 3 7 | 


'D | Pia 


DB papa pen 


n. 0 Reclining Plains. 3 
CH A P. IX. 


' 
o % 


A in e Plains ew were.two Varieties, 
wiz. Eredt Direct, and Ereft Declining ; ſo are 


there of Reclining Plains alſo, For ſuch Reclining 


Plains as do ditectiy behold either the true Eaſi, | 


Weſt, North, or South Points of the Heavens, that 
1s,:. whoſe Poles lie either in the Meridian, or 
Fu. Vertical Circle of the Pl ace, ate called Di- 
rect 0 1 

As Aix, Thoſe Reclining Plains which do not 
Healy lie in, or their Poles be not in the prime 
ee or Meridian Circles of the . but 
eviate 


—_ r e 


n * enn 4 A 
nm nm 
| ö To * 


deviate therefrom, are called Declining Reclining = 
Plaims. Of both which Sorts I ſhall give vou an 
Account, and the manner of inſcribing Hour-lines 
upon them, for in theſe Plains there is far more 
Variety, than there was in , or 1 
Plains. 


3 4 3 TS 3 


of Dired Reclining Plains, Tc. 
Zn 1 of Eaſt and Weſt 2 1 wa 


Lay 
e 


1 H AP X. Wy zwi Ae: 
N "i 


19 31 LES 2 


How fo EO 180 Elin line; upon. a Hireck 5055 „ 
Mieſt Reclining or Tnclining. AIM: 


As. in upright declining Diale, trro Tp 
muſt be given, and three Things muſt 

found, before the Hout lines can be e 10 
in theſe: direct reclining Plains, two Things muſt 


aſo de given, and three muff be found, before” 
the 1 can be made. £ 


- ® + * 


| f 1 2 
| — wit b} ahhei are a 
are . The Latitsde of he Pee. 
ing 2. The Reclination of the Plain. 
ne | „Tus Reclination of a Plain, (as hath bed 1 
that fore declared) is the Arch of an Atimuth'or Ver- 
FM tical Citcle, intercepted | between the Zenith of 


Di- the ae ow we N Plain. 4 Pa A 


* 
8 oi x , G * L * by 5 A 
N 8 N ; 1 8 4 i 4 tes #5 N 
FX * { 2 5 - 7 3 8; L 4 5 
13 1 3 „ # OS #0 7h #44] Eo} CARTS Ca e5 
no N : TOY EONS * * 
* 
* 
« l — 5 
5 — ** 


1 


7 — 


1 xs 9 
n p q 
* - - 
* — 
i = 
* 
N 
by 


8 eee Dialling. 


Example Of an Eaft or Weſt Plain, Rechnigg 35 
, - in the Latitade ef LABGND,. 5r . 32 min. 


d. m. 
Latitude of the Place "qt 038 
eee of the Plain 35 oo 


"The Height of the Pole above the | 


Plain. 


nent The Diſtance of the Subſtile from the 


Meridian. 
The Plain? $ Difference of Longitude. 


Firſt, Draw the Circle NES R, repreſenting 


the Reclining Plain, and crofs it with the two Di- 


ameters N Q.S, the Horizontal-line of the Plain, 
and tlie Hour-line of 12 a Clock, and EQR for 
the prime Vertical Circle. 
- ;Secondly,, Becauſe the Plain reclines 33 dep. take 
$5 deg.. out of your Line of Chords, and fet 
eee eee 


© Thirdly, Lay a Ruler from 8 to a, and ie will | 
cut the prime Vertical Circle in Z, ſo is Z the 
Zenith of the Place Alſo a Ruler laid from 1 
S to b, will cut the ſame Vertical Circle in W, 
by which Point the Horizon of the Place muſt be 3 


drawn. 
Foarthly, The Points Z and W being found, 


vou have three Points through | 

| Eoft andWe 2 which you muſt deſcribe the 
8 Plate Meridian, viz. N Z and 8; and 
4. Fig. 2. , as many alſo through which you 


muſt draw the Horizon, namely, 
N Wand 8. The Centers of both which Circles 
will fall in the Line E Q R, a if need be) 
and 


f = 
n 4 64 oo od . 


my. ty, n, „ „ rere 


0 


35 


ou 


:les 


ind 


5 the alder hw to | fnd wem, hat been of- 


ten enough already ta 


3 Becauſe e of the Plact᷑ is 51 
3a min. Take 51 deg. 32 min. from your 


1280 of Chords, and ſet them upon your Plain from 


S to c. Then lay a Ruler upon W, the Welt- 
point of the Hor:z0x, and the Point c, the Ruler 


will croſs the Meridian Circle in P the Pole of 


the World; through which Point P and Q, the 
Center (or Pole of the Plain) draw the right 

Line P Q, which ſhall be the Subſtilar Line of 
your Dial. 

Sixthly, Take 90 deg. of your Line of Chords, 
and ſer them. upon the Circle of your Plain from 2» 
c to d, then lay a'Ruler from W ca 4% and it wil = 
eur the Meridian Circle in E, 1b is ® one Poiit | 
in the Meridian, through! which the Equinoctial 
Circle muſt be drawn, and W the Wet Point of 
the Horizon is another ; fo have you tw o Points 
within the Circle, through which. you. mult de- 
ſcribe the 7 C rrcle, bote 31 19522 
be in the Line P | 
cended if 
hath'alteady been raught ſeveral 728 1 

Havi thus projected the Metidian, Horhon. Fr 
and ne you OO find the three Requi- 5 
2 followeth A > nifaitc 2 31170 

1. 75 find the Hei mY of the Pole above the Pl; 
P , Lay a Ruler to g and P, it will cut the 
Plats on 125 Oppoſite fide in 5 0 #5 bes- 
| fared u on the Chords, will be' 26 deg. 41 
min. The He br of the Pole above the Plain. 
3. To fihd the Biſtauce of the Subſtile from the 
2 Meridian St, Take S'Fin.your Compalles, 
x Mars meaſure it upon "the Chord, Bi Dal | 


- + & 


3 2 * YN ; r 1 : 


i ”% £4 7 
N ein 112k "FELT 4 


Geometrical Dialling. | 


* +l 5 N 2 
588 . F 7 
_ 2 d ..£\ 
a Is 
_—— 
* 
5 * Ws 
01 2 1 
> wo 
3 


" found 45 deg. 52 min. The 7 ene, of the 
275 from the Meridian. ES | 
8 the Plain's Difference 4 Longitude, | 


A Ruler laid from P to \ will 
ow the plain in e, the Diſtance from O the 
. -Subſtile, . to e will contain 66: deg 27 min. 
ol the Chord, which i a * Plain pee 


© of Langitude. . 41217 20411 1 


* 27 ö 


Fs 
- . 


> Page Requiſites Wr you may pro- . 


ceed to find the Hour e Na the Plain 


Ruler to Pike Pole, d K 

eridian With the Equi- 
b 11 it A * e Plain in e. At e be- 
gin to a ide Be 1 into 50 _ Farts, 


8 « the Points, . 
Fan ins 855 Lay fer * and the. Senn 


5 XY = en 


A | CH 1 . 3 Yd! 
P. J 2 aud the & 11 a 


45 By Re Cut the 1919710 3 


5070 1 pk gegen 
0 K. fe e $6 hy f 
11425 i rough hs Points 3 1 1, PP ks 
the true Hour-lines belonging to 
Flain. n 
AND > thus have y ou finiſhed” your. es and al- 
191 in it 4 D: 4% ot the Dial ts as it here ſtands i in 


e Scheme, is N an Faſt and Welt Ixcliner, 


but being turned upſide down, as you. lee the 
Hours. numbred, and the Word exith ſtanding 


upwards, it is : an Eaſt l an if. th the our- 
on 


the right 
R, as in 


3 


lines be turned, (or ſuppoſed to 9 0 
d of the prime Vertical Line 


this Scheme they dq on the left —_ and the 


Hours 


EY, OO" 


ww id od ad et 3 ods IE 0. 


a 


2 F_rM 


Hours of 4, 3, 6, Er. in the Moming chan- 

a Weſt Recliner. And if the Hour - lines be drawn 4 

then decome Eaſt and Weſt Izclizers ;- the Hours 
the Denominations of the Hours. chauged, r. 


Inclinert (oppoſite to them) the South Pole. 


: 3. q * 
4 Fs * SH *.2 
ART BS WW & $ 


Geomdtvical-Diallng. 6s | 
through the Center of either of them, the Plains 
and Subſtile in all retaining the ſume Place, only 


you muſt remember, that in all Eaſt and Weſt 
Recliners, the North Pole is elevated, and in all 


CY 
i : » 4 


* 


* 


— 


# * i, 4, 4 * * 6 2 6 5 4 * Oo 4 

* * * ws 7 7 e - £ 
ff rt hoe 
124 of 5 ot » i a#. 44 4-# '% & £4 pg fn 53 
» 

as. . » . o 
0 8 5 
— * * * - : - 
— s £ ? &S . 2 * 7 £ 4 OI 1 4 of 
34 *＋ * + 7 I F Y a 2 ». 2 2 1 


: — 
4 
F £54 
hs 
I > IT #4 
& Sf % 7 
s * 
1. 
a * 


* 
> 


N the Eaſt and Weſt Reclining and Inclining 

Plains, before deſcribed, the Meridian, or 12 
a Clock Hour-line did lie-in the Horizontal-line 
of the Plain, and the Poles thereof in the prime 
Vertical Circle. S0 (on the contrary) in theſe 
South and North Reclining, and-Intlning Plains, 
their Horizontal Lin lieth in the prime Vertical 
Circle, or Hour of 6, and their Poles in the Me- I 
ridian, and from hence they receive their Deno- '- _ Þ 


mination. e 5 | 
OF theſe Direct Reclining Plains there are fix 
Varieties, viz. Three of South Recliners, and as 
many of North Recliners. For, | 
1. THE South Plain may recline, ſo as it may 
juſt fall in the Axis of the World, and ſo paſs 
through the Poles of the World, and then it is 
En ©" ib called 


* / W 8 8 : 28 
1 FL * f * 
” 
: 
; : * 
* 
>, c 


T2 * . 3 | on 7 
4 
* 


called an Equiaedtial Plain, becauſe” the: Poles 
thorebf lie in the Eęgaimctial Circle, and neither 


of the Poles have any 


- 


ee the Axis of the World, 


or Weſt Dial were. Only, whereas the Stile 


food upon the Hour-line of 6 in the Eaſt and 
Weſt, in theſe Plains it muſt ſtand upon the Hout - 
line of 12, and be of equal Height with the Di- 
ſtance between the Hours of 12 aud 9, or 12 and E 


3. which are equidiſtant from the Meridian. 


, 
as 


3 


above ſuch a Plan. Or, 


3. The South Plain may ſo recline, that it may | 


fall between the Horizon and the North 1 8 and 
| 5 is the North Pole 8 ; 


Wy hes 


4 1 


. agg 4 theſe three #7; ee South Kecl. 


r tne f ot «11 


2 2 "hab CSE + 3 80 
* 12 ? "D447" ; "I FI IR # 31 & < 7 25 11 
» * # * 2 1 1 
_ 5 o * * 
"+ 3 , 
* Li 7 
oy 
23 : 
* 2 
14 12 
S 4 , a 
"43 7 9 94 
1 wt 3 
FI 
. -A 
# $5. F 
"© * + 
9 . 122 
. 
2 4 
- 


7 Elevation above it; where- | 
fore the Hour-lines muſt be all parallel one to the | 


d the Dial muſt be drawn as; the Erect Diredt g 


2. On. Secondly, The South Plain may ſo re. 
| nnd, that ĩt may fall between the Zenith and the 
' North Pole, rs then is” *the South Pole elevated | 


| The Fir Va aricty.. 


A 1 N 


"CHAP. XU. 


How to draw het n FE. on an 8 
Plain, or a Plain reolining. juſt to the ole N 


ERST, Draw the right Line A B,. for the 
Horizontal Line of the Plain, and rc it a- 
bout the Middle thereof at right Angles, with _ | 


Eine 14 C 12 kot Te Meridian and | 
of 12:- 15 23 ie $4 Y 10 #1 18371; * 2115 4 bf 


441 8 


Secondly, Upon the Line 12 Q 12, either „ 
bove or elow Q: aſſume any Point, as 8, _ 
letting one Foot of your Compaſſes Worin, 
being opened: to the Radius of your Line 
Chofds) deſetibe'the Semdeirele C DE, which di- 
vide imo r equal Parts, beginning lat D.. 

Poe 8 a | Ruler to S, and che ſeveral 
0 169%; atid it Wall erb the E- 
en 'A B. in the Feind TOs. heh 

Laſt 25 'Thron theſe Points * „e. drr | 
155 rallel a A Aa Y 

12 8 85 Tang: is your” 41. Dise E- 
ral” 10. i e ue modal Dial. 
Tuk Stiſe may be Fs 


na late 3. Fig. 8 I 
ſtrait Piu, of: the 1 
Line 8. 2 ſet” Pos tet =, Plain upon 
the Point Q; the Sd cw of the Top thereof b 
only giving We Hover, Or it may be a Plate of 4 
the Breadth of td that is between We 
3 in nd 3 ot 14 and 9, and en 


-the' Shadow of the- upper E exhereof we |. 
| Fr Pn ＋ 8415 "Bt 0 


= 


The 


The Second 7 rity. 


EY < H A P. Xt. TIEN 1 84 tg 
on 4 Direct South 


How to 4 the HB up 

355 3 0, which re; eters * Z * 
4 = Pole. a 0 ba a 38 . \ 

"Le the Example be of a Soath, Pla, Ele 25 
PF. 5 in _ g 0 VOY. 51 "nr 32 


we? "Y 83 7 1 2 * I p of: # 6 3x * 7 . & "op N * 


Kg. — the Circle W D E R. croſs it 
with the two Diameters DR. for the Me- 
— and Hour - line of 18, and W E, for, the 
- Horizontal Line of the Plain, 806k N 


5 of gtx BP ©3538 2 (33 10101 [ 
| ; Eber b. 


dont of your Line; o Chords, : cl 
b _ "ſance from D to 4. —＋ gm vids. 
"Thirdly, A Ruler laid ftom W to 
2 the Zenith of the enen A 
from W to , will give 8 the Souff 
_the Hotiron: both wh h Cireles W. 
| prime Vertical and W R . 
| Plate 4. may be: drawn, as hath often enough 
Fig. 3. already dem nem their 1 5 


Nd 1122 WR > 
19 Fourthly, Becauſe the Pole of the 3 6 0 al- 
ways diſlant from the Zenith, the Compiemen 
of the Latitude of the Place, vis, here af 


. 


— 


8 
8 


* 


4 wy , 
EET 


* 


5 2 = 
N £4 
eo WOT: 


ar 00000 RE. BONE / 


„* 


r : 1 : ö . n 5 2 rem TR CONS * f f WY” 
g : 4 Ls F a e N 1 7 1 

- , * F 

9 4 . 4 — Fo A 5 PR * 

n 5 n 

l . 8 a © of 8 * ” * 
. & * EA * ; * * ” © 2 

a of 1 7 * 1 * 
* * E f 9 

* 

4 


dow, 38 MY 28 min. Take therefore 38 geg. 4 
28 min. out of 1 Line of Chords, and ſet 
them upon your Plain from a, (the Point Which 
found t 3 to C. 
Fifth, La uler' Rem W to C, and it Rs 
1 cut the Merid 0 DQR, being thus extended)” 
ia P, fo is P the North Pofe of the World, and 
Y becauſe it falleth without the Plain, it is evident 
the Scheme, that this reclining Plain paſſeth 
rough the ayes? between the Zenith and 
the Pole. And again, becauſe the North Pole 
P falleth without *.* e Plain, it alſo demonſtrates, 
that the South Pole muſt be elevated above this” 7 
Plain. Wherefore, 
- *Sixthly, To find the Point of the South Pole 
upon the Meridian Line DQR, do thus. Be- 
cauſe the two Poles are 180 deg. -diftant from 
each other, vix. two Quadrants; or twice go + 
deg. Take therefore go deg. out of your Dine 
of Chords, and ſet them twice upon your Plain 
from C, 'viz. fieſt from C to e, and then ftom e 
to 1, ſo ſhall the 180 deg. end in : And a Ru- 3 
let being laid from 'W to u, ffiall croſs the Me- 
ridian in A, the South Pole; fo is the South 
Pole A elevated above the Reclining Plain, the 
Quantity of AR, which is equal to the Arch R 
», Which meaſured upon the Line 'of _Chotds, 3 
will de found 13 deg. 28 min. = 
Seventhly, Lay 4 Ruler from W to 6 and it 
will cut the Meridian in E, ſo is E that point 
in the Meridian, through which the EquinoRtial 
muſt paſs. As alſo through the Points E and W, 
the Eaſt and Weſt Points of the Horizon. © 
Eighthly, For the Hour-lines, they are to be 
drawn in all Reſpects as the Hour-lines' were up- 
on the upright South Plain, without any Altera- 
9 * there the Stile was elevated accord. 
e | D 3 : ing - 


D th oy e 
s W —— 


_ _ a IC "oy" g N „ * GS, 
K ” 4 4 1 2 * n COST" 10 AD : — - 9 = XY 9 P g ” N 
ets ALES * a L * 9 
1 1 8 ” I 
x4 n 5 - 
oj * ey * * 
- 5 
3 * 
* * 4 f 
. 
I 
* 


| ing toxthe eee 1 the. 

| 28 min. here it muſt be. elevate Ns 18 42 
238 min. as in the Scheme. he. manner how 
| the Hour-lines are to be put on, 1 
peat; but, I ſhall, „ Push draw ing them, 5158 
that to your Own I 


ER and ſo 6 $$) al Parts on either Side 
| Ne ien b G 3 


E laid from P to every of thoſe. unequal Parts 
in the Equinoctial, will divide the Plain into 12 
other unequal Parts, through which laſt 12 une- 
qual Parts, and the Center Q, if you draw right 


Ines, they ſhall, be the true Heer ine ener 


„ mb 08 51 owl 2% T 


And here by che Wa ry nate, Pick that: the . - 
1 ö 


wodtial Circle in this Scheme is a very ob- 
lique Arch, the Center of it will be very 


LO 


| alſo, upon the Plain) will be very close 


-- together in theſe ſmall. Draughts, which is | 
*.. occaſioned by the ſmall. Elevation that the | 
South Pole bath above. this Plain, viz. but 


13 deg. 28 min. which you t find with- 
....out, drawing of the Scheme, by ſubtracting 
the Plain's W en eg repreſ-ated 


| 25 Nam, 
in the Scheme by the Line (or. Ciccle), DZ, 
from Z P, the Complement of the Lati- 


ST tude of the Place. And therefore, foreſce- 


ing that the Pole hath but mall Elevation a- 
dope the Plain, and alſo what .* whether 


he better 
Way 


North or South mo is e 


ſhall only re- 
| ce, in regard there is no 
To EE nd 
: Plain WR E into 12. equal Parts, e ee 
Then lay a Ruler to Q, and 


every of. thoſe 12 Dividanh it will divi e the 
Egquinoctial into 12 unequal Parts. A Ruler 


remote, and the Hour - ſpaces upon. it (as 


r edt i alt IM 
es > a s — 


"# CF V A 


63S: OE CEE. ⁵ĩ⅛—E . 7˙..,᷑̃Uu . bers 


e hr be 


\ 


# 
4 


” 4 - yy! 4 
7 8 ? LG rd 7 
"4 ws A 
7 A 


Way will be to Won Stile, and to 
draw the Dial e to En > 1 
Diete. = 


How ro draw the Hoar-lines . the Plain. - 17 


bf the Scheme: loioming, os. i Rig: Tbe 
right Line W QE, for the Horigemal, and per- 
pendiculun thereunto, the * S QR, fot the 
Metidian and Honr-line of 1a, - which extend; 4 
bove the Horizontal Line to 8. 

S:condly, Upon 8 as a Center, with 60 der 
of Res 2+ Chord, . a 1 Argh 8. a Cir- 

189 


*. N 1 Fe) 7 


8 n * 2 2 Nan N * * bo r F . * * 2 * 
Geometrica! Dialling- | 
| * *. 


_ min. yn memes of the South Reclining 
Pole above the Plain fr 88 © Plate 4: : 
to B, and draw the Line'S Bip b 
for the. Seite. | 

Thirdly, At anblconebitn! Diſtance anfvorss 


ble to 105 gels of Ia Err draw a Line 


7 aß the 3 
e Set 805 Poet of your dene in 1 9 


D, and wah the other take the Hantel Diſtance t . : 
the Stile SB, nag re hos upon the Meri- 1 
dian from D to H. 21 * I 
Fifthly, Upon the Point H, (your „ 4 
opened to 60 deg. of your Line of Chords) de- 
ſcribe- the 8emicircle K QL, which divide. yo 4 
12 equal Parts in the Points OO ©, Se. 
Sixthly, Lay à Ruler unto H, and upon ever 
of the Points OO ©, Se. and it ſhall cut the, I 
Equinoctial Line GDF, in the Points *, e. : 
through Which the Hour⸗lines muſt paſs: Wuere-⸗ 2 
fore, if from the Center+S; and through the-ſever, Þ 
ral Points **: „ Vc. in the Line C D F, you : 
dune, de Lines, bounding u dem between any 3 
+ D 4 8 þ emo 

id : ba | 


4 bak > * Serie ä 4 2 es i ** PENNY W * TIES 
3 So ac WB 5 * 3 ä R * 2 * * ** 8 
is bs Dat N : * 1 
6 1 5 a 
OFT” 
wy : ” 
2 * - 
„ \ * * * 
8 % 2 
p x" * 4 ” "5, bd D | RY * 
1 am * 
| ; # . 3, 
> 
T 


two Lines as W E, and M N, they ſhall be the 


true Hour-lines. Or, 
 _ Seventhly, If you draw another Tangent Linc, 
and deſcribe another Semicircle, and divide it, and 
the other Line, as you did the former, - ſo ſhall 
the Lines drawn .through the reſpeQive Points 
* * c. in either of the Equinoctial (or Tan- 
gent Ines) be the true Hour- lines belonging to 
the Plain, without any R had to the Center 
at all, as 4 i _ n Uptighe far 2 
liners. 


"w 


eo 00000 


F -, 


+ lk The Third Nane, to 


4 


N . * "+ 
K 1 


a 8 £357 & \w 4 
* e e 
* — We 3 — * 4 + % A 


How t6 1 :bs Hout-lines pb Os Sonth 
Reclining Plain, which aße between i the Pole 
' and the Horizon. en 


Let the Example be of a South plain, Reclining 

J; deg. in the N of a ” N80 

. min. 5 GEES | 

| FIRST, Dive the Circle WN ER. fot your 
Reclining-plain, croſs it with two Diame- 

ters N'Q R; the Meridian, and WQE, the Ho- 

rixontal-Jine of the Plain. 

- Secondly, Take 35 deg. the Plains Reclination 
out of 12 Line of Chords, and let that Diſtance 
fon Ni de and from E to . | 

(3 Thirdly, Lay a Ruler from w to 

Plate 4 a, it wil cut the Meridian in Z, ſo 

Fg. 5. is Z the Zenith of the Place, which, 
—: whic 


7 TY 
met! ut 7 
. 7 - 


. ical Circle WZ ; 
"IS Lay a N from W io B, and it 
d will cut 4 Meridian in 8, the South Point of. 
I1 the Horixon, th tough which and the Points W and 
ts E, the Radu of the Place WS E muſt be drawn. 


equal to the Com- 


of the Place 38 deg: 28 


cut the Meridian in P, the Pole of the World, 
and go deg. of your Line of Chords being ſet 
from C to x, and a Ruler laid from W to a, ſhall 
d cut the Meridian in A through which. and the 
| Points W-and E muſt the EquinoQial Circle be 


deſcribed : The Center whereof, as alſo of the. 
Horizon and prime Vertical Circles are all in the 3 
Meridian N QR, extended where need requires; 
and how theſe Centers are to be found, is ſhewed 8 


al ready. 
Siæthiy, For the drawing of the Lomb. 


I ſhall ſay no more of them in this place, only 
take Notice, that the North Pole is elevated above 
this Plain, the e of the Arch mY C, which 


5 36 deg, 32 min. 


Tnzsx are the three Varieties of South TER 
Reclining Plains, and in the making of theſe 


much; for each Plain hath two Faces, the 


Nad of the Place. : 


o OE m. of 
y? | 7 4 « : : : 4 


Hfebhy, 7 The Pole being $i distant from the Zenith 
| 


plement of the 1 ſet 38 deg. 28 min. 
from a to C, and a Ruler laid from W to C, half 


they muſt be drawn as in the-Ere& Direct South, 5 
Plain, or as was directed in the laſt Plain, and ſo 


FO TO * 7 g 
x” 9 * T 
: _—_— 7 by 
” 0 * Ls 
2 wk A 
5 Y 
* 1 
* * 
* 


e W which, and the Points 2 and E, — the prime 


you have alſo made the oppoſite Incliners as 
: one open to the Zenith, and the other to the 3 


; ” * r , "& - 
- 1 3 ue SF? 2 5 3 * 2 — * 5 9 1 
en e 1. FEE WA ALY 


1 eb in 74 


i 


* 
+. 8 
* 
. 1 Fi * * o 
mts „ 1 T * © > 3 F , l 
* 4 3 5 * * * * 47 Sy * * 
N 4 ROS... þ 337; ; F 
* 


Er as draw the Hour-lines 28. 4 Pires North 


AF in Soueb: Reclining Plots the. were 0 thiee 
N Varieties, ſo N my ey in the 
3 North Revliners.. For. 530 18. 

3 1. Fur North Prin nyt; — that it 
. 3 thay paſs through the Meridien,” uſt at the Inter- 
ſection of the Meridian with the Equinoctial, the 
Plain it ſelf lying in the EquinoRi! Cirele,: and 


* 
* 


Y | the Foles hereof in the Poles of Meg, _ 
ſo it is called, A Polar- plain. Or. £ 
3 Tun Plain may fo recline, that it may but 
we 9 between the Zenith and the Equizoc- 
Mal. 

l may recline fo far, as to ent the Meridian 


bervreen the EquinoQial and the Horizon.” 


= Kaner of theſe n Varieties of Non R 
lining Plains follow. gs 


* 
ik . _ : 
k *q * — # og 
— 4 . * a * 
* o 
4 # 
G 2 Va * 
- = a - * * * 1 * 
„ 1 N 6 
* * 4 * * 8 1 #3 1 3 
% * 
4 ce ; 474% ' 
4 * 4 e Ex 3 3 # 53 A434 gt Fxt E 
* 
* 5 
1 52 10 4 74 of 
% * ES „ 1 40 
„ CI 
5 © 4 
% 
* 
A ” 
- 
* 
8 a : 


wk. /7 © 


© <2 044 


"1. +_ 
+. 


E 


* 


. 


4 

_ 
WOW 
_—_— 


— ew 


2 
Sos * * „ 5 
— — 
r — * 


- 
uot oO. 


—_— 


8 * * 
e 
PO op 
„ * , 


= * 


R | 
2 r W TI 
4 ** 1 3 
- SY "ICE > T 
. 
* G 
; 4 ES - 
* H 
: in? 1 
wh, 4 
— ES og W 
. v2 
8 ” 
5 bo. 
15 Bo 
— * . 


; : . j ; $ "* 4D . 
it 91. fp 115 7 01 20 FFF 


8 (ti aba ghe 850 Variety. Wt = 
94 914-23) 


271} Ns 8 #1 Hines 22.70 70 1 i 5 
h 10 9101 2 of 10 10120 
: 8 Hod Hat Gt. AS, „XVI. ; ne Grow 
Hou . Its he Hous"lives \upon a Direct Polar- 
""PHig Whit reelinerh fee zo the Eqginogaal. . 

. Ht 19s 
Example of A N dunklen, Reclining Ii deg, 2; 


mid; equal to the Layfrude* of the pla 
London. e en HIDIT JH, 2715 


yib Joy 1-107 Ko iis to teils 41 
Flas, Deſcribe the Circle E E W R, for 
your Plain, croſs it with the Diameters E 2 
R. fr the 28 and mn 2E for the beine 
Vertical Gisele oonotd zent 2071 103 265 
Secondly; Set 31 deg. 32 mina ithe Rectioation 
of the Plain, (hich in this Example is alſo * ; 
to the Latirude of the Place) from 1 to 4, 1 i 
Torah, A Ruler laid from E to. a, will cut the 
North part of the Meridian in Z the Zenith a 7 
the place, and being laid from E to &, it will cut 
the Meridian in N, ſo is N the North poly — 
the Hartz. E 30 oeill 1 27847 I; 1 <2 | 2 
» Fonrthly, Through the Points W, Zand 1 | tby 1 
former Direction) draw the prime Vertical I 
or Azimuth of Eaſt or Weſt, WZ E. And IG 4 

I thronghs W's db and E, "oy my Horizontal Un 
„h — akt Sen e World, is at 
ways:removed from the Zenith of og ono @ :3 
much as is the. Complement of the Latitude (im © 
this Example 38 deg. 'D min.) Set 38 * 28 
8 1 


; 
82 


F * 
1 * 


„ 
999 


* p * N * 0 «ag: 1 * by 
P'S f RENE NE” . vs IF 9 ä 22 9 A R a oe ak bk 
9 " N 4 +: <a R : # e * ; WEN : 
_ be WIE © oe - AS nnn J 7 
* 47 T. 5 1 5 Wn th Wet 
Pos ; 
Z * — * 8 * » a” 4 s 2 , ** 4 
* 2 ; 1 . . 
| | | * 5 
E = Q 5 
„ 
* > 


min. from , (the Point in the Plain, which found 


| the Zenith Point Z,) Northward of. the Zenith, 
| and the-Compaſs-point will fall in W, the Weſt- 8 
point of the Horizon; ſo that if a Ruler were laid 
from W to E, it 1575 cut the Meridian in Q, | 
orld, which is already the | 
Center of the Plain, fo that the Pole of the | 


for the Pole of the 


World, and the Pole of the Plain, fall both in 


one Point, and the Pole Q is elevated above the | 
Plain 90 deg. viz. the Quan- | 
“Direct Polar tity of the Meridian Line E 
| North Dial. Plate Qi or rather the Arch AW, | 


3. Eg. i. Which is the Meaſure thereof. 
S:xthly, To draw the Hour- lines upon this Plain, 
it is eaſieſt of all others, for if you divide tte 


Semicircle E R W, into 12 equal Paris in the 


Points OO O, c. and through thoſe Points 
draw, ſtraĩt Lines from the Center Q, they ſhall 
be the true Hour- lines belonging to this Polar- plain. 
1" AND this Plain, by Reaſon of its North Recli- 
nation, is, in Summer, capable of receiving all 
the Hours from Sun-rifing to Sun- ſetting, and 


therefore the Hour- lines of 4 and in the Morn- 


ing, and of 7 and 8 at Night, muſt be drawn 
through the Center, as you did in the Vertical or 


Horizontal Dial, and as you ſee here done in this | 


5 


Figure. 


. Stile of this Dial muſt be a ſtrait Pin or | 
Wire, ſet perpendicular. upon the Plain, from the | 
Center Q, and of any Length. And this for the 


firſt Variety of North Recliners. 


Tux South Inclining Plain oppofite to this, is | 


directly the ſame, only the Forenoon Hours in 
this muſt be the Afternoon Hours in that, and the 
Hours of. 4 and 5 in the Morning, and, of 7 and 
$ in the Evening, muſt be omitted. ' © — 


. "UE 


at Ws fr. nds an 


Let the Earle be of RA GAP Plain, Reclining 


the Place. n 


North Point of the Horizon: © So have you three 


„ A n Wy 8 * * > > alt F * 
4 . . 2 \ - 
9 NR * PREFER 8 n N 2 
* 2 l A 
: . : . 
* 
1 
A 
7 ez Br yy — 
Þ 1 Dialing + F 1 * f 
4 * 
4 
= 
Þ 


£28 0 Fs bye 1246920) 20) p49 14 

evo 
1. Jechnd ee 3 

* "CHAP. XVI. hw vt 


How to 35 the Hear ref aon a Noh Rec- 


ing Plain, which interſeds the en Wen, : 
the Zenith and the Equinoctial. » 40 


1 


Fl. R 67 Drew | the Circle ES WR, eat] 3 
ing your North Reclining Plain, and crols it 
with the two Diameters 8 Q R, the Meridian'o 
the Place, and E Q W, the Horizontal Line | 


Secondly, Set the Reclinatiowof the Plain 2 3 
et wy to 4, and from W to 6.fF 108. 
Thirdly, Lay a Ruler from E to 3, it will cut. 
the Meridian in Z the Zenith. And a Ruler aid 
from E to , will cut the Meridian in N the 


Points E ZE and W, whereby to draw the prime 
Vertical Circle E 2 W, and three Points: alſo, 
25 3 and W, whereby to draw the Hotizon 
Foxrthly, Becauſe the EquinoQial is always 90 
deg. diſtant from either of the Poles, ſet 90 deg. 
upon your Plain, from c to d. Then laying a 
Ruler to E and 4, it will cut the Meridian in E, 
ſo is Æ the Point of the InterſeQion of the Equi- | 
noctial, with the North part of the Meridian; 
wherefore through the Points EE W, hs 
e 


the Equinoctial Circle; he DO 3 as OY 
Plate. 5 ſo of the Horizon, and prime Vertical 

80 Girele, will fall in the Meridian SQR, 
Fig ; extended where need requires, 

Fifthly, The Horizop, amines and Pole be- 
ing thus > ſear in 1 their true Poſitions n the 
Plain, the T hing regui 7 4 in 8 Dial, is, The 
Height of the 1, which may be 
found i 1n this Manner. — L a Ruler from E 
to P. and it will cut the = Lay 
| Sc; meaſured upon your Line of Chords, ' Will 
contain 63 deg. 28 min. which is the Fat - 
* the. Poſe a wel Reclining Plain, 

E C©Lafth,* For the drawing of the Hdurl, that is 


i x CN the ſame Way as in the EreQ Direct aan 5 
Plain, only here the Seile muſt be elevated = 


the Meridia Line 63 veg. 28 min. whereas th 

it Was only 38 deg, a8 min. the Complement: of 
the Latitude. I lorth Hole is elevated above 
this Plain, and the Hours — the Plain is capable 
10 7 are 4, 5, 6, 77 
ing, and 3, 4, 5, 6, J ane 8 a. e 


| Taz Height . the Pole (op: Silo). —f this 
5 7 may be found by adding the Comple- 
291 . of Js tude. 38 deg. 28 min. and 
Sr 5 Sr, of . SS Wh 
ve ANNE is 63 ;deg. 29 min. t. 
the Stile, as before. E. ete n HEE 


f. "4 
4x4 1 
8 2 f 4 > * 
45 L b 6 5 Fi . * 1 l 0 3 A , 
2 — 1 ' 2 5 N . M f * 15 ; 5 i 
> « 5 . * "+ A N ro n £84 * ? * 1 7 g X 2 
T — - as þ 3 L £ 1 2 9 1 2 4 1 10 1 4 . E <> * { * [4 * 2 * F * # * 3 > » ; 2 
* we F A A % 1 5 
: N * 3 


LIY 
. 1 N 
* : I 8 N «a 
* * 11 ney Buff 41212 315 5 4 "Fi 1 * ; II. 101 14 FS 
p 4-5 C24 374 fi); LS AT i: 3 1 7 a1 » 7 % " Sada * . g 
c a3 rxr $£,u 1/4 124 es, 1 42 141. 1 2 7 4 +, 
1 7 1. . # IT. 14 34 * nt} — 4 1 # * © - 4 þ 37 1 Py O * 1 * * * * * 6, 


c, the Diſtance | 


8, and 9. in the Moru- 


SF -IÞ 
« * 4 


S, K. 7 7 


— , 


210 Ai di r lo oniund 50135 Ns l n 


een eee 


E 
51710 


; 1 


1 mafted "The Third Parkes: hw 2400 


& F "M1 Fa {3} 


n HAN P. N. FORE. 


y Fou 65 * the Abar-tavs pow 4 Dies North 
Kecliniug Plain, which interſedts the Meridian be- 
- ere deer „Aer 1 1 "Sa. 
* : e £51699 
: | iu amis de of * Dreck North Plan 
Reclining 70 deg. in the Latitude of Londen, 


1 deg. 32 min. Ne Fig. 3. * e by 


FIIAST,. Draw the Circle E S WR, repre- 
ſenting your North 1985 Plain, and groſs 
it with the two Diameters 8 8 for the Meri-⸗ 


dian of the Place, and with! EQW the Horjzon- E 
tal Line of the Plain. 50 


 Secondy,, Set the. Reclination of the la 70. 
deg. from. Se and from W to . T 
irdly, Lay a Ruler to E and à, is will em 
the akg in Z the Zenith, through which, and; 
the Points E and W, 8 the * Vertical 
ele EZ W. — Alſo, uler-from.E to , 
it will cut the Na in the Inter ſection of 
the Meridian with the North Part of the 2 
now through the Points E N and W, deſc deſeribe N 
the Horizon of the Place EN W. 


Foerthly, Foraſmuch as the Pole is didant from 
the Zenith of the Place 38 deg. 28 min. (equal to 
the Complement of the Latitude) ſet 3B deg, 28 
min. from a, the Point which gave the Zenith Z. 
to e, and lay a Ruler from e to c, ſo ſhall ic croſs 
the «Meridia in P, the Pole of the World... 


Epi, 


— 

4 RI * 8 9 * p 2 8 * * * n. 
_— e "AE: * vi 9 * — 4 ä * * * * * 

a 3 Egon” © | Fa : . 

: - . N © 
T - 
- 4 
- * 

” + 

_— — 
3 to * 

27 * 1 
4 

* 

N 

2 
* 


Rfibh, Becauſe the EcuinoQiat i is in all Places 


ſituate 90 dey. from either Pole. Take 90 deg, 
in 3our Compaſſes, and ſet them off from c, (the 
Point hien gave the Pole P) both ways, to e a- 
bove, and to g below. So a Ruler laid from E 
to g, will cut the Meridian (it being extended) in 
E, without the Plain, which ſhews that the 


# North Part of the Equine@ial Circle lies below 


this Plan. Therefore lay a Ruler from E to e, 


and it will croſs the Meridian in E above: So is 1 


ZE the Point where the Meridian, and the South- 
point of the Eqzizodial will interſect, and thro' 
that Point and the Points E and W. muſt the E- 
quinodtial EA W, de drawn. 

3 * 5 Pole, and. Erste, 


being t * Fer the Thing required in this 
Plain, a; debe of the Pole above it, viz. P 
R, which The Height of in this manner. — Lay 


TOs from E to P, and it will cut the Plain in | 
c, the Diſtance from R to c meaſured upon the 
Chord, will be 71 deg. 32 min. Which is the 
Height of the Pole above this Reclining Plain. | 
Or the Height of the Pole above the Plain may be 


found, by adding the Plain's Reclination 70 deg. 


to 38 deg. 28 min. the Complement of the Lati- 
tude, the Sum whereof 108 deg. 28 min. which 


taken from 180 deg. the Remainder willbe 7¹ deg. 
ou min. as before. © 


eh For the draying of the Hour-ines, they 
are done in all ReſpeQs as thoſe before in South 
Erect Plains, only in this make the Elevation of 


the Stile 71 deg. 32 min. — ey iind it e | 
Projection. ä | 
Your Hour-lines being an eredt the Stile 
7+ dey. 32. min. above the Meridian or Subſtile, 
letting it point up to the North Pole, becauſe 


7 * above this Plain is ſo much — 
an 


. ». ͤ =, ̃⅛—tt ü C1 


— 


—B . INTO» od ” * p of kd 

- Ef * * 1 n * * N 1 A 4 2 * . £ as] * * 
4 : * = Bd HT 28 * OY ** N % of * 4- "RK" * 

1 1 by "7 2 vo % A 3 OY . 1 
# . 

- . 
* 8 F 7 _ * 
0 ; . * $5 2 
* +. 3 I Ln” * 
; {> - : 5 
* * s * 


and bein this Plain is but 20 Wi? raiſed above | 
the Horizon, vix. the Complement of his Reclina- - 
tion, the Plain is capable to receive all the Hours 
from 4 in the Morning to 8 at rl : 
and therefore the Hours of 4 and 5 in Plate 3. 

W the Morning, and 7 and 8 in the E- Fx. 3. 
vening, moſt be drawn through the 

Center, as was done | in the ee or *. 
9 


4 thus have you had An of all me 


ns Te | 33% ðͥUV £6 SME) oft. rs 
2” 


aw. 


1 
Y | Varieties both of Eaſt, Weſt, North, and b 
* South Reclining Plains; and no other can pof- J 
- bly fall out in any Place whatſoever. ''''The J 

, Inclining Plains are the ſame with the Rechi- I 
is zers Oppoſite to them; and muſt be drawn in 3 
P „ ; 
y e heretofore hinted; and ſhall be more at 
in diledutſed of hereafter,” when 1 have 
he | od done with 'Decliniug 9 An, ok 1 
he en 111 n to ne” ung 3 
be L * I 
85 "ol 
di- | 4 
1! rv. Th Deckvin Reclining * Plaine, | 
ey Þ 
— : 8 H A Reg xIx. | *Y 3 

0 5 e 6 
dur AS there were fix Varieties of Direct North and 

. South Reclining Plains, fo alſo are there of 
tile outh and North Declinin "Reclining Plains, viz. 
ile, hree Varieties of South Kinder Declining, and 
uſe many of North Recliners Declining. or in 

; © e Kecliners Declining, 


, 1. Tux 


24 ak etl ___ 9 
43 "WM, uy 
TOS OE - N 
* c 7 A . . 
NN n K 5 7 « 
Mn Year" 8 


port « Dechning wits ener South 


Fo = Plain may cut or fall upon the Meridian, 
juſt upon the Pole - point; and ſuch R celining 85 
1 Plains, are called Eeninoctia Dechiueri; 


An —— — be ſuch, that the he. | 


cling Plai ſhall interſect the Meridian between 
| Wards. 


$. Tux 3 ay be | ſuch, : "that the Re- 


clining Plain ſhall croſs the Meridian between the 
Eoie and the Horizaen. OY n ee any. 


4551 2356 Aves. A "Is." * 70-305 iin / 


are theabree Varieties of South Recliners De- 
Yay — North Recliners A aber e 


art bree er 3 Far, Nr 
7 * * 74 © +4 © had * Ir 9 157 927 {yy r OW D 


* bt Tun 3 may be ſach, that the North 8 


Beolining Plain may greſ the. Meridian in the 


Fein Whare:the, Ears“ inderſocis the Meri- 


dian. And then ſuah Plains are called Poler De- 
clining Plains, becauſethe Poles af them lis in the 


Axis-of the World, and the Subſtile in ſuch Plains 


— be al Ways perpendicular to the 'Meridian of 
oF * n 
0 Tr Da $556 HY be ken, wat ind Re- 


| clinivg Plain my interſect the Meridian, between 


m 2 enich the Eq 

| Far 54 ad "Th AG," char 1 the 
Reclining Plain may fall upon the Meridian, be- 
tween the Equinoftial and the Horizon. 


iis Exinples of all aſe Vatieis Ge. es, 
It . 78 4 acer 5 £77 Ye Bel iK £4900. 
EIS: phe, leet 9H uti cr1{5! 4 e B £125 
| ene tl in e hei mein 421971 


f 1 
* 
. *4 0 ; {| 5 1 . i : * & 4 4 4 2 * 4 
E 1 . LO þ 1 8 s * +4 : „ * 72 x EE 28 2 4 oF 1 of 
au 44 * k 4 . 4 7 . 7 
4 80 3 * 5 1 _- . * W-x 
1 „ Ss 4 A +25 * 


— of the Flags, as. the Pole of the 


7 * 


— 


TS» 


« 
aan 


How to draw the Eb 

. ' Declining Plan, e ot e 2 
"HR the Pole Post. fic qu fl [2 5119 12 brig wor 1 
Nas | Ys. © $M 4 

IN Declining Reelin Diats, before the Hour- 1 
lines can be drawn, der Things muſt be gi- 


* 


e ven, —— Tung on Tbe Things given 
5 1418 8 2 * i, W „ 3 * if 
i- are, * # [tt 157 DT LIES / 28 4 Nn A 1 3443 2 *. 48 * 1 & 'Q3 : N 
La: 1 4. PR j da bad | 1 
_ any p13 i 70 GON by 107 | 10. 006353} : 
je 


1 * * 

22114 

22474 
* 
3 


* 


C3 The dau Reelle. SEL 


Fe”. FEY TIE {x "SA 7 #3 £2 LS, 9 bi £21 ef by 12 11. 8 1453033 "uni H os 
"OE! ; - 4 3 
2 The Thing, required, ans e e 

| 24 * * * * 7 | 
en B33 2% i 240 RP, ; 


. The H Height of the Pole above. the. f 
5 „ 1 7 9 
3. The Diſtance. of ibe Subs d, 1 


— — 
N 


8 1 
. i; e ieee, find ooh A gi one 'Y 
Z Wl ol 4-'/Dhe,. Plain's Ditexence of Longi- 
+ 12008 Eon 7; * 1 3 18 LLLOR tig 4 2 © ny. 
Nils EN Hole ting, e&bat HS 28 0 


a Ward, take 30 deg! out of your Chord, and ſet 


2 Ruler from Z the Zenith to e, it will croſs the 


32 2 * WINE 9 * | * 8 HE I * * 
3 * o j 
2 * 
: 
; . 8 
2 * 
4 


warty = * of a South Plain Declining Eft, | 
30 4. Reclining 34 deg. 32 min. inthe La- 
3 of London, 51 deg. 32 min. : 


Fiſt, Draw the Cirtle E A O N, aũd croſs it 
. N with the two Diameters H Q O, the 
Plate 5. Horizontal Line of the Plain, and A 

' #Sig. 4. QR, the perpendicular Line of the 

| Plain, etoſſing each other at right An- 

: gles in Q, the Center of the Plain. 

. «Secondly, Becauſe the Plain reclined 34 deg. 32 

main... Take 34 deg. 32 min. from your Line of 
Chords, and ſet them upon your Plans from A to 

a, from H to &, and from R to c. 

Thirdly, Lay a Ruler from O to 4, and it will 
eut the perpendicular Line of the Plain in Z the 
Zenith of the Place. Alſo a Ruler laid from 0 
to , will cut the Plain's Perpendicular in K, the | 
Interſection of the Horizon of the Place, with 
the Plains Perpendicular.” And a Ruler laid from 
'O to will eut the perpendicular of the Plain 
AR, (it being extended) in N the Nadir-point. | 
: Having found theſe Points n the perpendicular | 
Line of the Plain. ef : 

 Fourthly, Through the Points H K ©, draw the 
Horizon of the Place. And. 
Fifthly, Becauſe the Plain declines 30 deg. Eaſt- 


„„ hk ms 


5 Ws 
"woes 


them from R to 4, and from O to e; and laying 


SAS a.©'=m'o '» 


Horizon in E, the Eaſt point thereof, and the 
Ruler laid from Z to 4, will crofs the Horizon 
in 8 the South point thereof; ſo have you found 
three Points, viz. ZN and S, through which you 


may draw the * whoſe Genter you ny 
find, 


4 $; 


Gamen ical Dialling. , ö 


sad, as oth been before taught : - o in this 
„5 Manuer, 


Dive the Space between Z and N ü in to e- 
qual Parts in C, and through C draw the Line 
D parallel to QO, extending it as you 
ſhall have Occafion. Alſo from Q, through 
E, draw another Right Line QE, extending 
it, as Occaſion ſhall offer; the Point of thoſe 
two Lines Interſection is the Center of the 
Meridian. Which being drawn, 


4 | 8 2 „, Lay a Ruler from E the Eaſt point of 


to the 177 © Z the Zenith, and it will cut the 
Plain in 
ill is diſtant from the Zenith 38 deg. 28 min. equ 
he to the Complement of the Latitude, ſet 38 d 
0 2 from & upon the Plain, and it will fa l 
we} | en P, which is the Point of the Plain 1 wH 
7 — tion 45 the Meridian, which demon 
5 the 15 25 e you Tea Tk 5 Xs 
x tO inoctial Decliui 
8 7 Sevent Draw the Line PL ſqt 


5 
lar of 7 0 and uff the Eq inoQial 'Cj 
is in, all Ls SH * from either Pole 90 05 3 
tem F O, 


(99, de Pr nd theoy y 
= draw the Line 2 © Qs, bo i th hh 2 | 
t pan ras pag A 9 85 ine, 5 

r 


* 25 1 8 
mf 1 a 15 N the; Ta 
ng 9 1 Pl ary 
the WC 6: it ought. to 
the cheme "being thy S fr our Re- 
on aiges from i ice eaſily obtained: "For, "> 
2 us Is id the Diftance,of- 15. Meridian "He 
wy 60d C bd The &t OP mbaſired pon 
1d, 


t 29 ae its 26 get io to vas N 


* 
1 4 
* 


2 
29 


* 


And becauſe the Pole of the World | I 


8 


- =. 
1 


r 
r 
* 3 


3 5 FI 
4 bay 8 E 


your Line of Chords; wilt contain 72 deg, 
53 min. the Diſtance required. 


- -quinoQial Declining Plain. 


3. The Diſtance of the Subſtile and the Meridian, | 
the Paint P alſo. Therefore that, as alſo all 


the Hours miſt be parallel to the Subſtile. 


A To find the Plais's Difference of Longitads 1 
PB. Lay evg hea bon and it 

will 3 the Þ in n, the Diſtance LM 
Chord, 5 bog Plain's j 


und, f "will 


your 
7 e 'of gn yo tude 24 de 


„ Requilites 8 FL 
now s Is Fy 


LEAST: . 55 5 * 
3 7 * oy 


W 2 8 1 


gy A nn 198 Gr 


Point Needs as 
59 8 wh 15 2111 Pep” 


| bY ATAINS'S$ 5 5 
1 77855 From our Eine 6 of. ;Chortl Veake 71 
Hh, 11 5 Dt An 13 5 e an 
v 
'th de 8 le. 70 P, anc v8: 
575 SD 5 50 en *tbe PH Dif- | 


"Find, Take 24.468 
2 e 2 9 5 


„ Divide 


30 18 


A hin 4 1 8 Hh Ding ge em . cen | 


 clining . — N Points = ©, 
the on at 
e 4 1 75 5 ee 


19 1 „ Mida un Point 


0 „(or _y other ys 5 at all Adventures 5 
the 


2. The Height of the Pole above the Plain (the 
point P) oo deg. oo min. therefore it is an E- 


heron | 
i eg eetivenient f 

or the 
Rr ede 8. ; 


rom D 4 


Os: 4 2 


as BE on a of 


. 


2 r 8 44; N 9 
0 * 9 n * enn 5 
Pt" 7) PREY +. Oy 
* II l 3 22 2 
is * — * 0 * 
% CY : : 8 7 
©, 11 ' * * a 1 5 * 
N Di N | h 3 
* * N 
* 


the Subſtilar Line) draw a Line MO N at right 


b: IF A les, (or perpendicular) to the Subſtilar, re= 3 
he W preſenting the EquinoQtial. Y 
E- Pe bh, Lay x Ruler from A, and every of the Y 
Points O © ©, Sc. in the Semicircle, and it wil! 

_ croſs the Equinoctial in the Points , Nc. 4 


Laftly, through theſe Points ** 5 Sc. you 
draw right Lines parallel ta the Subſtilar, the 
ſhall be the true Hour- Hines belonging to your | 
Plain, the Hour- line of 12 being that Where you 
began to divide your Semicircle, that is, at the 
Mark (or *) which was made from the Point E. 
Fox the Stile of this Dial, it may be either a 
ſtrait Pin or Wire of the) juſt Length of the wy 4 'Y 
AO, erected perpendicularly upon ſome Point Sf 
the Subſtile (as at A or O) the very Top of che Sha- 
dow thereof, giving the Hour egy 46 Hour- 
lines upon the n N 5 
On elſe the Stile may hes a Plate ot Brut or 5 
ron of the:Breadth of & O, ſet perpendicular to 
the Plain, upon the Subſtilar Line A O D, the 
Shadow of A e Edge: | ive xhe om 
booty the oe He nenn 550 80 


. 
. Sin 2 S 


OS, PO ao 


x T Py k 5 + n 10 — r 5 
N | lo 1 ( n 1 [+ wolf 4 11 a 30 ( 4x] 
2 + £3 #0 1 * 4 TX: A . 2 188 7 : $ 
3 1 240970 hrs : 0 $343 2 Fire LT 5%, 41 a 140 * 73 
22 ES” 3 „ 3 15 ERS 
Tt A CHO canh On: div 227810 HA 1811 


dee Das, 


1 9 * R - 
* W 
* 5 of \ * - 

- * — ,- 

225 o 

* 5 

* 0 

* * 
7 
Fi * * 


ee een 


. The Second ron. 


I Fr - A: XxI. be Pio 


| How 20 * 125 Howr-lines = a South Reclining 
Plain, the Zeal Eaſt or Weſt, which paſſeth be- 1 


ren the Z and the Pole — 


1 N this, 2s in all other Decliners Reclining, 
three Things muſt: be knowyn, and four muſt 
be found before the Drawing of the Hour. ines. 


Les the 3 be a South Reclining Plain, De- 
_-| olining Eaſt 30 deg. and Reclining 20 deg. in the 
C2. #4 w Ih 51 deg. 3 an 8 191 
. 40 i Jr: 3115 15 ani, 4:45 


2 7 a 


1. The Diſtance of the Meridian and 
| Horizon. | 
FL he Height of the Pole above the 


* Plain. ©» 

Required 3. The Diftanee of the Subſtile and the 
| Meridian. 
4. The Plain's Difference of Lon- 

gitude. 


Hirt, Deſcribe the Circle HA O R, repreſen- 
«ting your Reclining Declining Plain, and crols it at 


right Angles, with the 1 two Diameters A R, 00 
the 


- 


metric ob: Dealing * uy. 


the Perpendicular and H O, rege enen! 
Line of the. Plan! I gh Hd td 
Secondly, Take a0 deg. the Plain's - Plite's. 1 
Reclination, out of yoùr Chord, and AK, 6. 
ſet them from A to 4, from O te, ee, 
and from R tog. „„ 
rah, A Ruler lad from Hoe N will give : 
Z the Zenith, and laid from H to 6, will give 
you K the Interſection ok the Hortzon with the 
perpendicular Line of the Plain. And the Ruler 
laid from ¶ to c, will give you N the Nadir; then 
through the paines H, K and Os draw the. Hori 
20n FO . o d 
;  Fourthly. Take g degl the lai 's/Deelination 
t out of Nur Line of Chords, ànd ſet them from 
R to d weſt ward, (becauſe the Plain deelines Eaſt- 
ward) and alſo from O to e, fo a Ruler being laid 
from Z to e, ſnall cut the Horizon in E, the Eaſt 
point thereof, and laid ftom Z to d, ſhall cut the 
Horizon in 8, the South point thereof. Thus 
have you three Pomts Z, S and N, through which 
2 to draty the Meridian Cirele, Which you may ex- 
0 tend without the plain to Pand N, occaſion fome-- 
O times requiring it ſhould be ſo. N47 
Niabiy, Fo teſmuch as the Pole of the World 
is always diſtant from the Zenith equal to the 
n Lati e of the place, as here 
at London, 38 deg. 28 mid. Lay 4 Raler from E, 
to Z, H II eut the Plain in 5. from whehce 
= way deg. 28 min. to A. 80 2 Ruler laid from 
we Fr wo out the Meridian (extended) in the 
rips the North pole of the World. And a 
Ruler laid from P:ra Q, fall croſs the Meridian 
in L, the South-pole, and the Line F QL ſhall 
n- be the Axis of the World. 
at S:xthly, Take 90 deg. of your Chords, and ſet 


8 tem from (the * * found the Pee. 5 
he | OW 


; : © ” . 4 a 
ö n E 
+ » 


to u: e Jaid Pa to a, mall cut the 
ee in B, through which point, and through 
the point E, the Eguinoctial Circle muſt be deſcri- | 
bed, whoſe Center will de in the Axis PL extend- | 
ed, and the Manner how to find it, hath been ſeve- | 
ral Times already diſcovered. . 
Tu Horizon, Meridian and Equinodlial Circle 
being thus deſcribed upon your Plain, by their In- 
terſections and Diſtances, the four Requiſites be- 
longing to this Anne e Pos Re be 
obtained. As, 


| = To find the Dj ance of Is Meridias and Fho- 
he Diſtance HV upon the. 
e — — upon the Line of Chords 
Will contain 18 deg. 30 min. the, Diſtance | 
of the Meridian and Horizon. 
| 2. To find the Heighs of the: Pole or Stile,, above 
tie Plain Le. Set 90 deg; from c to l, then 
= 25 lay a Ruler from 5 t L, and it will cut the {il © 
= _ plain.at , the ance. from. to , mea- ll | 
Rae upon your Chords, will enten 13 deg. 
4 min, the Height. of the Hole or Gala v | 
dove the Plain. 
„ of tharinbile fone che 
Meridian Vc, meaſure the Diſtance Ve upon 
EF. . _ .. the Line of Chords, and it will contain 
2" 30 min. the Diſtance required. 
4. To find the Plain's Difference ef Longitude 
B L OD. Lay a Ruler from L. to B. it will 
on the plain in , ſo the I 44 met | 


CT TIE 


{ned upon the Line of Chords will contain 
23 deg. 32 n, © a be of 
Ee gitude. 711 


> — 1 
K 
9 
12 
1 


IP" N n ien "we W — * . 6 
N wag Tr PET II SORE WY 2 p a 7 0 9 : 
ww - 1 5 1 
5 : * » , * * ; T 
: : « „ 1 * . : 8 
Geometrical Dialling. 
Ll ? 9 4 
U : - $ | 
5 4 3 * 2 * 8 " : K , : 


Tavs are the four Requiſites belonging to this 2 
Plain found, and in this Example, two Things 
tl are very obſervable. 1 1 


x. WaeReas P the North-pole of the World, 
falls without the Plain, and the point L, re- 
preſenting the South Pole, falls within the 
Plain, it denotes that the South pole muſt be 
elevated. = 3 .Y 
2. In reſpect that the Line or Arch Lc, which 
is the Height of the Stile or Pole above the 
Plain, is but of ſmall Quantity, viz. 13 deg 
40 min. it will from thence follow, that ve 
Eęuinoctial Center will be very cemote, nd 
that the Honr-lines near to the Subſtile will . 7 
de very cloſe, ſo that in ſhall Dial theis 
Diſtances one from another will be inſenſſble; 
\ and therefore you may fave the Labour of | 
. - deſcribing the EquizoZial Circle, and be fu. 
tisfied in finding of the point B, by 585 1 


the Plaus Difference of Longitude is found. 
For, in ſuch Caſes as this, the' Plaiss Di? gl 
| ference of Longitude, the Diſtance of the 
Meridian from the Horizon, and of the Sub-: 
ſtile's Diſtance from the Meridian, and thb 
Height of the Pole above the Plain being 
gafted; you may proceed to draw the Dial © "| 
28 followeth, not much differing from the I 
drawing 'of the Upright far declining Dial, 
Chapter VIII. rg | 
How 10 draw the Hour- lines upon the Plain 
Firſt, Draw a right Line A B C for the Hori- 
_ WU 2074] Line of your Plain, and aſſume any con- 
Tus venient Place therein, as B for 4 Center; upon 
| : EE > Which 


65 
7 


„ 
N "OREN ON" OE ROY * 9 * WP LE * 4 9 1 9 5 ; 
- . 5 Los 
* Ci „ p 6 
| 5 Dy . | | 
4, za: $884 5 i 
3 W 4 * "by" F "4 e. M 


For it. is neceſſary, is, but 
for dos 28 1 G. to . ee or 
* "Scales of Chords upon your Ru- 
South r ler, 2 5 wc e 6 
, Rech- ſupplies. them 4 
F:: Flat. Arch of ine Circle AD. 


| 18 de 50 min. the Diſ: 
4 8 Hue the A Horizon, aud note 
* 155 Pier Ehe 2902.00 
"th "Secondly, FromD+ to E ſet 7 d. 30 min. the 
3 _ Diſtance of the Subllile, from, 1 g the 
inf Way as on;find it 1 nie in your Projection, 
Wo draw the Line B Ie or the Jubltile. Al up- 
oh the Rn 75 13 LG a5 min. the 
f the, $t)e.fram E to F the 
F fot che Stile. e. Which being 17 75 Imall 
be . 13. deg. 40 mſn, gage: to be aug- 
2 ald tfietefore (at any Sonyenient I nce 
BIN x to the. BELA N K Dial- plain) 5 — a 
72 parall 
Axis. * 5 3 
| 25 , Throüg yew wa, Points. taken at Ad- 
> --yenti hi in the Subſti 1 Line, as K and L, draw 
| 0 1 955 Lines petpendicnlar, ar NEB 1 An les 
1 W.. ne a. the Lines MK N, and GL 
Then: from the Point K, take 
Ke to the augmmenied St ie H. and ſer that 
Diſtance upon the Subftilar 1 % . Alo from 
the Point L, take the neareſt Diltance | to the aug- 
mented Stile G H, aud ſet that iltance upon the 
6 from L.to R % El 
| * . Fourthly Upon 8 Points Qand R. as. upon 
5 twẽo Centers, with co deg. of an ny of your Chords, 
5 eee W A; Other. ML. of 
. ir- 


_ ul 
_ + th 5 we q wy 
8 , 7 - a * 1 4 
* . 
Bo . F « LY 5 


hich point, . 80 > wat of any large Line of | [1 


r 2 th this. Arch, from A to D, 


not t the Mieridjan. 


Ee, or ARE * 


leaſt Di- 


op i 
< 


# 


. * —— 2 — 


” 


a. * _y 


4 * * 
„ 
2 


- 


Sr ty; 


c w vos. 
923214 a „ 


R 
3 5 FEY 


D K ES ads 204 dds T0 OE TRIED F of PR 4 
W ö * 9 N 4 . l 6 N Th 0 » 8 x "* 75 dee po al ti a wr 
” 2 * FR INE BYY ; — 3 - 7 TY T ELSE 
* , * 
* 4 4 2 N 
* > 
— 
» , . * * 3 4 
F * : 0 „ 117 „ "To g 
; onetric ö I mg ; 
. — 


Circles) and in either of them ſet 28 deg. 32 min. 
from V to I upon one of oy and irq AI ; 
8 upon the other. 752 Ion . 
Fifebly, 1 Lay a Ruler from Q to ” * it will- 
| cut the angent Line in V: Alſo lay a Ruler from 
R to 8, and it will cut the other Tangent Line in 
Z, and a right Line drawn through the Points Y 1 
and Z, ſhall be the Hour-line of 12. : 
2 ' Sixtbly, At the Points S and T, begin to 1 3 
the ſeveral Semicircles in 12 equal Parts or Hours, 
bytaking 15 deg. of your Chord, and ſetting them 3 
from 8 and T both ways at the Points O S, 3 
Ce. ſo many Times as the Plain: Wil TAP 1 
| Hour-lines. 85 2 
_ Seventhly, Lay a Ruler from the Points Q and, 
to every of the Points © © ©, Cc. in their 2 
relpective Semicircles, and it will *roſs t their pk 
ral Tangent Lines in the Points , N des A 
Laſfily, Through the Points * * 5 in both the 4 
Tangerit Lines, draw right-lines, each to, ;bip Gt: 
reſpondent, which the Hour- line of 12 Wi Tag 1 
you how to do, and thoſe ſhall be the ide) ob- 
lines of your Plain. 3 
For the Stile of this Dial, it may Her dK-s 
Wire or Plate, containing an N 1 to be 
Height, of the Pole above the Plais, but it muſt 
de augmented anſwerable to the augmettted Stilg 
as you ſee in the Figure, and muſt be ſet ii 


per Place upon the Subſtilar Line, and ſalſo per⸗ Na J 
pendicular or ſquare to the , LON an 2 is ahis 


Dial "aye oa 


3 * % 284 N | > 
Fl ks asd 100 3 60 — 


6 , 4 1 
* Fg - * £ ot ; 1 T 
E & CESS * „ $4.68 ; E 0 e * va 3 + 64 37 — 1 
* * 


* 7 
L * x *% "2 
„„ 
* N * 38 0 _ 3 
2 1 n 6: : L hs * . > — 
% + * 7 . a; * 1 SS 2 7 * 18 N 430 4 * 2 q P 
4 . - +. 
. % » * 
- = 


a — abc x 280 
I* by * # MI 


a 4 * * ; a * . N . 
ET OE Ys "6% 2 le abs Tus 2 * 
N >. 2 . 
* . * 
X "es - 
h . 
* MY 
Co - . 
* % * 
1 nn 
b 
4 * 
r 
A 
4 
__ 


I of a South Plain 5 e of 
| "MS ng 55 Jar? m the Lati * fs 32 


be. 
+ 
. Wo 
% 
4 * 
5 43 
Ly as F : 
- "St 


Game Daus 


Eg 


5 7 he Third Varieey. - 
HAP. XXI. 


How to draw the Hour-linet upon 4 South R eckiwi 
Plain, declining Eaft or Weſt, which inter, 
the Meridian between the Pole aud the Horizon. 


TE: T the Example for this third and laſt Va- 


riety of South Declining Rechning Plains be 


2. 
Jy ; 
„ 


2. The 2 — kadwad 30 oO 
3. The Reclination. $5 oo 


ſi. The Diſtance of the Meridian from 
I the Horizon. 


bove the Plain. 


tude. 


Draw the Circle AH RO, for your re- 


|  elining declining Plain, and croſs it with the two. 
| Diameters A R the Vertical, and H O the Hori- | 
| Zzontal Line of the Plain, 


5 Serendy, 


ward 30 deg. and 


J=- The Height of the Pole or Sule a- | 
Js. The Sudſlile's Diſtance from the 
Meridian. 

The Plain's Difference of . 


r 


a wr” oo As 


a” a = > . > ac Sf +. % hong iow 


af 5 wu Sw aa O% 


a oa w np o©Xxxa fu wh, wk fc _ 


3 9 25 e " 9 * wr 
9 ! ? EO Rs L 
- 
1 2 
: . 
10. * ; 
# 
; ; We. iS) 
2 8 
* 
4 * 
{ 
* 


e So 55 — the Plain's Roechingtion- | 
55 and from O to-b. 

Thirdly, Lay a Ruler from H to 4, Pl. 2. ys 1 | 
and it will give you E the Zenith, and laid from A 
to &, it will give you K, the Point of the F N 
Interſedion with the Plain's Vertical Line. | 
have.you three Points H K and O, thro wrong which 5 
to-deſcsibe the Horizon'of the Place H E. 
Foarrbiy, Set 30 deg. the Plans Declination 
from Rio c Weſtward, (becauſe the Plau declines 
Eaſt ward) and from O to d. So à Ruler laid from 
2 io e, ſhall give you 8, the Inter ſettion of the 
Meridian with. the South point of the Horizon. 
And the Ruler laid from Z to 4, n you Bs 
the Eaſt point af the Horizon. | 

_Fifubly, Having the Points 8 and 2, 8220. ; 
them you may draw the Meridian Cirole LS$ZP,- 


u hath been aiready Teveral ways' fe che Cen- 


ter whereof will en en T bang er- 

Setkh, Lay a Rae Fi E 10 L, and ie wilt 
cut the Nlais in e, from which Pointe, [et 38 deg. 
28 min. to f, and a Ruler being laid from E to 7, 


fhall give the point - P, upon the Meridian Circle Be 1 


for the Pole of the World. And a rign | Line 
drawn from P through Q, ſhalt de the Axis of the 
World, and the Subſlitas Line of the Dial. 
| Seventhly, Set 90 deg. from f to , (becauſe the 


Equino&#ial Circle is in all places 90 deg. diſtant 


from eicher Pole P or L.) So laying a Raler- 
from E to þ, it will give you the polar” B in the 
Meridian, through i and E, the Eaſt point 
of the Horizon, the Equinedial Circle muſt pals; - 
may be drawn as in — t Examples, the Oenter 
e n ure 


th hoody x Gitcles, »#&.,\the-Hori- 
zom, Meridian and Equinoctial, T being deſcribed, 
according to their true Situations upon the Pla, 
the fame forementioned Requilites may from thence 
Fr 8 ner i lin 
. [£21799 7 241% 203 rin. i: 21101 
431. 70 find'the Diſtance bf the Meridian Pops u. 
Horizon OC. The Arch O C, meaſured up- 
on the Line of Chords, will contain 64 deg. 
41 min. - "The l, 4 ene from the: Me- 
mary 18 Oc mai 664; het. 
ET ths Height. of rae Pole er Geile abe do 
by mg D. Set 90 * D toe, and 
ay à Ruler from æ to P, it will cut the 
lain in m, the Arch D meaſured on the 
Une of Chords, will contain — deg. 25m. 
\ The Height of the Stvle..* 
3. To ud the Snbſtile's: Diſtance 8 the Meri- 
25? eg GD. This Arch meaſured will contain 
#25 6 deg. 2 min. The Diſtance of the Agile 
from the Merid am. 
8 4 The 'Plain's Difference of Longitude B P O. 
A Ruler laid from P to B, will eut the Plain 
942 n. So the Diſtance F, meaſured, will be 
hb deg e 38 m. 2 Plains Difference of 
+; 5 W A Hel! 1 Rene mona 
| A 3 oli Daatilidze off bur ble 
＋ Aran Requiſites being thus found, you may 
"= to draw the Hour: lines in this as in other 
Plains. © Firſt, By laying a Ruler upon P the Pole 
of the World, to B, in the Interſection of the 
Meridian and EquinoQial, which will cut the 
Plain in t, at which point, begin to divide the Se- 
micircle- into 12 equal Parts. And from Q, to 
each of them, lay a Ruler eroſſing the Equincc- 
tial Circle, and dividing that into 12 unequal parts, 
to which unequal Parts pf. the N a Ru · 
3 ler 


„ rn ee _ 


WW 
- 
- 


taut: a 


ler laid, it will divide the Plain Pol 12 other un | 
equal parts, through which, and the Center Q, 
right Lines being drawn, they ſhall de un 186 
Hour. lines proper for the Plain. | 
Bur in this Example, the Sefa ot the 4 
| Pole or Stile above the Plain, deieg dat ſmall, 4 
27. 1/9: ideg.. 25 min. yon may, if you pleaſe, 7 
draw the Hour-lines by one Tangent-line, and 
the Center, às was ſhewed in the ſecond. Variety 
of Direct South, ee e. "_ and. as here 
 followtth<; 3 1 231 Al l ef 5 #15! ad Lo 
by aan 7 S043 £4 vl_s 
2 ous the Hour uus pon the Plain 
'4 221 Yall 629 ere eee mad 
Bl. Upon your Plain towards the Bottom 
ce (becauſe the North Pole is oa elevated) 
draw a right Line A B, parallel to the Horizon, 
and aſſume; A for the Center. of- your: Dial, upon 
which point, with '60. deg. of your Chords, de- 
ſeribe an Arch of a Cirele B E, upon which from 
B, ſet the Diſtauce of the Meridian and Horizon, 
64 deg. 41 min. to C, and draw the Line A 
for the Hour-line of 12. Alſo, upon the ſaine 
Arch from C to D, ſet 6 deg. 2 min. the Diſ- 
tance of the Subſtile fram the Meridian; ; and draw 
the Line A D for, the Subſtilar. : 
Again, upoy, the fame Arch ſet A Soutb Plain de- 3 
off 19 deg. 25 mig. the Height "aging Eoſtward 7 
of the Stile from D to E, and 0 4 and recl- | 
draw the Line A E for the "ag ming 55 deg. Pl. G 
is of the Stile. N. Þ 
Secondly, UporFgp pry 
the Subſtilar Line, aſſũ N point at Nene 
as F, through which draw the right Line G FH 
6 perpendicular to the Subſtile. 
Thirdly, From the Point F, take the neareſt 


Diſtance to the Axis of the Stile, and ſet that 
E 5 Diſtance 


| Diſtance eyon he Sali Line hom F 0, and 
upon the point 
- deſcribe the Semicircle ML N. . 

Forrebly Lay a Ruler from O to K, 
. 


dle in Ly ut which point begia to divide it into 12. 
in the points OSS, . 

5, Lay = Raler from O the Center. of the 
— — 4 points G O ©, ia the. 
Semicircle, and the Ruler will cut the I angent 
. in the ints *-*.*, c. 

from the Center A,, through. theſe. 
points * "WP „ c. w right Lines, they 
— be the Proper. — 


Fos the Stile it may be either Plate oe Wire, 

Sevaced above the Subſlile to an Angle of 19 deg. 
2 min. and ſet up perpendicularly upon the Sub- 
aar, as in all other | Dias. Aud thas have l don | 
* E 


ing a 


Y angent (or EquinoRtial Line) erofleth 
te 1 aud che Ruler will eut the Semicir- 


ines belonging to. your, 


II. 27 


: 
N 
l 


* 


4 


„ 7 8 


U 


n. p 1 Mr hare: n 
he e 


How 49 4raw the Howr-lings a 4 North: Rerlin- 
ing Plain, Declining. Eaſt or Weſt, which cat. 
oof the Meridien. at the ee Hero . 

th Eqninoctial. 


per the OST" be & a Noth ruin AY 

ing to the Weſt 60 deg. and Reclining from 
the Zenith 32 deg. 11 mig. in al ann Tar. 
ie 


8 


* 


' 


Co's ne place | 5 "2h 33 - 

| ination of the Plain? 3 

Giy North Weft. | oe $a 2 
8 32 1 
. The Diflance of the Meridian and 
. an 5 4 


12> The Height of the pole or Stte Ay 

dove the Plain. 5 | | 

; Meridian. | | 

6. The Phy Diane of ln. 
78 


* 
* 


2 6 3 "7M % 3 < 4 1 |. 27. 2g EE 


ering 


kr. 2. 5 A C for the 
| Vertical Line of the: Plain. 


my Av here for Variety; mote than for Neceffiy, 
= in theſe three following Examples of "North 

+2 Recliners Declining, f wil (in the feveral 
Schemes) place the Zenith and Pole down- 
Words, becauſe the Stile in all theſe Dials 
* gs muſt point upwards, the North pole being al- 

. . ways elevated; and in fo doing, e Hour- 
Ti lunes, Stile, and Subſtile, will, fan in the 
== Scheme as they are to ſtand in the Dial ; and 
= _- the manner of the Work will be the fame as 
before. Wherefore, - bs 88 1 


| Saas; Set z 325 deg. 11 min, the Plains Re- 
elination; m Oto 4, and from C to B. A Ru- 
ler laid from H to a, "ſhall give you the point E, 
© through which, and the points E and O, the Ho- 
E _ Tizon, HE O' is to be deſcribed. | And a Ruler 
laid from H to 5, ſhall give. Tm 2 the Zenith 
point. es 
. Thirdly, Set. 60. deg. "he! Platt ; Declination 
from A to d, a Ruler laid from 2 the Zenith to 
4, ſhall eye, the: Horizon in 8, the South point 
thereof. s have you two points Z and S, 
through which to'draw the Meridian, whoſe Cen- 
ter will be in the Line QE extended, and may be 
found as formerly is taught, 


= 


Fanrthly, 


bo Y 
— 
21 a —_— 


| Fortbl, 


28 min. diſtanr from! the Zenith, ſet 38 fa -_ 
min. from * to F, and e lad fte Er to F 
will eut the a 9888 EA 
through which Pont and the Center draw 
he Line P Q for the Aris or che World, an 


Subſtile of the Dial. And again, becauſe he k E. 


quinoctial is 90 deg. from the Pole, ſer 9p d 
from F, and they will reach Juſt to oe on 
either fi de, which are the very Points that the 
Plain cuts the Meridian in, and 88. N 2, which 
Points and the Poĩnt E, in the Horizon,” t 

noctial Circle muſt paſs; ; Whoſe Center will al- 
"ways" be in the Axis of the World P © exten 


Tux Horizon, Meridian; and Equinodtial, being 


this drawn, you may find the four Requiſies jn 


inis manner. „ ; 12p 


1 To find the Diftance of the Meiden the | 


e A O. The Arch EO meaſured by 
your Line of Chords, will be found to con- 
tain 47 deg. 18 min. which is the Subſtile' $ 


_ '--> Diſtanceffrom the Meridian: 1 
2. To find the Height of the Pole 'or Keile above Mi 
the Plain P F. 5 Ruler laid from æ t „ MY 

1943 ur cut the Plain in O; fo the Diſtance" 8 1 
on the Chords 42 deg. 32 min. is the Height >" If 


- of the Pole above the Plain. 


3 The Diſtance of the Subſtile from the rid 9 


ee G, which meaſured upon your n 
wil be found to contain juſt 90 deg. 
ws The: Plains Difference of Longitude GP ©, or 
the Arch e G, as before alſo 90 deg. 1 


e 
3 1 
* 


The Horizon and Merid tn — | 
thus\dravn;; my a Ruler from Eto Z, and it will 
cut the Play in e; and ſeeing the Pole is 38 geg. 


the Pole of th World; 0 


* 


Egaui- 


ps 
* 


OY 
. s 


* 
re, 1 7 
5 % £3 ” 
1 FE) 2 n 
» 
* % 40, ww 


51. „ Du Pl {cutting the Meridian inde 1. 2 
* N With the Equinoctial. And, * 
1 HE Axis of the World paſſing through the 
ee Poim of the H both which de- 
note the Plain to be polar Declining, and the 
lila to be the ſame with the Hour-line of 
, and the Hour-line of 12 at right Angles 
* ' thereto, .. wherefore the. Ines e_ be. 
We is followed. 


T draw the Hude apes the Plain... 


E Fr Lay 2 Rules from P to E, e the- 
Y Meta and. EquinoRial interſect. which is up- 
on the Plais at the very Point , wherefore there 
begin to divide the Semicircle AG e, into 12 - 
- qual Parts at the Points OO ©, c. 

. Secondly, Lay a Ruler to Q, and every of. the 
4 Points ©-© ©, &. and it will cat the Equinoc- 
E tial in the Points“ , Te. an that into 123 


unequal parts. 
h A Ruler lad 10 p 8 and the ſeveral 
Ppints „ c. in the Equinoctial, will: cut 
{ the Plain in the Marks 1 1155 „ | 
Tah, A Ruler laid from Q to the ſeveral 
3 Marks, 11 Sc. and ſtrait Lines drawn there- N 
E ſhall be the true Haur- lines fitting this polar 
. Plain. 
Fon the Stile, it muſt be a Plate or Wire ſet up- 
* upon the Swhbſtilar to an Angle of 42 deg. 52. 

min. and myſt A 58 77 to \ the vos 4," 4p 


The a 


* ge th ns 


* 


* hm 3 OW 


e . 


5 KI 0 _ N 0 pee Se 
* | | TATA * LIONS 'X KI CP 


* a ca #4 on * 5 [1 15 N 


; . 51 

» $ 5 4 1 

arid 2 46 50 hs y : 
» k 


6 HA F. e e 


Hen ts drow the Haar-lina 

Plain, þ the dee, idle 
thro 
the al 


Things 4 wa given, and four found, ber 


225 <P, he 7 Plinp 52 _ 


* 


8 8 
8 S 
ot at ee A 
: de Se Si 


# 4 5 

* o e 1 3 
1 

1 


"2 42 deg. 
i 159447 15 £ Rt 
4. The Declination of the | 
Plain North W. C0" 7<0ts 
3. The Plain's Neclination- 16 bo 


A 
I 
4 2g 


ka ; 
#% + p 
* * - = 
” * 3 / 
32 5 is N. 
1 * . 
„ f Fe : MB 1 _ = 
Ee. # I T4 '+, = 
5 # 1 
4 , 4 5 "2 
2 > - = 
J N 3 .." = 
, 4 oa BS 2 1 5 


_ 
— a 
: "a 


LEI 


is % 

+ 
4.8 
* 


p $z 5 4" wn o44 5 18 

4. The Diſtance of me Men from - | b 
the Horizon. 4 
oy The Height of dne Pole or Stile a. 
bov e the Plain. 1 2 4 
3, The, Subſtile's-/ iſance. lem 1 
Meridian. | H 1 
+ Tha Plain's Difference of Lou. 7 
An 

Firft, Deſcribe the - Circle A HC o for the 


* * 


TY) 


=; 


1 and croſs it with the Diameters AC, and 


H O, for .the Horizontal and Vertical, Lines 4 


> | Seconds 


9 n 3 * 
> n I 1 * 8 WV 4 * 22 
r eg. N 
a+ 


- 
N 
* 
bo E 9 £ 
* * 
9 "Ss g * 
8 * Pp 
* 
'2 2 
= * & 
3 3 
* * * 
va 7 
4 


Secondly, (As in the laſt Example) ſet 16 deg. 


due Plaats Reclination, from 
Co North Dial. O 10 a, and from C to , 4 
Declming Weſt 60 Ruler laid from H to a, ſhall 
Reclining =—— 16 give the Point B, through 
Plate 6. Fig «Jt bY Which, and the Points H and 

0, the Horizontal Cirele H 


B O is to be deſcribed. -; Alſo a Ruler laid from 


H to 5, ſhall find the Zenith Point of Z. 


A to 4 and from H to e: So a Ruler laid from 


2 to d, ſhall cut the Horizon in S the South, and 
laid from Z to e, ſhall cut it in E the Eaſt point 
thereof; and now having two Points Z and ö, 
through them you may draw the Meridian Circle, 
us hath been already taught. 

Poartbiy, Lay a Ruler from E to Z, it will cut 
the Plain in F, and 38 deg. 28 min. the Comple- 
ment of the Latitude of the Place, ſet from F to 
F; and a Ruler laid from E to ; will cut the Me- 
ridian in P the Pole of the World, and 90 deg. 
more, being ſet forward from F to m, and a Ru- 


ler lad from E tom, will cut the Meridian in , 


the Equinoctial's Interſection with the Meridian; 
fo have you two Points ZE and E, through which 
the Eguinoctial Circle muſt paſs, and a right Line 
drawn through P the Pole of the World, and Q 
the pole of the Plain, will be the Axis of the 
World, and the Subſtilar Line of the Dial. 

Tus three Circles, viz. the Horizon, Mer:- 
wvian, and Eęuinoctial, being deſcribed, the fore- 
mentioned four Requiſites may from thence be ea- 
ny ons. Tor, 5 


. The Diſtance of the Meridian from the Hori- 
tion, is the Arch F H, 64 deg. 29 min 
| ; : "2. 


«<2 91 c Q Hyr gs) * 


mn — > © 


= "Charge, will giye.76 deg. 10 min. for. the 


Pointa OO O, &. and it will divide the Eg. 
noctial Cirele i enen paris in the Pointe 


$3 * EN ene RS TOR 
p . N N 
* 6 7 1 = * = 
F- C 
* 
3 b. 
>> 
- 
R 


+. The Hei ght of the Pole or Stile above the Plain 
* 806 R. ae Ruler laid from æ to P, vin cat 
* Plain i in v: So the Diſtance R = meafur- 
Will be 5 to be 30 deg. 39 min. 4 
"on Supile's D ance Ken ehe Meridian, is 
| Pa Arch I M, 64 deg. 26 min. ; 
4. The Plain“ Difference of Longitude is the An- 
HE E P Q. which to and, Ia lay a Ruler from 
and it will cut the Plain in D, the 
21 19 . D I. meaſured upon the Line of 


Plais 8 Difference of Longitude, week late 
91 eee uu, wpow! e Plain." 1 WO 
Da) v Rüber pen Pho Pole of the World. 


pi the IncerſeQion: of the Meridian with — I 
Horizon, and it will cut the Plain in D,. at which | 
Point begin to divide the Semieirele I D into 73 


eqval parts, at the. Points G See. F 
3: Secondly, Lay a Ruler from: Q to the ſeveraf J 


© * * 5 


oF Fg Ser. Das © 0971 1397 14. 0 207141 at 26% 122 121 : 
:Thiekly,' A Ruler: laid Gar P to every of theſe 
unequal! Parts *, c. will cut the Plain in 
theſt Marks 1 th Se. Wr on into 1 other 
ine parts. 14 ene e 
Laſtiy, If you drawsight Lines from Gees 


every of theſe Marks: 1:1, c. they ſnall be the | 


true Hour-lines belonging to your: Pla. 
Tux Stile may be either of Wire or Plate as in 
other Diali, and mutt be elevated above the Saë- 


tile, to an Angle of 30 deg. 59 min. and muſt: 


ſtand e or at right. ge eee 1 
HAT * fie ith cot, 


* 1 - * 6 ö * * G IT * 
0 g , * 2 nn * ; * 1 7 rg” * COT FL OR . 
K ” * x 8 2 l **,. ., = 7 "4 a 2 
2 — 9 . 
Ss 
* * = 
„ 
: 81 4 „ 
$a 7 ts 


| CHAP. KV. 
| How 35 as Homr-lonies ab a North Reeli⸗ 


ning, or Inclining Plein, Deelining Eaſt or Meſt, 


tubich duterſectt the ere. and Fe: Equi- 
 woltial and abe bigrizen.” 


L. T. his third and laſt: Bamse North Re- 
eliners Declining, be of a North Plain, recli- 


the Latitude of Lenden, 52 deg. 32 min. 

Anis being the third and laſt Variety of decli- 
ming. men Plains, 1 mall de fornewhbat the 

larger in the 

in any of the fbregoing; not but that this Dial is 
to be made in all teſpects like (and with the ſame 
Fake} as the former. But herein I ſhati ſhew at 
large the Manner of Projection, and how all the 


Cemers: ere Geomerrecally found, and the Reafons 


e their being in ſuch and ſuch Lines, and at ſuch 
F  and-{uch Diſtances; And alſo, I al project all 
| the Hour. lines belonging to the Plam upon the 
Hair it {elf by circular Lines, by which Means 
may attain to a more competent K now · 
ledge i in what hath-been heretofore in this Treatiſe 


4 delivered: For from this Projection following, all 


_ the aforeſaid hath been deduced. And therefore 1 


ſhall deſcribe the Manner of the delineating of this 


Dial, en following Propoſition. 


ming 54 deg. and declining Weſtward 60 deg. in 


rogeQion: thereof, than I have been 


8 c / PR O- 


PROPOSITION. 


I P L A T E VIL. 
i» | | | 
| 4 Circle * deſcrib Deelin 
fs | Cine king dhribe, 2 caving 2 place ms 
Meridian, Horizon, EquinoQial, Pale, Zenith, 
Sc. with ol uber dete, belomginig 10 ſuch a 
— Dial. Aud alſo, ect tbe — of cela 


: 2 pro 

* Sphere [elf apox the Plain, and. from thence 20 
n draw the — of RN . 
: "ng to their true Siuation. | F 


Le Circle HSO B. EIT, a Dion 
in the Latitude of London $8: deg. 32 

from the North towards the Welt 6a C 
deg. 00 min. and reclining from u Zenith Nen 
ward 534 deg. 30 min. 


S B, cutting each other at tight Angles - 
in the Center Q 1 3 the Plain n 

54 deg. 30 min, take 54 30 min. out vont 
19 —— and ſet that Diſtance upon your 
Plain from & to 2, from O to i, and from B to c: 
Then lay a Ruler from H to a, and it will cut the 
Line 8 B in Z. ſo ſhall the point Z be the Zenith 
of the Place. 

Secopdly, Lay. a Ruler from H to b, it will cut 
the Line 8B in i, ſo ſhall 4 be @ Point in the. 
Line 8 B, through which the Horizon ſhall paſs :- 
And thus having three Points H 40; you may 
)- - I through them deſcribe the Horizon, w ee; | 


205 Ceols Aug Cacle with the two Diameters | 4 | 


will be at m, the Diſtance & being equal to me 
ut of the Complement of the Reclination of 

the Plain; namely 36 deg.” Or Geometrically 
thus, Draw the right Ls k O, which divide into 
two equal parts in-z, and upon the point u, raiſe 
a Perpendicular „ m, extending it till it cut the 

Line 8 B in , ſo fhall m de the Center of the V 

. Horizontal Circle HO. th 
- Thirdly, Lay a Ruler from H to e, it will cut 

the Line S B (being extended) in the point: N, ſo 

ſhall N. be the Nadir - point. N 2 

ti  Faxrthly „ Becanſe the Plain. dedlines: 60- deg. | 

| from the North Weſt ward; ſet 60 deg. from B th 

to % and laying 2 Ruler to 2 the Zenith, (which (c 

is alſo the Pole of the Horizon) to 4, it will Cut PL 
the Horizon in 8, A which _ the: Meri- 8 | 

- dian muſt paſs. 1 a: 
Fifthly, Take (always) gene <5. of your Line if 

„ Chords, and ſet that om 4 to e, and} | © 

E . © laying! a Ruler from Z'to e, it wil cut the Hori- th 

20 in w the Weſt point thereof, and a Line _ 

draw from to; through Qthe Center of your Plair, | be 

will cut the Horizon if you extend it as here is I + 

th 

tl 

ſe 

te 

th 

2 


done) in E, the Eaſt point thereof, and in ſome 
part of this Line (extended if need require) will 
the Center of the Meridian be; me WROE: that 

; Point wilt fall may be thus found. 

_ ** Sixthly,' Divide the Line Z N into two Guat 
parts in F, and upon F erect the Perpendicular F 
D, cutting the Line Qu (extended) in D, ſo ſhall 
D be the Center of the Meridian of the Pace. 

Seventhly, If with your Compaſſes you take the 

Diſtance B P, and with that Extent upon D, as 
a Center, deloribe à Circle, you call find that f 4 
Cirele exactly to paſs through the reſpective points 1 
Z and N, if ages PO no Tour * red tt 
in your Work. ee eee 011 | 

Hye E f  Eighthh, 


__ e > 


* 


Eighth, 8 the ers of the Pole abot e 
the Horizon, is equal to the Latitude. of, the place 


| viz. at London 5 1 deg. 32 min.; ſet ff 51 deg. 
ally 32 min. upon he. Meridian, from 4 7 5 n 
to Manner. 
iſe Ninthly, Lay a Ruler from 5 the Weſt-point 


the of the Horizon, (which is: alſo the Pole of the 
the Meridian) to S, and it will cut the Plain in 5. 


laid from w to 5, will cut the Meridian in P, ſo 
lo is P the pole of the World, diſtant from Z the 


Zenith, 38 deg. 28 min. and a Line drawn thro? 


eg. Ip the pole of the World, and Q the Center of 


* | | the Plain,” will be the Axis of the World, and 
. See will cut tne Meridian 9 M. the South 
ag Sn 02 11-604}: 
1 Ted, ye Meridian and Horizon 3 thus 
n . drawn, it is. eaſy to deſcribe the Equinodtial ; 3 for 


ad if you. confi der the poſition of that Circle in the 


through the Ys and Weſt -points of the Horir 


«9; | | 00, and cutteth the Meridian, atfright Angles, it 
„I being in all. Places go deg. diſtant; from either of 


the Meridian) you lay a. Ruler to P the Pole ef 
oe 1 any it will cut the 8 85 — if, you 
et go deg from f to g lay a Ruler tom u- 
to g, it will cut the Meridian an in A; fo have you 
three Poiats, through which the ZquinoQial maſt 


Equino@tial will be the Axis of the World, ex- 


muſt, 


* Line E w, erect the Perpendicular, GK, cutting 


Center 


then ſet 51 deg. 32 min, from 4 to. . A Ruler 


the Poles. Wherefore, . if upon * (the. Pole o 
0 


Eleventhly, Divide the Line. E Wh into two e- 
qual parts in 12 and from the point G, upon the 


ä "WO TN * "I ö 0 * 
” q IS "= — e 2 N A 2 r 4 
#7 l * 1 O * 7 TIE > FE 9 Y 
Kew” Ss , 6 * * 
— * 
_— lung. 105 N ö 
3 - 
* 


N ſelf, you know, 72 it; always paſſes 1 


paſs, namely, E & and 1, and the Center. of the 
1 | tended if Need require. To 0 Which. ow Bo 


the Axis of the World in K, fo ſhall K be hs M 


eee nar: if upon 


Kess Center, with the Diſtance K w, you de- 


ſcribe a Cirtle, that ſhall be the EquinoQial, and 
(if your Work be true) ſhall paſs through the 

ints E and w]; then for the dividing of the 
| umoctial. 

> Twelfebly, Lay a Ruler to P the pole of the 
World (w ich — * the pole of the Equinoctial 
to E, the Interſection of the Meridian and Equi 
quinoQial, and it will cut the Plain in the point 
x2, at which point you muſt begin to divide the 
Circle repreſenting your Reclining Declining Plain 


into 24 equal parts at the Points 0 ©, Sc. 


2 


This done, lay the Ruler to the point P, and eve- 


ty of the 24 equal Parts © © O, and you ſhall 
find it to cut the EquinoQial Circle in the points 
, Oc. dividing that Circle into 24 unequal 


parts, through which unequal parts, and the two | 
Poles of the World P and M. in muſt all the Hour | 


* Thirteenth, Divide the Line p M into two e 
quat parts in the Point L, (or, from the Point D, 
the Center of the Meridian, let fall a Perpendicu- 


— paſs. For the deferibing whereof you | 


Jar upon the Axis of the World, which will fall | 


in- the fame Point L) and through the Point L. 
draw-an infinite right Line at right Angles to P 
M, namely, the Line C T, for in that Line will 
the Centers of all the Honr-liner be found, and the 
Manner how to find them'is thus (one way) to be 
effected. | 

Fourteemtbly pos the point'P as a Center, at 
the Diſtance P L, (or to any other Radius of a 
Line of Chords) deſcribe the Semicircle X LV, 
and divide it into 12 equal parts at the Points 
3 Se. beginning your Diviſion at the Point J, 
Su 1 where the Ruler being laid from P, 3 


F on. at an Odin a Mak. 


EF Eo eo Cy ne oY 


. ²˙ . ES HS I It) 


and the 2 
cut the Plain, you draw ſtrait Lines, thoſe ſhall 3 
be tfie true Hour-tines proper for ſuck a Dechnation , ð 


drawn Circle. Then laying a Ruler from P, up- 
on each of theſe: Diviſions, you fhall find it to 
cut the Line C T in the points 15, 30, 45, 60, 
Sc. on either (ide of the Point D; and here note, 
that 15 is the Center of the firſt Hour's Diſtance 
from the Meridian on either Side thereof, the 
Center of the ſecond, and 45 of the third aur 
Diſtanee from the Meridian, ce. 
Hffteenthiy, If you place one Foot of your 
Compaſſes upon 15, and extend the other to P the 
Pole of the World, and with that Diftance de 
ſcride a Circle, that Cincle-ſhall be the firſt Hour 
from the Meridian, and (if your Work be true 

dall paſs through M the” South Pole; and alfb 
through 5 „%, the two firſt umequal Diviſions of 
the Eguinockial Circle, and ſo all the reſt. 
Lafiiy, If from Q the Center of your Plaix, 
ve Points where the Hour circles 


1 .. 1 5 4 N f = 
Ez * f 
7 , us you dlection 
. 
- * 4 N EF 7 i Wa 7 * 1 * — 
+ W 7 43 £* * * | * 18 N x 7 3 
43 Ci» 44S i * 4 1 N 
5 * ; 4 
A: * 47 


FIR » 
y «7% 4 * — 4 = * 1 
for 229. 2 75 
" 7 C 2 
"br" 3 S \ | : 4 * « * » % * ; 
; ? + 1 F; # 2 1 2 — 4 1 4 4 a >, & z 2 my 15 1 þ 11 # 4 2 4 3 


+ LF 8 n 1 
4 3 q 7 
\.S 1. 74 4 
* EDA 4 4 

163 EST 


£7 2 
%. 3 14 TE? 
3.3 n 


_ Geometrical Dialling. 10 ; 
D (the Center of the Meridian) cuts this laſt 


_ — 
* . * > 
N 3 n * 
a * * 8 
* z . 
4 : 
* "24 
5 4 
8 8 J * 
x VE * * 
*. » 
4 * 
4 
YL £ 
. 


F # 


3 


e Nn ps Han 


The Height of = 10 
Pole above the 
Plain. 

. The Diſtance of the 
Meridian and Ho- 

Ei tizon. 4 I 
. 115 Diſtance of the 

+ Subſtile . from the 

Meridian. 


4 2the. ep Ms etidians. 


p ALL which may. N. 38338 CE Frojec 
tio Gang Meir Quantizies fund, As,. ., 


TP * 44 10 42 wg 2 HOT 18. 241} 31 
ke wag _ find e Rulet. Ram P F $0:w, 
| ai eure dojinter 


BY _— NE 4 eK Rake cut the Plain on the 


FX 


Line of Chords, will be 54 deg. 43 min. the 
Height of the Pole above the Plain, (or PQ 


Ub 5 @f half Tangents, 
b will c Aeg. y mi ng he Comple- 
2. To fin} Fr, e At N 1 meaſured 

upon the of Chorke, will give 53 deg. 


31 min. the of Meridian from 


the Horizon. 

3. To find C A, the Arch T A meaſured up- 
on the Line of Chords, will give 56 deg. 41 
min. the Diſtance of the Schale from the 
| Meridian. 


10 


. the es 26 eee 1, n 


& „ The Angle 8 1 3 * 6 47 


other ide at x; ſo A x meaſured upon the 


Geometrical Dralling. 


 "Geomerrical Dialling.” 


7 To find P Q, Lay a Ruler to P the Pole 
of the World, and the Interſection of the 
-- Meridian and the EquinoQial, and it will cut 
the Plain in o, the Arch o B meaſured upon 
the Line of Chords, will be found to con- 
_ tain 61 deg. 47 min. which is $ the 200m be. 
2 tween the two Meridians. EIN CERT, . 


Tuus have you in this Scheme, delivered the 
true and genuine way of delineating Sun-Dials, 
deduced from the Sphere it ſelf, by which the Rea- 
ſon of all that hath been before delivered, is ren- 
dred obvious, and ſufficiently. demonſtrative for 


this place. But here you ſee, that the Centers of 


the Meridians or Hour-circles fall out to be very 
remote, and that there will be required a large 
Tangent-line for their Deſcription, which will: 
(for the moſt part) run out very far, and fome- 


gent- line, or without projecting of the Hour - lines 
this, though this be more ſatisfactory to the inqui- 
ſitiye Reader, who will not be ſatisfied! only with 


what he does, and it is for the ei of ſuch, 
that l have here ERA this e cath 145 


* 1 
x" 9 as 


F N 2 
Legs” hs. 
% F4 F L . 7 - * 4% \ 
* * #1 7 . © = 
; 7 7 7 * * 9 
5 "- * 7 ; * 
X* x . 
* 
* 


% +» 1 


times, almoſt to an infinite Excurſion. I therefore 
choſe rather to ſhew, how the Hour-lines might 
be drawn, without having any Regard to this Tan- 


pon the Circular Plain, and therefore the Ways i J 
before delivered are far more apt for practice than 


the doing, but of the underſtanding as well of 


= E450 ME . 3 in 4 
e. H * P. Rn. 5 
= * Nonlin ling} both Bark ws 
| E: 3 5 c lining. | 5 
5 s tine ick ai no 's rr 
05 Realining Plains there are but two Sorts, as 
'Y [hath been before inſtanced; and thoſe are ei- 
- ther: Direc: or Declining. The Direct are thoſe I 


1] | 4 Reclining: Places: which: doidirxctly beboldi the Eft, 
* M̃eſt, North and: Sogrth! Points of the Horizon. 
2 Aud, the Declinert/ are thoſe which) (beſides! their 
3*—— the Zeni * 3 
2 r Cardin Points, 2 

1.) Tbe Sozrh and the Meſ. ig; 2: 
The North:andithe Weſt: « 63 ate 2 
Thee and the BAH. . 00 
_ - 3,14) n and: che ligt. * e 


„ 4 
10 2 23 2.2 2 


bicd beton bed, Had Ae e that 
2 es Recliners, there werd three Sorts, vi. 
x; SUCH as Reclining from the Zenith, do be- 
Ry hold either the due Eaſt, or due We ſt Points of 
tze Horizon; and of this Sort there is only one 
2 Kind, and no Variety in any Caſe. —— 

N Seh 1 of, which there are three 


4 # ny 5 2 Recliners, of which alfo there 
| 4 1 ae three Varieties.— 


Sas — 


* 


* 1 
2 j —̃ ＋— 


ä — — RN 


— 


— 


7 


3 


. 
2 ek es, oe 


+ +> + #4 
* 
— 
” 


o 
7 1 * 
c * 72 0 «hs 0 
2 X , o * „ 
+ 8 — Ly" * 
f . wi + 8 1 


* * 


p 


. 


1 
85 1 - 1 
f 
Co '4 
; : 4 
4 * 
2 2 
a FEST 
2 * = _ 
* : N 
: + . 
>» '% 
* wE- > — 4 


: 


F 
= 


3 td" 
* 


pe bn 


. Tx 5 N 
N , 8 : 4 
* 2% * ay 2 - Y 
5 _ y-W „FEE ²˙ TT ns 
x N 3 


« * 


Lf. n * 5 

2 by „ . 

2 A 
5 eee 


5 1 i e e 
2 PAS ICIS — 0 8 #: £542 | 


i Crag 


"a 8 
S LI WADE a5 


„„ 
* ” 4 


755 F 


F 


"D 1 


ai 
: 


** 


— * 
i 
* 

[ os. - « 

Oh 
* 

- þ * 

3 1 bs 

. 


1 


9 Os | £58 
F4 < . ts * "RET 
3 1 CY 


r 
3 7 


2 3 
e 
* * ” * 1 8 O 
: i ? % WW 
" 7 3 
8 8 0 f 7 \ 
£ * * by L 
« : -% " 5 4 
A 


WA. 
1 
2 2 
= we 
os 
: 
250 
r ee, 
> 
_ 
2 
. 
* 


— 
. 


2 
»% 


* 


ee eee eee e eee 
* 
3 
0 
{4 
$26 +> 
1 
* 
Pk. 
* 


Tz, 
-— 


oe hs 
* 
* 
25 
* 
* 
N 
1 
* 


* 
NN 
96*«„v 
: 


* 
of 


5 
> 
- 
- 
* 
Nv 0 
* 
o 
. 
. 
8 


„ 


„ Ae bk at 50 — 
$4 i * K 3% a” * 


” * 


* * 4 
* Su . 


per n — K oy 7 3 5 
£ 9. 
— 4 


= * * 4 . * 
4 4 * v rn” e 72 — 
— 1665 te Sv 2 . bs „ af SO E oy 


l 3 6 1 Bf , . . N a 1 me * 1 _—— >. 
; %% ĩ ET ot Eo ei es ag. eee eee Wi ror ts CR ef Be 
x * ? 3 e * , 1 5 
4 


* my * 5 


1 : ; 3 IP EY ; . 3 1 r * . 
1 : ; : 5 — 4 2 "8 


5 ea OL 5 


„ OY e ney rep. ah 


» 


8 — 


T2,” 


t. Genmerriit Dialing J 


PI Of Reclining 7 Declining, Itold you wee 
were ſix Varieties alle, as there were of Direct 
Recliners, viz: Three of South Declining Plans 
reclining, and as many of North reclining Decliz 
ning Plains; of all which I have given Exam hey 
and ĩt may *be now expected that I ſhould do the 
like for the Inclining Plains oppoſite to them, of 
which there are alſo as many Varieties, but ſeeing - 


177 


that the making of the reclining Dial, whether 
Dire or Dethning, doth alſo make the Inclining | 
8585 *whether Direct or Declining oppoſite there- 

nto, I:ſhall dere the Labour, and commend to 
the Ingenious Reader ſome few Rules by which he 
ſhall eaſily frame the Inclining Dial out of the Re. 


eliner. : Ta 


FE: Of North and Sonth leren. 


1 will take for Example a South Plain, weiin 


ing. 55 deg, which is the third Variety 


of South. 


Recliners, and I would from that Jedioe the Hour 
lines proper for a North Plain inclining as much, 
viz. 55 deg. And it is eaſily effected. For, 

Ir you draw the Hour-lines of the South Re- 


cliners 6A B 6, and the Stile thereof al- 


fo, quite through the age 
oppoſite part of the Plain, 6 C 


ſet the fame Numbers to the Hours on- 


to the Plate 6. - 
0 6, and Fx. 4. 


the right Hand in the Recliner, and the con 


as the Figure clearly demonſtrates: And let the © 8 2 


Aris in the North Incliner point downwards to 


is finiſhed, Or you may 


the South Pole, as the Axis in the South Reeliner 
doth upwards to the North Pole, and your Dial 
effect this Work by pre. 


ing off the Hour-lines through the Paper, and 
turning it upſide down, and that will effect the 


Tame thing, only change the Names of the Hour: 


a» . — 
5 2 - ö 
0 1 
: 5 1 
8 ; "—— * [3 * 7 * 
£ ſ 
» 
* 9 zo 
© * 
— * 
# I {3 * of 
x 
* 3 i 
TE * . re = 
8 9 * 
l 9 5 
8 1 


= % 
= 
4 4 

* 

4 > .— we 
of * 


3 


- = 
4 70 by” A 
_ % 1 + 
5 . = 
a 1 i 
+ 


x bs bY A 


4 . Ax 


4 3 damm Dili. a 


again, is you turn the South reclining. Plain, 

'A Bs about, upon the Center © till B Line 
A'B come to be in the place of C D, then will 
the Hours, Stile auch all, = truly. named and poſi- 
ted; and the very South Recliner will d the 
North Incliner withpur any Alteration. 


k 8 1 of: Eon and Weſt. Incliners.. 55 


139 is little Difference i in drawing. of the 
Eaſt or Weſt. Iuclining Dials from the reclining 
Dials oppoſite to them, from drawing the North 
| Incliner before from the South Recliner. For, 
_ -» In the Example of the Eaſt and Weſt reclining 
and Inclining Dial before going, Chapter 10. The 
—= Dial. as it there ſtands, repreſents an Eaſt or I eſt 
= reclining Flas. But if you turn the Dial about 
=. upon the Center Q, till fle Letter N come to be 
in the: place of the Letter 8, in that Figure, then 
Will the ſame Dial repreſent both. an Eaſt and I eſ 
Dial Inelining 35 deg.-as now it doth an Eaſt or 
= Feſt reclining, as much. The Subſtile, Stile, Meri- 
= dian, and the reſt of. the Hour-lines retaining the 
ſime Names or Denominations, as now they do. 


3 ul. Of North or South Declining Inclining Plains, 


1 Or North and South reclining Declining Plains 

: there were fix Varieties, Examples of each have 
= largely given. There are as many of North 
and South Incliners, but ſeeing they may be fo 
= <cafily deduced out of their oppoſite Recliners, |[ 
ſhall forbear giving Examples, and the Way is not 
much differing from the, Rules. before given for 
Direct reclining and inclining Plans. For ſeeing 
the Reclination is-alike proper to each, and the 


„ee er the Subltl from the Meridian in 
de 


Y A * _ 2, Pp Pp ; 1 a , 
5 — n . ; a ah (20s $0 EN . * ane 8 9 2 . armee . 

r 9 * * n Tot * 82 1 a el ; 

ve 9 e SLES | 2 N * * TVET N 
by bf TY : , = * 4 * 48 8 de Ru * % OX ar” | OM | 4, 7 * 

$445 = a 13 . 
, ' f a — 
# £ C | 
| . . 6 0 
. F , : — 

* * : be 
. I 


the Declinations do ſo directly agree, they may 
both be reduced to one and the ſame Dal, as the 3 
other were. YO a ol donogs, 5 

"Taps, If any reclining Dial be ſo inverted, 
that the upper Part thereof become the nether, nd 
after this Inverſion the right Side of the Recliner  - i 
become the left Side of the Incliner ; and the con- 
trary, the Inclining Dial having the ſame Declina-- 
tion, ſhall be framed out of the Recliner, and the - FF 
contrary. Only the Denoniinations of the Hours - 
muſt be changed. For the Fore-noon Hours in 
the Recliner, will be the After-noon Hours in the | 
Incliner; and the Afternoon Hours of the upper | 
Dial, the Forenoon Hours of the nether. 


« _—_— 
- ? = 
N * My - PE: 1 
- a " id 2 * bar N 
by = 
- ' 4 — . 
: L . 85 1 5 7 A 
4 1 - y | 4 
; \ 2 +. =» 
Y — 
= 3 7 oo 
* E „ 4 
. : 4 +4" - 
* 1 
0 8 o& . 
0 — 1 3 1 . 
8 * W 4 by \ i 
— 550 * 74 
« 4 9 
i * 1 X , 
7 * : 4 5 4 1 8 1 
5 * A + 7 
* - 3 8 Fe % 9 
5 
, 4 1 
x - 3 X 
*» 


* 


AP. XXVIIL 


A General Rule to know which Pole, whetber be 
North or the South, 1s to be elevated over any Mi 


Plain. 


'F HE Stile of every. Dial reſpecteth (or rather.” 

lieth parallel with) the Axis of the Word, 
and always: pointeth upwards or downwards, to Mi 
one of the Poles. Now when you have draw n 
your Dial (though truly) you may be. to-ſeek, = 
whether it be the North or the South Pole that. Þ 
muſt be elevated; wherefore to avoid any Miſtake, 
and to inform you which Pole is to be elevated, 
Obſerye this General Rule. | 70 


£4 
9 1 


— 


; ; 4 
e . + + -£ 
| [25 5 9 

of « * » ©, N — 4 # 
5 . 1 * 
, 4 F "2 
1 * 
8 2 
4 - - 82 


4 - nt 
dn uno 
udo -ap 1 
Pon 
10 
a 


*. 


uml 
a 1 
nog BOLTS. ufo yinog 

10 D wo 
TR 


1 


: nog 0 S2UHul, 
5 30g ap | 


1310 N - eee 


5530 
pur ye 
lle uodſi 


JON aogy | 2y2 uod muy. 
2049 2p 2py < -ap 10. Pop eh“ 
ns ) "SUPLq de lie node! 


qznog © 


** 


.. - - © w 


TT R on 


— 


ft 


WS 
=o5 
<q 


1 * 


red, thete' will be 


no Difficulty to find which is elevated 


$27 = ® 
4 


+. 


2 A 


* « 
* 


* 


being duly obſe 


# 


* 
* 


— EI 


— —Lͤ—ͤ—— mn”. — — 


„ : ; 4 f I”. 7 P 2 a * : £400 > 7” 
= = Lit ; AAS 0.7 £3 2 Þ TLV Ann 2; "+02 % . ile 


+ 
S* ky” 8 " 5 a 4 ; . 7 * LY 
G * * 3 e ; , n 2 l 4 / 2 E - 1 1 3 F% 
8 ee I x » al E 5 Has Chas ES 1 3 11 1 * ME 5 
» * N * * * * * * - % 
: E Gs wo „3 4 9 N 25 th n 5 , 7 Wa . 
Fes N 2 * . 3 * „ en > f5 * 'F i 9 3 F 4 3 * f 8 E 
1 x 4 # 5 FY WY E*q f : Ex. + 8" ; * 5 l * s Py ** * 1 "ey 4 we & 5 ® 4 


1.0 b 


110 2 bot END 


„ 


yy ta + "2d k LES ST MES OY : 5 9 * 
ide vs VT e009! einn waeren N — 
, * . = 
d) ; "= 


1008 gy . 0. NC 1 8 | forme . 3 
— AJCOINCTLICALEY: | Perfor, N 


— * . 7.8 

x 5 « 0 —— * * E * N N ke 

„ IT A 0 wet (4661 2443 5 : a qu oak 80 74 e Az 

: * 1 * *  $* 7 * 

1 4 * * =- t 7 
a þ 4 

3 N | 7 J 
* 
2 N * 
ae hk 
* * "7 ” } A 'S * | 
3 


N e loregving Firſt Patty 8 don. 
a moſt abſolute and perfedt Way of 
delineating San Dials upon all forts. 
of Plain Superficees in what Poſition 
ſoever ſituate, and in any Latitude, 
whether the Plains be direct, or do dociing, . ge R 4 
Whether they both decline and recline ::: And 2 MY 
you may. there find, not only the manner how » i 
to make Dials, but to know the Grounds ang 


F 8. of delineating 
* ; arid in all Places, as is 8 taußht; 5 Jet the Ways 


? dual Divitions of the 


* ing) till afterwards : And the reaſon 
ing, will of it ſelf appear, when I _—_ come to 
= ww 2 them. : 


n . 
N e R 


r 9 
8 
ä 


* * Ka OS te ae > eas ES As tet i e « WY Oo 
—_ A a N N 
$ g ; 2 a : — 
« ON, ty» - f 
- 5 ” 4 
5 © — 
A ; * * 6 4 
by 
J 2 
6 WA 


mn of Diali, . deduce 


Su 
hy; wipes penn the ExaQueſs and Rati- 
Homr-lines upon all Plains, 


ere de ed, - may. Cin f Caſes, at ſome 
imes) be found inconvenient to 2 in Practice: 


As (1) When the Centers of ſome of the Circle 


fall out to be very remote. (2) When the une- 
Equinodial Circle come very 
near or cloſe together, which they will, al ways 
do, when the Pele hath hut mall Elevation above 
the Plain, and ſüch like. For the” removal of 
which Inconveniences, I ſhall in this Second Part 
add another Geometrical Way of Dialling, which 


3 hall be both plain, eaſie, — 3 and quic ' of Dif- 
1 patch ; and all of it performed by ſtrait Es, Wi 


not by Circular Lines, as the fotmer W 


EF quires. And moreover, this ſecond Way hath 
| A Convenience, 

Mays ef Di. 
- ofa the Plain, by almoſt infinite Excurſions: For | 
min this Way, having firſt made a preparative Scheme | 
upon Paper (or Pa 


whereas moſt other Geometrical 
are liable to out-run the Limits 


rather) you ſhall have 
but very few Lines to draw upon the Dial. Plain 
but the Hour-lines themſelvee. 


Ix this Second Way, I ſhall be brief, beginning 


frſtto'ſhew'how: to deſcribe the Hour-1 lines upon 
Upright Declining Plains; referting the Delineatj- 


on of Hours upon the Horizontal full North, South, 


Eaſt, and Weſt Plaus (whether — 2 8 5 
r myTo do- 


e r to eige- 


from the; Serre of 
18 Globe  projegcd in Plant, vpon the DiaFplain's 


—_—_— 


c . 
Y — . XI 


dau Dialing: 117 


| 0000000000020090909! 


= 


* .-= 

, : » * 

- * 2 i 

Cc T 0 N , P ; Þ 

8 T N i ; 13 5 
7 5. 

- * 0 
8 * 
x 4 


Hew to 2 the Homr-lines upow an Upright Sonch \Y 
Plain declining from the South towards the Weſs 
20 deg. in the Latitude of London, 31 d. 3a 


Av IN G: the Latitude of the Place, and 
the Declination of your Plain given, before 
you come to draw the Hour- lines upon the Plain, 
you muſt elt am Your PRE: ark as» 
art followeth.... ' 9 


H 


Ch No 4 
E L Ham, zo ug a e Scheme 2 to- 
1 a Declination i in any Latitude. Pl. 8. Fig. 14. 
e; 

th Firſt, With 60 deg. or the Radius of your Scale 


al of Chords, deſoribe the Quadrant of a Circle A 
ts B D, F Side BA to C, ſo that A'C 


r de equal to A And then draw the Right Line. 
e | 2 
e  Sacondly... On the kost B, erect the Perpendi>- 3 
n | cular: Das mn +: . 
Fah, Take 51 deg. 32 min. (the Latitude) 
g cout of your. Line of Chords, and ſet them from 
n | Bto F, and from D to G, and laying a Rulet 
from A to Hee and Anu tra) the two Lines F ws 
„ ad Glo. 
- | Fourthly, From the point, 6, draw 721 Tie 8 
- H, 2 to D A, or perpendicular, to BA. 
d | ufthly, Take 20 'd (the Plains Declination) ' 
2 out of your. Scale of "Chords, and ſet them from 


| D to E, and through the Point E, draw the Line 


EL, lel to D A. 
13 „ Sixably, | 


* * 


* 


2 ä n 3 9 
* c * 4 * 
1 7 * 7 N % 


Scale ot Chords) taken in your Compaſſes, . ſet 


one Foot in the point D, and with the other de- 
 feribe the Arch A O, which divide into three e- 
-” qual parts in the points P and Q, for the whole 
Hours, each of which three Hour-ſpaces. AP, P 
Q. and QO, divide into four equal Parts at, 
, '**>. for Halfs and Quarters of Hours. 
Which dene, if you lay a Ruler to the point D, 


and the points P and Q, the Ruler will cut the 
Line A C in the points 2 10, and 1 11, and by 


theſe points the Line A C is divided into three un- 
equal parts in the Points 3, 9, 2, 10, 1, 12 and 


12, repreſenting four Hours. And if from D, 
you lay. a Ruler over the ſeveral Spaces in the 


Hour-line A C into four.unequal parts for Halfs 


and Quarters of Hours. And thus is your prepa- 


rative Scheme ſo far finiſhed. Wherefore now 
Iansgroceh. 


II. To dram the Meridian, Stile, Subſtile and Hoar- 


ue apon the Plain it ſelf. Flas 8. Fg. a. 


A Frrſt, Upon your Dial. plain draw a rigbt Line 
25 ST, for the Meridian, and Hobur-line of 12. 


Upon which, aſſign any convenient point, as R, 


for the Center of your Dial; through which point 


N, draw the Line R W perpendicular to 8 T. 


_ ©. Secondly, Out of your preparative Scheme take 
* "the Line B K, and ſet it upon "your Dil plain, 
from R to T; alſo, from the preparative Scheme 


take B I, and ſet it on your Dial plain from R to 


W, on the right Hand, becauſe che Plain declin- 
eth Weſt, and from T to V, make the rectangled 
. Parallelogram RW V T on the Eaft de. 


r £ 


Sixthly, With 60 deg. (or the Radius of your 


4 


„ % 14 
* . 0 
7 4 I . E 


4 1 


nnn ard3-tn 4 * A . [PR OY" „ \ nn * 
FP R 9 * * * 25 — Þ, 2 . 
* CER Tg ' J 

1 L * 

* > 3 8 


ö * i * x N . 1 . BY TY * 2 ea nn N 4 
OP 7 % [5 : , WIE Ny * by THE = "7 N 
” A T3 5 > EC 
. - I 
x 
4; 
* * V 
1 5 5 * 4 
þ{ 1 : 5 
* 
4 
be. 
= o 
2 
8 


birdy, - Ont of the nconarative 9 we 
the Line IL A, and ſet it upon the Dial. plain from 


T to X, and from W to ©, and draw the Lines | 


R X for che Subſtilar Line, and R © for the 
Hour- line of Six, which draw. quite through! the 5 


Center R. 


Four Out of your preparative Scheme, take ; 
the Las E L, and ſet it upon your Diaitplasn 
from R to 12, and from X to V, perpendicule 
to R X, and draw the Line R Y for the Axis . 'Y 
Stile) of your Dial. 3 
Eifthly, Out of your preparative en take — 
the Line G H, and ſet it on your Dial-plain fim 
Rto Z, and draw the Line Z 6, parallel to W 
V, till it cut the Hour- line of Six in 6. . "0 
Sixthly, Make R 6 above the Center, equal to | 
R 6 below the Cerner; 4 draw the two Lines 
12 6, and 12 6. | | 
.Seventhly, Out of your Dial pla take the a 
Length of the Lines 12 6, and 12 6 ſeverall > 


ſet them upon the preparative Scheme from B — ” 3 
and from B to 2. And laying a Ruler from © t- 


a and , draw the Lines MC, and N G. I 
Laſtly, From the point A or $6: S5 take the 3 


2 Diſtance to the Line N C, and ſet that 


Diſtance upon your Dial - plain from 12 to 5, for 
it will (if you work truly) divide the Line 6, 12 
into two equal parts in 9. Alſo ſet one Foot of 
the Compaſſes in the point 2, 10 in the Line AC 
of the preparative Scheme, with the other take the 
neareſt Diſtance to the Line N C, and ſet that 


Diſtance upon your Dial- plain, from 12 to 8, and 


from 6 to 10. — Again, ſetting one Foot of the . ] 
Compaſſes, in the point 1, 11. in the Line A C oft 
the preparative. Scheme, with the other take the 
neareſt Diſtance to the Line N C, and ſet that 
nce from 12 tO 11 1 *7 from 6 to 7. So is 


* 


DO IS * T9 8 AD N TIF : A 1 2 WI 4. 1 R Ad aid . 2 
2 * 9 S 2 * fn. In. 7 of 12 as dh Aha * 6 . 
W 3 2 „ ĩÜwüꝛꝛ ⅛ ůͤ -Uu-n;fßf 88 9 2 Wn r 


ä 
$f 4 ES 2 
x LY * 
3 
A | : 
: * 8 1 F 
: 8 ; > % A 1 


the longer Line 6, 1 on your Dial plain, [divided 
into 6 unequal parts in the points 7, „9, 10, and 
11; through which points, Lines drawn from the 
* Center R, ſhall be the true Forenoon Hours. 
Fon the Afternoon Hours, the ſhorter Line 12, 
- 6, on your Dial-plain, muſt be divided from he 
Line M C in the preparative Scheme, as the lon- 
Line 12, 6 was before divided; by taking the 
Teaſt Diſtance from A or 9, 3 to the Line M C, 
and ſetting it from 12 to 3, or from 6 to 8 — 
Alſo the leaſt Diſtance from 2, 10, to M C, in 
the preparative Scheme, will reach from 12 to 2, 
und from 6 to 4. Like wiſe the leaſt Diſtance 
taken from 1, 17, to the Line MC, in the prepa- 
2 rative Scheme, will reach from 12 to 1, and'/from 
s to 5. So is the ſhorter Line 12 6, on the Dial- 
7 =” divided into Cunequal parts in the Points 1, 
= 3, 4, 5- Through which Points, and the Cen- 
ter . . right Lines being drawn, they ſhall be the 
E true Hour-lines: upon the. Plain. And ſo is your 
1 | Dial finiſhed. 
= © Ir-you would inſert the Halfs and the Quarters 
E of Hours into your Plain, you may eaſily do it, 
if from the. preparative Scheme you take the near- 
| *eft Diſtance from the Half and Quarter Points in 
"the Line A. C, and transfer them to the A 12, 
h Tune e 


, : | % 


Full Seni, North, Ea 
ring Plaiur. Plate 2 g. 3. 


1 N' theſe kind of Plains, which 5 
the four Cardinal North, South, Eaſt and Wet 


1.4 Erect or e 


4 


of the Plain being known, there is. nothing requt 


Pole above the Plain, which how to find, is fufff- 
ciently taught in the fourth and fifth Seckions of 
the third "Part of this Book : And therefore 1 
"ſhall not here mention the fame again, but refer 


| draw Houts upon any of theſe Ereck, Diet, or 

4 Direct Reclining Plains, when the Height” d = 

65 Pole or Stile above the Plain | is found, vou have flo Y 

4 more to do; but, 3 
=. Draw a right Line: A B for the ib fide 4 

, of Six, and another at right Angles thereto, fer 


the Hour-line of 12, as the Line O Xx. 


"0 Ia. 3 TIM * 8 * * ä 
5 R * a 
* TOP: 's a FRY "SAL Tl * 188 
=» 
» 4 
” a Dialing | 
& 4a 
* 


= * % 3 i 


$19 917 ee 8 C TLON H... - of * F 
How to Are the Hour- lines a ae i «viz 8 


you to thoſe fore-mentioned fourth and fifth Se 
ions of the Third Part hereof. Wherefore, to 


Points, the Latitude of the Place, and Reclination A 
red, but to know the Elevation, or Height of the 2 


. Secondly, With the Radius of your Ling of F 
Chords 60 deg. upon © as à Center deſcribe the 
Semicircle AX B. And the 1 ht of the Pole 


above the Plain being known, (as 


r an Horizon - I 
tal Dial for London, where the Pole is ctevated 31 


i 5 | deg. 32 min.) Take 51 deg. 32 min. from your 


Chord, and. em upon the Semicircle from Xx 
t E X to l, and throu 15 the Points F 


bs Lines 6.F and. 


parallel to Þ 


. £ ; 5 "uh 
bo | 8 X. and 3 


"= 
8 


3 Length of the Line -X6,. and ſet it upon the pre- 
| Parative Scheme from B to c, and laying a Ruler 


dab, In the preparative Scheme from the 


fte preparative Scl 
= Diſtance will reach fr 


2 


* 
* * 0 „„ 
* i 8 a * 9 LY g 4 * 3 8 * * 
& N 28 * 88 2 r R 9 I R 
W — OTIS OR * 28 R > 9 122 ö * ee Shs * n $5 i Has Wy ©" 
, 0 r. r r 1 R F 55 * 2 n 3 
_ SS —_—_— - — 5 ors a EIA AE, 5 Te COTS * N * * + * 
r 9 N EIS OM, MP” : 
” 4 - 9 : 
* *% . > 
- = __ . "I. ” Y N 4 
"4 þ. | 
7 * ” * » "7+ «4 
>. 1 
8 5 — 
5 * ; * 5 * 


KX, and draw the Lines X 6 and X s on either 


Tbiraly, (Having Recourſe to your former pre- 
parative Scheme) take in your Compaſſes the 


from C to c, draw the pricked Line C 4. 
Point A or 9, 3, take the neareſt Diſtance to the 
Pen X to 3, and from X to 9. _ Alſo from the 


int 2, 20, in the Line A C of the preparative 
cheme, - tak 


and that Diſtance ſet upon the Lines X 6, and 


=. X 6, from X to.1e and a, and from 6 to 8, and 


from 6 to 4. — Likewiſe, take the neareſt Di- 


reparative Scheme, to the Line A C, which 
om & to 11, and from X to 


or 


= 1, and alſo from 6 to 5, and from 6 to 7. So 
E - > * — X and X s divided each of 
them into fix unequal parts, the one in the Points 
, 5, A and 5, and the other in the Points 11, 


are the two 


10, 5, 8 and 7. Through which Points, right 
Lanes drawn from the Center O, they ſholl be the 


pe Hout-lines proper for an Horizontal Dial, 


dor the Latitude of London, 31 deg. 32 min. 


3 vw 55 
Hon the Stile of this Dial, a Line drawn from 
the Center O, through either of the Points F 


3 


E 


” 


* 


a - 
1 
S + 
#7 
* 
2 
* 
. * 


and I, ſhall repreſent the Axis of the W 
S Bil of ine lil. 


* 0 - 

13 7 | 5 > £ x? , 23 4 

2 2 4 Gy * . . = : - % £ bp 5 y * * goin * 3 * ; 1 
* 


Line A Q, and ſet it upon the Lines X 6, and x 


e the neareſt Diſtance to the Line A 


orld,. p 


* 


Hrs eee Erect dul bal, "he ens fr 
titude 51 deg. 32. in. 


Tun Tleight of the Pole above à South Pumn in 
the Latitude of 51 deg. 32min; is 38. deg. a8 min. | 
the Complement of the Laritude. Wherefore; -- 

Firſt, Take 38 deg. 28 min. from you Seale of 
Chords, and ſet them from X to G, and from x 
to H, and draw the Lines G M and. H panel 

Sema, T Take the Length of the Line x NM 

1 ply it to your: preparative Scheme 

ng en 4 and laying u Ruler om 

— icxed Line . 

Aly, The neareſt Diſtances taken ries the 
3 10, and 1, I, in the Line A C cf. 
the preparative Scheme, Will (being transferred 
from thence to the Dial plain) divide the Lines & 
M and X L, each of them into fix unequal parts, 
through which Diviſions, aud the Center G, 1 
Lines being drawn, they ſhall be the true Hour-.. 
CC e of 

ondon. . "TIA _ 


A Line drawn from G (the Center of dhe Dial) 1 
en the * — EH or n 1 9 
0 Dit. dd 24) 255 1 555 2 8015 21 2 


l 251 51% bighe ! 


* 4 Dives. North Ricliving — e 


Lr your Example be of a Dired North plain 
Reclining from the Zenith 25 deg. and ſuch a Dial 
is: deſcribed i in the 17th Chapter of the Firſt Part, 
and the Height of the Pole or Stile above the 


2 


"Th = a +2 
7 © 2 


„%% % 


. IND was there found to. vs 63 deg. 28 or 


a" * 
A " 9 a * 
7 2 a " 8 ** bp 
CE” „„ R * * 9 WY C * R 
CO OT OO SITIO nn nn Os te OO OT EOS yy 8 b 
{Sal ed ES 0 * 
' 7 : ; N 
— as * . 
- 1 5 0 * 
$ 7 
on 2 2 5 
1 | a th : 1 * 55 > - * 
* 1 { — 1 ö 1 1 q « 3 s 3 
_ . . 
* 9 — . 
* 
5 
n SY 


And fo it will be found to be by the Rule deli- 


Firſt, The Height of the Stile being found to be 
z deg.” 48 min. take 63 deg. 28 min. from the 
Scale of Chords, and ſet them from X to E, and 
from N to K, and draw the Lines E C and K D, 
parallel to the Meridian O X. Alſo draw the 
1 243 ne Seng of the Line X C or 
from X D, and ſet it upon the preparative Scheme 


: nne and draw a third pricked Line as e C. 


The neareſt Diſtances taken from the 
2, 10, and 2, 12; in the Line A C, ſhall, 

being ſet upon the Lines X C and X D) divide 
them each into fix unequal parts, through which 
and the Center O, tight — ons they 
ſhall. be the true Hour-lines of a North Direct 


F Plain Reclining 25 deg. in the Latitude of London. 


Tux Stile muſt be drawn from the Center ©, 
+ throughtbe Point E or KK 


4 VC l 
9 4 . 
* 5 
* 0 
* - 
* 


0331 £57 nn r 
* ; © j P 4 „ L C2 — 
Br Direct Eaſt or Meſi Plains, . whether Erect or 
5 ; ; 5 7 ++ A 
; $ Ws; * 


Reclining. 8 


Fon Ered Dired Plains, where the Hour- lines 
ue parallel one to another, the Stile or Pole hav- 
ing no Elevation, the heſt Way to make them, is, 


as is directed in the ſixth Chapter of the Firſt Part. 


And therefore in this Place, nothing more need be 


1 . ö ES e 1 4 


* 2 q ＋ * wy * * 5 — 2 * $0 
485 1 8 : „ % „ 9 6 W 7 * 1 . 7 
Ez 1 ; 3 « . 3 \ 10 * . 83 5 * — * £ 5 4 4 E oy { +} 
% . * o N "IP - we” 2 . * : 2 &. 3 hs 
* * 


0 » = 
# & - > * . 
; 3 3 1 1 A. 8 b ; 1 & 
1 * s of 4 * N : * 0 BS! * 


# 7 o : i 
JVC 18 
I 45 

* 


: f 2 

2 4 & bf LO #4 + $4 5 F <4 # 4 1 ; 1 * 0 
++ + 8 os FFF r 
F 


7 
„ 


_ * 6 - 8 y # b 6 

l * 5 . 5 wy s 2 ; 2 Gs 

— * # — * R bob „ I„%ͤö» ͤv— 9 * was © 3-5 
; bs 8 


ee 


IK 


* A pn he ts r g — * 
5 2 * "3a 99 * * R ** 2 - r 8 THE" * * 18 a a. beth. 9 * , 
* * LY * 7 . r # R bs Da 7 ie Bk Fn od t $4 Bhs ES 
8 Y * N t ö * ME 
: 0 7. * 
, q 
. » 4 

3d a ” 4 x „ * @ 8 

ebnete 5 | p 
0 5 
e. 


"or Ea and We Recliner n 75 


Tus beſt Way to deal with theſe kind of Plaine, | 
is to refer them to a new Latitude, and to a new 


WY 


Declination in that new Latitude, both which are 
"OF ined by this following GENERAL Rur x. i 


has 1. The new Latitude, is akuays the Complement | 


of the old Tan A 
2. The neu Declination in that new Laut. E 
the Complement of the Reclination. 8 2Y 


80 that if a direct Eaſt Plain, in the Latitude 


of Londen 51 deg. 32 min. ſhould recline 40 deg. 
and you would find the new Latitude, and new Þ 


Declination; 4 
Firſt, The Complement of the old Latitude 5915 


deg. 32 minis 38 deg. a8 min. . muſt 


be the new Latitude. 
Secomly, The Reclination bei 22 The 
Complement thereof is 50 deg: 1825 the 
new Declination. j 
So that if (by the Direction of the firſt Se ion =o 
here of) ou make an Erect Diab to deeline 0 d. 
Latitude of 38 deg. 28 min. = 'Diat 3 
ſhall ſerve for an Loft or Weſt Dial, 55 lining 4; 44 
deg. in the Latitude of 31 deg, 3a min. 5 
Thirdly, Although this Declining Plaid be trul I * 
made, yet the placing” of it upen the Dp 


differeth from Ere& Plains : For, in all Ere& 


Declining Plains, the Hour-line of 12 is always. 
perpendicular to the Horizontal Line of the 
Plain. So in all Eaſt and Yet reclining Plains, 
the Hour-line of 12 mult lie parallel to the Hori- 


Tontal Line of the Plain, As you may lee i in the 4 
| FEA» 1585 10, of a Firſt. 9 


. 


bf: 


3 


+ 


ng Declining Retliving Plains, 
-which this Geometrical Way will very well per- 
form by referring them ro a new Latitude and a 
. ew Dedinition,” where they will become Erect 
', Dedlining Pian; but there are three Ways in this 
Book already taught, How'to effect the fame by o- 
ther Means. I thought good to omit them in this 
5 es; and to gi give Brimnptes: in Ere& Direct, in 
Direct ang, and in Ere& Declinin 8 Plains 
bes; 2 al others the muſt ufeful.) 1 0 
I ſtall conctitde” this „ Way of 


> 8b aan 4 fi 31 213 ant! © 
27 b. nd Ree a en TN vidio. * 


5 = OIL 9 n bor: | dF 15 SS; 7s F129 FT 


* 
8 - 5 — = * 
+ Yo 29 # 7 : 0 : * : 8 . . a t 4 F 215 4111 12 7 % 
- * - 7 „ 8 4 


- 
* 


WET 903k 


peat. bs 


„ 


N 


NN 


155 — gba” 


I 


— 


„ 


, . — 


——ä—ũ . ·P——.• ͥ ũ. 


7 x - 
* 
* 
N 1 
yo 
- 
Þ as * 
_ 4 
- 
5 1 

= $ 

$ 

v (> 

. 

* 
2 
% 
* 
* : 
4 
4 
N . 


— 


F 


= 
— ee Ween 


N 1 * 


"4 Fg 


2 ly a lot Bus W R 


p f . 4 : . 4 84 8 : FOR A "+ we, - = 
i 1 + f as 4 * : Wa iS « 8 3 p x o ; * 8 1 65-4 2 
0 2 ® 8 - 7 * > 
5 1 — 1 . 
of „ 
e 1 | | - = 


* 

<4 A FS 1 * 3 ff, 3 A. Toy 4's ' Y kk 4 
or” Ig : 85 N INT a „ 47 3 -* 
Ng Sm * 5» 44% * * 


2 


Te Argument 4:4 {55 
* 0 D % r. AE SEN” = 0 | 4 Ck A 
'H EREAS the two for oing Geo= | 1 
metrical Ways, of:delii _ * 

of Suw-D:als,) may be te 

me; and a more acdurgte "A 1 | 
+ mance of the ſame required riot. 2 
Ethonght ge od, (to make this Treatiſe the mos 4 
A which om a'Geomerrical. mw e 


* 


Mi 8 attained; b 2 Help 
| 45 the 2 or Tables of Actificial es and 

| ; wy -which there can be no exacter 
Tables are already in moſt Mens 
he geben Ufe of thenrno lefs com- 


= as dut proceed to the finding the Forementi- 
* oned 3 as 5 And, 


a 3 £4 2 . # ogra 


£ 2 4 >. 
—_—_ ? . 
2 , 1 
* 4 
a+ 
= * 
a 4 
2 ry ” 
SS ” . * oo 
4 


| of A1 0 


3 * 1 15 LI 67 110 1 5 
* * 8 f . . 


arm or Horizontal Plains. 
Height of the Po ole. above the Plain, which in 


| 1; 55 Plains there is nothing 3 but the 
Places is equal to- the - Latitude of the ina 
* for 6 ae 


: hy 7 * 5 5 
4 — * 


nn. . 


5 2 ere 


Ew P ²˙ m FUF ²˙... Y ac pres 7 ne... 


SECTION, It 


of North and South Ere& Direct Plains. 


12 theſe. Plains4lfo. there is. nothing „ 
ahnt the Height of the Fale + Se Plain, 
— — — Places is equal to te Complement 
of he Latitude of the 42 ""Wherdfore, ſub- 
tract the Latitude of the Place, for which your 


— 


agar wn _ ark e the Re- 
70. gf DS 4 75 1 ; CITY . by mainder 


alling, 
mainder' is the Height ef the ko above the ""Y * 
—. or North 2 ane e e 8 ol 


b „ e e eee eee — 


* 9 2 — 90 8 | © or 
Subſtract Latitade — * 32 0. en 02 85 
8 — _ ' _ / 


| There remaing—38 28 8 1 


Wich i is the Height- of the Pole tier: a Di- 
red North or South Flaw i in - Fan of 
51 deg.” 32 min. _ . 1 9 2 8 


8 E c T 1 0 N UI. 5 EQS | 
3 _ "AY 14 0 
Of North as and South Erect Declining Plan. 


RB UT in Erect Declining. Plains, 4 ö 
Latitude of the Place, and the 1 


| of the Plain) there are three Things requitite to 
7 de found, before you draw the Dial, and they 


5 = 
—_ Height of the Seile Gor Pole) above 4 
„ 
2. The Diſtance of the Sabſtile from. the 25 
ridian. 


= 33; The Plain's Di Herence of Lowgitnde. «2.0 


Ex le, In the declining Plain in Cha 2 
2 eclination was 24 deg. 20 min. in the 


Ag FINE 
| © Latitude of 51 deg. 32] min. Co SE 
N $95 02. 19 17 
| S590 4 10 FI0N 


8 


n+ 
7 e 
* 
s 
* 
F 
* " 9 4 A 
I% 5 1 * 8 2 ” 2 t, "5 
PILOT Y SE I att N , 
* of . 18 W *K x 


nh A * : L 
. * "Op mm, 
& * 
" ; ed OTE x 


K. Fer the _ ff the Pole above the Plain: 

As the Radius. 0 deg. - An 10. 00000 
5 els 

pb 30 1 ee EAA 9793851 
| So is the Co-fine of the Declinati- ee 

e 1 parry 9.95959 
To the Sine of 34 deg. 33 min. 9.75342) 
Which 34 deg. 33 min. is ; the * 


dne Pojo. above the: Plain. 
5 For the Ditance of the Sahfile from the | 
= | Meridian. 

. the Sine of 90 | + 10.000000 


© Is to the Sine of 5 Plain J De 

® elination 24 d. 20 . 9.614944 
So is the Co- Tan 2 of” the Lait 

© tue 38 d. a8 m. 


| athe. Ta .of 184d. 4 ; 9.515030 
HK i 3 ich. 18 deg. 8 min. is the Diſtance cl the 
2 "M 4 - Bah, from: the Meridian. 


: the Plain s Difference ef L OA 
| ts Latitude 38 d. * $7938; ; 


« 38 min 


4 15 to the Radius 90 deg. „ 19,000000 
So is the Sine of the Diſtance. of 
e Subſtile from tne nnn. | 9493080 


n deg. 8 min. 
70 the Sine of 30 


eg. QI min. * 


Which 30 deg. of min. is the Plainrs Diffe- 


t | ** — 

5 ae 

4 wht 4 F 

V's 8 E C- 
* 

Y 


2 


bak, i 


9 sEGTIOR Iv.” 0 


. 


* os *. 


07 South Direct Reclining 2 | 
Fed 
JP theſe Plains, (the Pativulle of n and 


the Reclination of the Plain be f there 
is only required the Height of the Po 


you may find the Stile's Height, as*foll 


1. Ip the Reclination of the Pleis be leſ dan 5 3 


the Complement of the Latitude of the Placs, + 
ſubſtract the Reclination out of the Comple- 


ment of the Latitude, and the Remainder : 1 I 


will be the Height of the Polt or Stile above 
the Reclining Plain. But, 

. Ir the Recijnacion of the- Plain be more than 
the Complement of the Latitude, fubſtraQ 
the Complement of the Latitude from the R 

clination, and the Remainder ſhall be the. Ep 
levation of the Pole above the Plain. 5 

3. IF the Reclination be equal to the Cam boo 

ment of the Latitude, the Pole hath. ny. Lies 

_ vation over ſuch a Plain, but is an Equinedtiat 
Plain, and muſt be made by the Rules ti 
vered in the twelfth e of the Firſt Part 
of this Book. 3 „ Ren. 18 


. | 18 bs a : : 2 1 3 $3 E 354 „ 


; „ 3 Y 2 * \ &. os 2 9 S. E N o ' 
4 * 1 4 'S Ys 2 2 T1, 940 * 1 1 1 * 10 2 35 * 


above the q I 
Plain: In whieh there are three Caſes, i 10 which, 


113 


e 5 SECTION'V. | 
Rd bins Aondy Ma 3 


1 IN theſe Plains alſo (the Latitude and Recli- 
= = nation, being given) there is only uh the 
© . Tg of the Pol above the Plain. "_ 

= _ To find this, 
nn Compleinent of the Latitude to the 
Eo: Reclination, and the Sum of them is the Height 
of * Pole above the e Plain. 


1 8 5 7 * IS | * + . 


. — — 3 22 3 


| 5 deg. min. 

het 4 32 min. Compi. „ 
KReclination | . 

ae the Pri ws Og» 5 

BE... Es 23. But 


"drithmetical. Dialling, | 


2. BUT if this Sum exceed go deg 
wy it from 180 deg. and the Remainder 
the Height of the Pole above the ans - 


2 


— I Letude 51 deg. 33 min, Compl, , . s * | _ 
18 denen es 8 a - BY 


þ 4 | 55 SE - Ws 34% - Swi 109 10 
23 TSS a from... „ 18 00 


Tnere remains 10 30 
4 Wuicn 70 de + min. is 5 the Height of de 
Pole above the P , 
N 3. Ir the Sum of the Complement of the Lati-. 1 
nude and the Reclination added together do make. 
juſt 90 deg. then that Pla is a Polar-plain, wi 
the Dial for ſach a Plain muſt be made in all 
ſpects as is direQed i in the 16th Chapter of the k 
"et of ay Book. 


$34 - AED 75 L $] ww 89 5 an het " 
SECTION. VI. N 
of 257 and Weſt. Dire&t Reclining Plate, 


JN Eaſt and Weſt reclining Plains (the Latizwds' - 
of the Place, and Reclination being given) chere 

ght re required the fame three Things as in Now ante 

South Ere@ Decliners, namely, 4 5 


nin. 1. The Height of the Pole (or Sile) Een Plain. = 
28 2. The Diſtance of the Subſtile from the Meridian 9 
12 3: * Plain's Difference of Longitudm. 


40 Example, Of the Eaſt or Weſt reclining - Plain, - 
Part I. Chap. 10. whoſe og perm. was 35 d. 1-5" 

But ſW m. and Latitude 8 deg. 32 min. * "= 
1. | ; Y 


* 


. For he 4 ER Pa ak ok 


8 dura dez. „ "20.0000 


6: 8 FR x 4100 4 * 
Is fo the Sine df t the | ade. Y 
34 115 ee n * 5% 


Jõ Is the Sine of the Reclination 35 d. 9.75859 
mon Br) ann 


: To he's Sine of 26 deg. 41 Ps 9.65233 
| 26Y 26 deg. 41 min. is * of the 
Pole 44. the 3 Plan. , .-.. 


SOT „ 4 5: Ar "IF rebels wh al | ; 


-+mY ** eons A P 2 LEP? 4. ET + 4 * $413 
3 4 } : 5 4 | 


2 — to the ee of the Latitude 


2 d 32 min. . e 


9. 91336 
— — 
"P's; the Talgent of 45 deg. 52 min. 10. 0132] 


hich. 45 deg. 52 min. is the Subſtile' s Di- 
Ves on the Meridian. 89 


Mo zit: 


BY 700 K bun- Difference of Eu. 


As the Sine of the 1 51 FY 32 m. '9:8937; 
” 1s to the Radius 90 —_ 10. ooo 
= 80 i the Sine of the Subſlile's Di- 

— from wh Ont: (pt - 9.85595 


"Toghe Sine of 66 deg. aj min. 9.9627 
Wich 66 deg. 2) min. is the Plain Diffe- 
Longitude. 


* 1 | 5 ES 8 E 0 


. 
9 
x 


FA ——& Lu — — PE 
. 2223 ˙ 
5s ak 3 2 
r * 
þ E P 1 4 7 4 
£ N Auer at 128 * : n * ren n N 
N — __ 18 A * * vs, * rn 8 
2 5 R © * N . * * 1 
N 4 1 N > f 9 * F : nt 4 
* ? — Pe . We 5 8 
0 a A > 70 5 i . LP 


N 
1 
8 2 
{5 
0 
2 


| . 98. = 5 E GC 1 ON VII. ben 917} 2 
— 2 and North, Declining Reclining Plains. 


#h. * 7 


"Deetining Plains reclining (befides the Lati- 
1 tude of the Place, Declinatien and Reelin«tion 
ot the Plzin; (which are for the moſt part 12 
the there muſt four Tun be found beſgre YON 
5 dune aa Bus ge, 199 7 o wog T 
oi det desc - Rat gt 355 72 dou. 
1. The Diftavte'of the Meridian and Hivizos. | 
. The Heike of the Pole bs Stile. , 99 
3. The Diſtance of the Subſtile from the Alu. 0 
. The'Plain's Difference of Lytgiraide: K 


Ox theſe Plains you have in the 20, 2x, 22, 23, 41. 
24 and 25 Chapters of the firſt Part, (ix 8 
"Varieties, which are all that in any C miy Þ 

8 viz. Three of South Declining Re- 
lining, and as many of North Deecliting re- 
© clining ; 1 ſhalt only inſtance in tWo of them, | 

vir. One of à South revlining Plain®Decli 
ing Eaſterly; and another of à North . 
ing Flain Declining Weſterly. The Exatnple | 
of the South Recliner ſhall be that in the 

_ "third and laſt Variety of South Declinerz 

e andꝭ that 3 of a South Plain d 
" afterly 30 deg. and reeli 
25 in Part [. Chap: . e 


_ 


« . a 

2 * 4 
S . 8 4 at 5 3 7 2 

3 95 1 1 < 4 4 2 „ A 8 5 Ns 5 
% 4 : ö * v5 Ln : «i 
- ; 3 

£ 4 7 re 

4 4 


12 In South Decliners Reclining. Mm 


For the Diftance of the Meridian from the 2, 
orion. 


* 


As the Radius 90 deg. 10. 0000 
ON ws & ini of” the Rechnen * 


Sei ge Thagent of the Declination 
30 405. r + F306 Law 1 6e 


&* 
* - HY 
3 
— 1 = 


as: 50 @201775 p | 
88 the Ta 2 of 25 deg.. 19 min 9.65480 
Which 25 deg. 19 min. being taken from go 
» 0's 05s: leaves 64 deg: - 41 min. (the'Diſtance 

2; of the a N the MEET 


. Plain. DN 5 
© £ 25 | e + ved tes | 
2 r will coqvis toro Operions, 
le Fadine e. dees 


I to the . Diſtance of 
the Meridian from the Horiz 


2 . d 41 min 10,5 
80 5 the ee a eee 


I» £% a4 „ Fs 4 . 
Ne 2 * 72 MH 5 +> Ht, . nk 1 
21 


21 * * F - 
* uh „ SO 4 ep 6 S 4 ; 
l * > "foe * ti 


2. 


Was 


18 11112 . 
e 1 deg· 24 mn. 9.714 
Which 13 by 14 min. being leſs than, the Ls 
as, tude 31. deg. 32 min. = (+4: + 4b 
Ee will rein, e 


- 
© : * 
"> * 


£45 + COM a1) 24. a8 Ab 1 | Then 


Sil Nane N 


I. 0 55 ii e * Ns n 1 
Then again ſay,” NEE ' _ I 

\ Abe Sine of the Diſtance TR 

of the Meridian from the Ho- 00 Ar. th; 

man deg, 43 19 Soo t BIT] 1 Ae he * 


1 

15 to the Sine of the Ateb laſt” 
found 20 d. 18 m. „ 
So is the FEM of the Dectinatn 3 
38 deg. hs TO 5 f 23 9.93755 1 


1 C313 #4 Kan [3s FA 2 
. 


To the eine of 19 . 25 min. 9.34163 
Wien 19 deg. 25 min. s the Height t ol Ns = 
Pole or Stile above ch the Plain. . 
"Note; That if the Arch found at the gelt o = 

_ theſe Operations be equal to the Latitude of © 
the Place (as there it was leſſet, vis. but A — 
2 14 min.) then the reelining Ptain "ji 
been an EquinoFtial Decliner, and, oak, 9 
made 8 by 7 hl 1 174 delive e fled : 

3 e che ff Par Mt 528 47030 n * 


i Dipan Gen Yell 78 7 Soap 
MT IN ae in 1 255 00087 
As the Co-Tang ent of the Declina: | 
tion 30 d. * Ar. Nene all 5 
Js to the Sine firſt found in.the laſt * 
Proportion, '» „td. 14 m. 
80 is the n of the Height of 
the: node 0e the Plain 1 deg. > 9.47/14 
enn Ja, Be 8 aun 92 


To the Si b of ry 3 min 2 api 


2.3 BAFWOITO! 5717 fat” Diigo? 85 8 Yr A 


1 ene Te 401 X, 4 Bi . 10, Wälen 
1 . * 


f 


e * Aach 7 , 2 

in 8 + 44448 L #3 +# 4 Fa 1 91 a + £2 ag $3 3 a 4 "I 
by * r 

8 1 * 2 0 "4 

ESE” ON 


. 
p 1 _— On ” TOTP 
tb OTE OF Il - 7 9 3 
n N * . 
2 « a a - 2 ; 
* * 
8 8 CO 
. 0 » > 
* % * 
FY — 
4 


arcs 6: deg . 5. min min. is ; he Ditanes of the 


"0 Subſtile from Meridian. 
: | ef3;fs «4 3 

vr the P u Differ er exce F; FFT ANN — 5 
Po 0 Sine of te Difference ern 5 
* firſt found, aud the Latitude >,..9,5402; MW 
8 1x. WT 8 As. 
| Is to the Radius yo; deg, .,-, 10.000c9 ill -: 
So is the Sine of the ubſttte's 7 1 
Didtance from the Meridian 6 d..> 9.023350 
3 min; Hier 7 2 2 81 1 911} 3 2 , 
* Sine © * 17 deg. 43 mins © . wal Di i 0 
+. 1 Wag 71. £8: 43 2 . the rung Nur. 1 
. {+ 9631 FE Loggicude. _ A it. 5 C 
= - i 5 en bebe, bende, 5 . 

_—_ 1124 Fer un 
A 5 31 Fi 28 N. 
tte of of the Place, 13 the 2 A of - " 
ain, Which ate commonly iven-) before the 4 
Dial can 1 "drawn, and Wc s are tl e e ſame as in > 
South Recliners, vix. 1 
8 15 0. 9111 WG TON 18 Tao; 3 510 2: : 
+ aid 7h Diſtance ef the Meridian Hem. 1. 8. 
Herzen n nnch id © 415 F 7 5 
1 abe of the Polt le. & i) ae) above " 
4H 8 P lain, : "1 l k 
1 . Bites , the u, from abe 1. 


a The Par; Difference of Longitade. r; 
n | 60 RT er 
"A , theſe may be bound by LEE. be 


"ſhall make e of. the North Plain declining 
r 


- 


Weben) 6 
in the laſt 


- Pac I, Chap - 5 


the! Diftarce * N eee from. 
: uno inc kü. 


un kale, 90 deg. 


enn 7 bs 
Tangent of "10 1 


HM 


* 2 2 
3 8 ia 4 N. 19 * ws 


Wa 54 deg. © 29 min. 
deg. leave 35 deg. 3 


+ Diſtance ot ee — rf and, 
hoof 57 nts 


Wn Nc 


"1 * Sr 88 
1. As the Sine of * Deginuion 


15 to the Ralle 90 deg. 
Co: ſine of the Diſtance of - 
the Meridian, from the e 3&7 , 
LD 35. mia. 1a * 


ein n dam. mig. 0725 fe 
To, this Sine of 70.deg+ » min, 


plement of che Latitude 38 deg- 
* will be 108 deg. 30 min. 


* bg a7 


1 Fan. "un 


F li 
* Tr 


rb 
. ier, 


ol 


et * 2 a] . 


* 


1 10. 00000 | 


Sg . 
1 ? — 


4 55 


4 d 


"that 7s the 


25 


| SONY. wall remain 5 deg. 30 miu. 


Ae TR, 
211 on al - 


9. 597537 53 ä 


2110 © . ode m0 _ 7 FE” 


1306 
om- 
the 


is Arch 


(being above 90 deg.) take it from 180 = 
a0 As | | | 


real Ding. 


nne uu of ch | 
1 MT» 2 e BL 0e. O. 0368 
4 1s to the Sine of the Reclination 5,7 
"38. deg. -o min. — boy - 5 58 9.90796 
80 i is the Sine of the Arch lalt found $ 5 
71 deg. 30 min, 9.97695 
aß | 3G © . 


To the Sine of 54 deg. .4 42 min. 9.91185 


Wuien 544. 43 m. is the Height of the Pol: 


or Stile above the Plain. 

Note, That if the Arch firſt found, viz. 70 d. 
m. had been juſt go d. the Plain then had 
ei deen 2 2 — Plain, the Subſtile and 
tze Hour of fix being the fame, and mult 
a made by the Precepts een in Fart 1, 

21. * = 
811 2 1 * bs 1 >.> 


3. Nb. De. 1 ha! Supt nt Moria 


| 1 ol the 1 v 
Ahe 54 2908 Berlin- 7 ) 586126 

- Is to the Sine of th | 
* b AT bs 80 1 
= 80 is the Nangem of the Height of) 
te Toe above the e 2 15 | 10.15021 
= "43 min, . et ik „ 8 | 


© Tithe Sine of: zeln ah ae. 9.92206 

Weics 56 deg. 43 m. or rather the EA or 

Ng thereof to 180 d. viz. 123d. 18 m. is the 

= Diſtance of the Subſtile from the Meridian, 

g _ * according as you pleaſe to account it, either 
_ e ee eee ee 


nn 2114 


mech * ? 2 5 A 4 
25 OST * ö 1 ; #4 


: . * * 
2 3 
= L 
4 - 
. * 1 f 
1 8 * « * A 4 R £4 3 L 
L |. Z pc F 4. or 
, f 2 4 7 
b 1 * 3x — ” 4 
. I ? bY 7 
l 4 n id * W „ 1 3 
5 5 5 . « 
2 7 * 
« $ » 


Aubert Dialing *. 
5 4 Hau. . e- ef <— 


© £12 21 


:\. 


of 5. 51184 4 
7 25 . 

5 | no” 

— N T ; 

85 0 

ole 


So is the nde i hg 1015 5s 85 e 5 


1 


Tobe Ta ent of 6 d. 10, / 
A . 61 deg. 48 min. mM the Ply 1 + Diff | 


ot i — 7enee of Lovgicade counte "om we Nont Nortty, 
1. WY eee Compliment! thereof'"10 185 dep. "wiz. Þ 
Th IS d. 14 m. is the fame c e 0 5 £2 : 

b conn from the South“ e 


10 il. 4 8 N nd my 2 18 * 2 7 9 MS, 
ko 8 ? 3 5 8. | | | a 
” oy 
V weed 8 Ne D J 70 N 9 8 1 29 
A . Noe - 
OLED Y Wel n SI'S 5 


- "SECTION am 7 of va, 


| 7 1 Re 
FFT $191: 34%) | > he Hh "47 1 


71 | of the Hour Diſtance aper . Pri. 


1 


"SID 


wi Hir HE RTO you ave be pes pla 
Method (and of alt dthers the molt : 
ent exact) delivered'the-Mauner bow to calculate the 
e 1 Requifites' belonging to all ſorts of Plains, whe- 
n. ter Direck, Reclining, Declining; ot both. It 4 
der reſteth now, to find the true Hour-Diſtances one 
tm another upon airy: of: theſs P, n for: 
— al}-Dials which have Centers)xhere 5 4 
one general Analogyor Proportion, and that 3 
this, Having found the Plain's Di Mere E 


bude; fay,, 
; 35 G: 5 | A 


bor 


A 
W 


1 P hes - cs ret a 2 n 9 . Pr WS Kaka ak 8 — * * R p - I 
N 6 * * x * 0 8 N * * "1 x * 3 * * * * * * * * 7 y 
$ ; a ö < * N 7 + 3 d . # * 
4 * * * 4 
F e 
N - ay 
* * K > 
” 4 _— - 
* by 
4 
x 
4 
- 
2 5 
4 | 
D ” / 
be 
© 
. 
2 _ 
= 
2 
1 
N 


4 We Nad or Sine f weg., 8 od 
Is to the Sine or Height of * the role or Stile 
© So ome Tangent of ach How's D 
Oist angent of each Hour's Diſtance (u 
on _ Tay: vr from the SubſtYe. E 5 
"Th ent of the fame Hour“ Diſtance 
counted from the Saane. 


b QI Nr 


Now wn Examples do more confirm than 
barely 'Preceprs), I ſhall by Precedent or Example 

ke plain all 07 hitherto. hath] been delivered, 
and one ſhall ler 19 of many, and. that ſhall 


Be in an upri 5 Xt decli I "Plaip which 
al Djal: zen Fo . * es * 
rg there or,” 55 


egg f Cllealatitn: © 


| BY the | Rules delivered in dhe third Section of 
theſe IO, you ſhall. find, 


bY * 128 


1. The Height of” the pole 2 or See) . th 
Rt 8 33 leg. 38 mn. 1 
. De Diltaste ” the. Snbftile | from: e 
ot, 4e 0 bes N. 24. n. And, 
3. Thei Plais s 3 e 10 
if . IS; min.. {x | 


e ao WH pu. ©; 17 i 1 141 
10 frre Requites being cs amis 8 
— 48 — _ on by lk upon ihe 
4 2 dane: hy che h 
eee Ky "alt ST ne woivet 


7 8 
* a 


xe Hh Bus 


8A 


mw Go & &© =o ca MX a: tk a +... >> OA xx , h IS ĩð 


Plain, be eaſily a — by the 
_nalogy,) I will Ahne in "rp 
_ _ and Wos! Iu." the reſt 


— 


„ ard, you are to conſider . 
the-Plain's. Difference of Longitude, which here 


TY 


in this Example, is found to be 29 deg, 15 mitt; 


nd becauſe every Hour's Diſtance upon the E- 
quinoctial is 15 deg. diſtance: fram the :Swoſtile, 
or Meridian of the Nlam; ſo n Hours: is 30 (deg. 
Diſtenee, and 3 Hours is 45 deg. Diſtance : This 
Plain's Difference of Longitadeveing above i 5 d. 
(which is one Hour's Distance) and leſd than 30 


. (which is two Houts Diſtanee) che Subſtflte 


(he Plaus declining Weſterly). muſt needs full be 
tween the Hours of 1 and 2! in the Aftemmoon. 
Wherefore ſubccaQ 15 deg. (1 Hours Diſtance/ 
from 29 deg. 15 min. and there witl remam 14 d. 23 
15 min. the Equinoctial Diftance''oF! xa'@lock:  Þ 
from the Subſtile. Alſo: from 30 deg. (which is 
wo Hour's Diſtance) ſubera& 29 deg: tg mim and 
the Remainder will be oo deg. 45 min: for de E- 
quinoQial Diſtance! of 2 2 Sicck from the Sub- 
ſtile. Having found the two Equinoctial Diſtan-- 
ces of the tWO next Hour-lines, on either ſide of 
the Subſtile (as of 1 and 2) the reſt are eaſily found 
by the | nual Addition of 1 nl and ſo is 
the Column of the 3 aces in the 


following Table mad * thus ptepared, the 
true ien from Subſtilg veg the- N 
going A- 9 

. F iſtance: 

30 2 W | 4 


hs Sap, bf. Indes 
"his. it * N to nd the Di ance of one 
a. Check ils Plain from the Syubſtile, fay,, 


Sp. 1 


Coed 
* . 
7 12 * 


N * * ö . 1 
> 4 pw * r * 2 „ 0:2. D &- Lane _— + 6/4. 6 2 
* 2 %EEEEkTk r data — W N 883 
* e 9 5 a . 
. PP”. Tx 3 9 * _ 2 wy 2b 5 3 Te 
ER e 4 8 * 
Ln & 3 f 
2 a n 
— - 4 5 ah Di uli 
> "x 1 4 
* ; Mg. 
1 oP 
+ 
vo 
A, the pes. % F ; 4 10. ©0000 
- ® 
ps . 
5 4 3 »” * 


Nane ee, TE 11 20 5 1. 
pl ag cho Sine of the Height the? 
Stile 33 deg. 38 min. EF) 9.7436 


mar. 


TTY 5 | — 
b To dhe Tangent 94 0 4 fake 8 9.44819 
1 8 d. o m. is the Diſtance of the 1 aClock 
- »{i{4dour-lineuponithe-Plain from the Subſtile. And 2 
e ia the ſame manner you may find the Diſtance 
ef 21g Clock to be o d. 25 m. Of 3a Clock 
03 Sd. 52 m. Of 4 aClock 19 d. 14 m. and fo 
+ + the. reſt; as in the following Table for every, 
hole Hour. And if you deſire halfs and quarters 
of Hours, you muſt inſert them in the Column 
bis of Equinoctial Diſtances, allowing 7 d. 30 m. 
or half an Hour, and 3 d. 45 m. be: a en 
kee. Ft we for a whole Heu.. 760 
"HEE! Leon SH 9:29 S775 brouoy grit 


fl. 


Table to the OY RET: 1 to be done = 


draw the Line. Ae the m of .o an. 
Clock. 


Tuus have you the Arithmetical G of 
= whole Dial; it now-remains to ſhew how 
theſe Hous-lines are to be transferred from the 


followeth. 


* 4 
1 2 | 


Feſt, hon » Fl Dull. * * an Hort- 
zontal-line A B perpendicular thereunto au- 
wn Line C D, "> the þ eridian and Hour line - 
Th. - " 


Rong» Take 60 deg. out of your Line of 'Þ 


Chords, 41 ſetting one oor n C, with the ae 55 | J 
* 9 


deſcribe the Semicircle E F G. 

Thirdly, Becauſe the Di- l 
ance of the Subſtile from Sub Probing | 
the Meridian was found to Weſt 24 d. Lat. 5X 
be 17 deg. 14 min. Take deg. 40 min. . 
17 deg. 14 min. from your 6. Fig. 35. 
Line of Chords, and ſet 1 
them upon the Semieirele from F to , per a 
the Line C H for the Subſtile. | 

Foxrthly, The Height of the Stile being 33 d. 
38 m. fet that Diſtance upon the Cemicizate Sonk! 
H to K, and draw the Line C K for, the Stile... 

* (Having Recourſe to your Table), 

deg. 39. min. out of yont Line of, Chords, 

ſer them upon the Semicircle from H to $, and 


po „ 2 10 wahr r 


_ K - * % 
4 9 3 -. o 8 4# #+ + d. * 1 J ; 
£ * 5 by ” F 5 4 s TX 2 * 25 22 
» 2&3 ++ > . #2 5 70 1 we 2 „ F * 4; 
85 * 7 5 1 


4 > Gd &, 5 
— = £54 2. 44x * ws , - g p i. 7's 2 . . 1 1 1 

; 27 £5 : « : 20908" oY 
: $5 we SLES Wo” "$1 7 * fe 4 Fwy 2 8 ; "WM 31 * 


0 e 8 


> 7 


1 * 
1 17 1 
"I ; 
4 


5 * if * 4 þ 4 
V = #44 * En 


* * I * * „ : — 4 
q I * 2 * «. e #- 
* IL 3 „ : 
3 i 4 * 8 1 „„ -— io os 4 


n 


ſame upon 12 


. ˙ — M * 2 2 UN — 


e ned Dia dnithed, Sly Ste; hich 
muſt be ſet to hang tularly over the Sab. 
Ae an Angle nat the Oemer of the Plain 

d. San cqualeo the Height of the Stile.2- 


= bt £0: H. mon eine 30 noqy mart 15: 

E 21: Aw tne dias: you an: Abfirat-of! the whole 
4 Ari of Dialling, after the moſt exact and com- 
4 pendious Way of Performance; others may be 
more 3 but none more exact. 


-* 


964 7 S.E CT- 


————"FZeTION IX. 


end) mo. Xhibit the'manner-© 


Add the Co lement of the 
thplement f obs oa qatjon, 3g DN T 
| 1 tie Sutf's Nit U 


a 1 7 
| * * 
1 * * * * ; F = 
5 ＋ 3 1 +4 we S008 17/3 2-26.66 A 


% 


L. Will be to. little Purpoſe to be thus curious in 
filding of che true Poſitions of the Meridian, 
Stile, Sublfile and Hour-diſtances: in all. Plains, 25 
in the f <going Prece pts is. W unleſs alſo 
we be as ae? or ſtrict in wean cog the Site or 


Poſition of "es, 1 Waich the Dial is to be 
made. For What n ie 1 ue to ery Ya Dial 
true and place it in a F \ 
in che Geometrical Part of this 8080 200 * 2 


to find | the Declination = any Plain, and; 5 — 2 
finding of it, Pn attain, the Fo. Azimuth the 
Sun is the Ingredi 23 how to beute 1 1 
that G hte 18 . d tw 4 2 
But that the like Exactueſs may _= the Perfor- . | 
of this. aL ſhall, in... th e.(hefore I 7 
Ti 5 45 8 Azi- 
eden e eee, 
tical Calculation. * R 


. Ad ads 2 
:: Exzanopley 1 In the Latitude „& NT 282 22 ES 
the Su Wc; oy, $6101 
: r5delimgtic ti Rh "od 
3 — to. find. his ren l 


727 


um, . I 
and take the half thereof, from = 3 
fubrrac rde Complement of the 3 and 
w_ the Difference as here is done. 4 

V N PER | N 


90 4 W7 6 i 
Vd Irs 


eee 


2 
3 


© 
2 * ö Y 
* 2 { A * bo 2 
4 : 
* - 


37 * n 1314 44 


377 1 


x _ 
12 ; £5; + 


Sine ol cm 1 et (11 , 
wk bn of 5 mi Pen i; fy A 


>» 


Is to the Sine e 
Hit 84 d7 £46 m. | he if 


LES * 4 Sine ut de Din erence | 215 - 
n Ls . 14141 . 
ee nus 210 bob a3 x 2 


* 


ö 
4 * | ; 
fr rr „ . 
: £2 464 #460 3 $54 5 © (2.008 is (20 dnnn 


v1} Jt Li- il en * mas: 


33 


Ft:0  10,00000 


R$ yo 1 FP, 1 wy 
b 8 ＋ 5 ws... . 114 . bee en rt! 3216. 33 775 


1A 


4 Doc 4715 4 117 100 10 ris 10 * : 
bas Ot. Hor y: . The Sug. js 19.580 


„ eb ei A 1 ng te 
| Wulcn 


: ef 
f 


© =- 


 Arithmetical Dial, 
Waren bs d the Sine ve 


plement wh ere is 
doubled-1 18 106 8 


main * Aeg. 
from the = 
Azimuth more e 
r thus 


Due 18 7. | Halt Oz 
b IT 1 3 * ad=as 16 
6855 2151 141 0 11511 


. A. 


oy 


I! fo abc Tb 


Geametrica Drrting; Se 


Jes of the 3 as * acſerited 17 


on Sum dia 


AN? * 1 Condlufions may 
be performed by deſcribing the Circles 
of the Sphere upon the Dialeplain,; 
of which I baue here made Choice of 
theſe following: 
x: Tur Parallels of the Signs, ſhewing what 
pit of the Zodiack the Sun is in at all Times of 
the 


R 2. THE 


2. 9 > Wor” 7 4 | fo . 1 
f 25 £2... 


2 This ede hewing g the Lingo; 
the Day and Night thr the Ver. 10 
35 The Hours from the Saw's Riſinꝝ, or Seating ; ; 
—_— I] Hort. b it I 
” 7% 5 Jewiſh, or Planetary En 

5. The Azimutht, or Vorticul Cirulet ſnew¾ing 
in what Quarter of the World, or upon what 
point of the Moriver's Compaſs, we the Sum is at all 
Times of the Day; + +, 1 

6. The De or Cordes of Altitude; 
whereby. the Proportion of Shadows to their Ob- | 
jets, or the Sun's Height may be knom nm. 
I . Of theſe ſome are great Circles of the Sphere 

achers{ſinaſl; The great Circles in al Pint — 
repreſeticed! by ſtrait Lines, as tlic Hour-lines ent“ 
{elves are: The om Circles are-deſcribed by 
nick Sectiontꝭ; and they are eicher Parabolasy ales Hh 
perbolas, or. EA Only the Parallels 0 


dns, and the furnal Arobes in Polar” W 
ane dre 15 EE 307 ow 11055 AI 
rn 1991905 $04.) — . 1 4 ach div 


DIR. FANNY 


+ bet & a 


9 
A 


[LF 356 
55997 115 10811 ni 48 0 0 6 ic & wind 
„. Ut K. 2 Fe e 55 J $63 inn 


Ain 9 1. 25 91 23 30) 


Ek 12 


ups. 2 Baal plan. $53 21 ey DOE 2 370 | 
Ne 2 e * 2 * | 
H 7 2 undaries -3 
the r ki Cove, (for he never: exceeds 
hat thoſeJuimits;): count it beſt, firſt to ſhew- thaw © 7 
of i they may be deſcribed; for that between them 
- all other Les (either 1 great or ſinall) muſt be 

- pro- 


2 * — 172 ; b . 4 N 7 | 
| proje qed, and the manner of'd er 


on TAN Plains is various. . 
Ix a Pear Dial they are pertect Circles, and fo 
arte eaſily deſcribed by Circles drawn about the 


=: Foot- of the p. pendicular Stile; Se 62 Plain 


n of 15 N e 
11. u. Equinogial end tires Ene We 
Dial. Plate N 


—_ an 3 Sat, a dire Eaſt Dial, in 
the Latitude of 51 d. 32 m. 4] 

How to deſcribe. the 8 upon theſe 
-Biains, is ſhewed in the 6th-Chapter of this Book. 
ſuch a Dial being drawn as in Figure 


- bb through the Foot of the Perpendicular Stile at E, 


draw a right Line M, E, N, parallel to the Horizon; 
for: the Horizontal Line in all Plains muſt be 
. drawn through the Foot of the Perpendica/ar Stile, 
and through the Point where: the. Equinodil 
Cireie eroſſeth the Hour-line of Six. Your Dial, 
ui the Equinoctial Line thereof H, E, 8, being 
drawn, come we to deſcribe the Tropicks: To e. 
fett which, 
, Upon a Piece” of fine Card-Paſt: board, 
draw a right Line O R, as in Figure II. repre- 
ſenting the EquindQial Lines in your. Dial; and 
ecauſe the Tropicks are 23 deg. 30 min. diſtant 
| the 'EquinoQial) with 60 deg." of your 
| 8, upon the Point O, defcribe an Arch of 
a Cite, and upon it ſet 23 deg. . ftom 
R to 8, and draw the Line O 8, 5 1 
ting the two e e this Angle 8,1 
call a Trigon. 
© Secondly, Out of dee 1 of 
.eu, , pg ws l 
| 1 1% 45: 1. 


Geometrical Dialling, 1 153 


Trigon from O to P, and row, K Dioper- 
3 | pencicular' to O R: Alſo, n 11 at 


t the Take the Diſtance from 6, to the — 
lain tion of the Hour-line Of. 4 


with "he Equi- 
5 noctial, and ſet 


10 Trigon from G 
11 90 oy | '% 


Havine ins pr pared. the, Titel, ol of i "= 
take te r Ditance P 6, and ſet it upon the C a 
Clock Hour-line from E to c: ——— Allo tak * 1 


" Diſtance 9 7, and ſet it upon your' Plain from 

_ [7 ind from VII to 4: Alſo take 7s, and fer Ie 
} be on your Plain from IV to 4, and fröm VIII to 6 
vile, — Likewiſe take the Diſtance 39, and ſet it upo 


214 your Plain from IX to f: — Alſd take the 2 
% unce 1&5 and ſet it from X tog: Laſtiy, 5 - 
ine 11, and ſet it on the Plain from Xl to . 
5 Tuxsx Points a, 6, c, d, e, f, fr b, are the Points 
through which the Tropick of axcer muſt be deb 
ſcribed ; .wherefore, if M them a Line be 
drawn with an even Hand, making no Angles, 
that ſhall be the Tropick of Cancer. O's 
Tas Tropick of Capricorn may be deſcribed * . 
the ſame Wer if for ** e ue 


ene d 214: d bag 

Thoſe ſhall be the Points 1 ke is Tie- | 

ons of — muſt be deſeribed; wherefore if 2 
1 85 | through Þ} 


WON 
* —_ - « 


St Geb bf Dialling, 


4 lun, en Bine be drawn with an ever 


Hand, it ſhall reproſent'the Tropick of Capricore gon 
N beds faid blbre. "that! the two-Tro 5 
picks are the Boundaries of the Sun's Courſe Ml II. 

II. 
vou are to note, That pI en ee let 
enn J : 15 bits g ION FE 
* I] e 8 55 ter 
6. I. ) the Nader the e 
10. Ctop of the Seile will Sat 


ent. 12.0 paſs alon e 
1 75 i 15 ines. 


25 2 9 80 a 1 1 ta . the Part 


2 2 of. Suns Entranee into the In Signs, JA. 
owe inſerted already, alſo Canc or a TA 
f >. "£3" 51 eee eee lu 4 

55 mo ads s > „i 1% de EW. ſo 

219070" . the 
i i tal 
of Deelination. 

1 Ir} a en in 


< * 
"4 * E: . FR. 
18 * = 62% ; 
** - * - 
2 4 ” 5 SS 2. +a 
* » 


F 18 - AHI ESTE $7746: fn th 


Wipes Ul 11 deg. 307 min. ** 20 der. Ml 6 

* out of your Line Chords, - and (tl at 

_ them upon he Arch RS of your Trigon, from at 

R to V and X, and draw the two 1 O UF 
ee N aud e n e ee Noll a 
3 ys Wan TEST 


1. 


1 eve 


FIcory 


„Tro 


Ourſe 


_ Geometrital Dinlimg: | 


Tuns Parallels bein 
gon,- they may be transferred into the Dral-plath, _ 
in all reſpects, as the ot were; " whe" 5 
N OA in the Feine J. 


22 


1. bs a direct Mund or Ge Diat: ren (ut 
7 ve n as is kaußhe in 
ter V. together With the Stile, your Erle w 
muſt be to proportion vour Stile to our Fam; 
which to do, aſſume convenient Point in the * 
Sadſtile. (here the Line of XII.) for the fatthertnoſt 
Tropick, as here the Point ; then the NN 
Height deing 38 deg. 28 min. add 43 dey." 30 
thereto, the Sum is 61 d. 38 m. and that is the'\ 
ndian Altitude of the Sun when he enters Ca 
and the Complement thereof 28 deg. 2 m. en. 
fore, upon the Point Cancer, malce an dre 
A to contain 28 deg. 2 min. 1 fall the 


I A cut the Axis of the See OA, in A * — e 


A let fall a perpendicular to O W,. as A .; and 
ſo is your Stile proportioned to y,. Pam; and 
the Line C B D, (being drawn parallel to the Ho- 
rizon, through the Point B) ſhall ad the in 
tal-line of the Plain. 


Tuis done, > eds A Trigo n, as | Figur re IV, 
5 2 TINS IT or 0 & B, and EG, to A 
in the Trigon, equal to 


15 oa. le 05 the 1125 O Ah in the al. 
FroM the Point E draw a perpendicular to E F, 
35 E 12, for the Equinoctial; and upon E,-with 
60 deg. of - your. ord deſcribe anArch H 2 L, 
and upon it ſet 23 deg. 30 min. from 12 to H 
and L, drawing the Line E H for the Tropick of 
. and E L for ths Troplck of COTE: 


- Daaw 


* * 9 1 
this put into 5 5 


45 
w 34 


> Wa * 2 4. n K 
, ee es ako GP 8 f 9 
We _- 1 
C - 
; c 
ot 
* 
— 
— 1 
iy 
92 


* 'Daaw the Swbſtiler bag F'G quite "ID 
_ the Trigon, crofling theRquinoQial i ins, and both 
the Tropicks. 

Tunis done, out of your Trigon take the Dir. 
tance from F to a, and ſet it upon the Dial. plain p 
from the Center O to e, througi which Point 
draw the right Line Vc for the Equinoctial: MW 7 
Then from O, the Center of your Dial, take the 4 

-Diſtance to the InterſeQion of the Homr-line of 11 

or with the EquinoQial, and ſet that Diſtance 

upon the Trigon from F to 6 — Allo take the 

:Diſtance from O, to the Interſection of the Hour- 

line of 10 or 2, and ſet it from F to ec: —— 

Likewiſe the Diſtance from O, to the Interſection 
of the Hour-line of 9 or 3, ſet from F to 4: 

And laſtly, the Diſtance from O to the Interſec- 

tion of $ or 4, with the Eq-::.o&jal, ſet from F 
2 and draw the Lines Fa, F , Fe, F 4, F 0 
H M0 the Trigon, marking them with 12, 11, MW... 


and 1, 2, 3, 4, e. r 

ow to find the Points upon the Plaip, tho , 
hich the ilpapichs wor pad; * 1 
FA 1 The Diſtance from F 0 | N 
. I win reac | H 


ne 
11 Center « 


„ [BOP "SHour-S1r 1 rhe; 
n of the Dial 10 2 If 1: 
« 1 bg ” 87 to + 4 ; 5 ine 


Through which Points the Tropick of Cancer, Word 
. be drawn with an even * And, ou 
„ e f _ 
47) ** Fr) , | 80 ; ; T To. | a oY NM 5s 


FIX? 9773 T7 wt 75 DR T 7 
12 14 4 4444 AS Wa 72 8 he ro, 


N „ - 5 r * | 
. . PH — nc} 4 - N RR 9 " ** 1 9 . 
2 4} a5 bu the * * N * _ " ad 1 — Y 7 N : £ 7 * ; * ip P + wk 86 L ("oF 
OO EB os ES CE ne rn ET ie as Ae: e A F , R 
ö N * 9 n x 2 4 1 TY 1 LY ST . . 8 Y * 4 * i, 
R Ne 3 ; oy * "8 aol o Es. a of of * 
5 by 4 = : " * * Joh. . . 
7 : * * * = 1 E - 

p c * E * o : * +, 

* » * 1 8 ” * 5 

* ky p 8 

- 
wh i 
N , 4s 

Fr « * | 5 8 . * 4 L 

de F a 2 + "0" 4 =S 
5 ö : 6 4 : * n * 2 ? e © "= 

* : 8 
” 
_ $ & F 2 
4 


The Diſtance from F to 
will reach w 5 
from O, the upon the 
Center of J/ >Hour-lines . 


* 


oh 5 2 e 
3 Through which Points the Tropick of E 7 


muſt be drawn. And thus have you the Eguissc- 5 


| " Wi, and the two Tropicks deſcribed upon a'dire& 
M outh Plan. |: 9 5 jo 
* III. How to deſcribe the Equinodial, and the two 
fee. WY 71 picks into any uprig bt deelining Plain; or 

m F into ſuch as bo Recline and Decline. _ 
oo Example ſhall be in an Upright Plain, de- 
laing from the South Weſtward zo deg. The 
bro Wing of theſe Dials is taught in the 7th and 8th 


hapters of this Book: Wherefore, having drawn 

uch a Dial, with the Stile and Subſtile in àa due 

'olition, you ſhall find the Height of the Stile to 

e 32 deg. 36 min. „ „„ 
Firſt, Make an Horizontal Dial for the Latitude 

32 deg. 36 min. as in the Declizing Dial, Fig. 5. a 

yhere the Subſtilar-line is taken for the Hour- line 

if 12, as it is there marked, and the other pricked _ 

ines, and the Hour-lines of an Horizontal Dial 

or the Latitude of 32 deg. 36 min. Now if ac- © 


ncer, Wording to the Directions of the foregoing Section, 
Na makea Trigon, and inſert the Eguinoctial ant + 
topics; and afterwards expunge the obſcure 
ies of the Horizontal Dial, the Equinoctial, 
The Wroicks, and Horizontal Line will be the ſame, as 
| they had been inferted from the Hour-lines be- - 
onging to the Plain. e 


* 


H 


25 2 25 
72 ; 


< mY Sd Go n agg N 288 os. | T 24827 8 £48 x * N * * : 
© 83 VE! R PRE * x [oO TOE ERR 7 . 15 / 7 ns OR r 
5 28 F . F * 80 „ * 1 
| 158 Geometrical Dialling. | 
0 8 FN 8 3 ; « 2 I A ) 1 
2 f * f 
; SA 


Ax as the Tropicks were deſcribed, ſo likewiſe 
1 may the Parallels of the Sun's Entrance into] Sur 
= - the other Signs, be inſerted, if into your Tribe) 
gon you put the Arches of their Declinations 
from the Equinoctial, namely, 11 deg. 30 min, 
and 20 deg. 12 min. And ſo are the Parallel 
=. of the Signs put into this Dial, Plate 10. Fig 

= AND in any Dial alſo may the Dizrnal Arches be 
E deſcribed, if you put into the Trigon ſuch De. 


by 


=  Cclinations, as the Sun hath from the Equinoc- b F 
FE  _ tial, when the Day is either 


BH © 2 3 35 
=. - 20( (1402S [it 37 
4 $5 BK * \ „ 

5 12 129 oo oo 


5 And ſo are the Diurnal Arches put into the Sont 
Plain, repreſented by the pricked Lines there, 
Fig. 3. and the Trigon thereunto belonging. Fig 


4. both in Plate g. 


ä 
aner . 4 

How the Hour-lines from the Sun's Riſing and St 
ting are to be inſcribed into all ſorts of Dial-plains 


THE Hour-lines from Sun-riſing are called th 
_ * Babyloniſs Hours, for that they begin the 
ay at the Sun's Riſing ;- and the Hours ho 


1 
* 


6 R 22 
c 


„ 4 ak 9 R 42 
N 0 5 9 A 5 2 IS 
0 ai ERS 3 5 7 
—Z—B BED gc, 7 
r * * « 
E 2 i 
i J 


Geometrical Dialling. 15% 


intoll San-ſetting are called the Icalian Hours, - for that 
Tri Wtbey count their Time from the Setting of the Sun 
the Day preceding. | | 
Tre Manner how to inſcribe theſe Hours, is 
allele fame in all Plains, and is eaſily performed: 
And becauſe that upon a full South, or Horizontal 
* del Plan, they will appear moſt uniform; I have 


noc. Ii Fig. 3. Plate 9. to inſcribe them: 
Your Dial being drawn, and the Equinodial 
a, and the two Tropicks s S, and v W, and the 

Horizontal Line, Sus riſe, Sun ſet; you muſt (by 

the laſt Chapter) deſcribe two obſcure Parallels of 
Declination, one when the Day is 8 Hours long, 
©8 ©, and the other when the Day is 16 
Hours long, as & 16 XK; The ee being 
de Parallel when the Day is 12 Hours long. 
Brix thus far prepared, the Inſcription of theſe 
ours will de very eaſie; for it is plain, that 


Sobüllrden the Day is but 8 Hours long, the Sun tiſes 
e, es in the Morning; and the firſt Line after the 
F MWon's Riſing is 9 in the Morning. Alſo when = 


de Day is 12 Hours long, the Sun riſes at 6 id 
de Morning, and the firſt Hour after is 7 in the 
Morning; —— Laſtly, When the Day is 16 
Moors long, the Sun riſes at 4 in the Morning, 
855 nd the next Hour after is 5 in the Morning: 
nd all the reſt as in the following Table. 


4 * - o 
Fer a ; 3 r * 
i ES 88 n 9 R W e 
N 7. n e 1 * N 
Ly oe * : £ Fe 
r N 1 
0 
5 


Pe barefore made Choice of a direck South Dial, as 


* Sr 8 
2 eh FE IPA 
4 


— > 


6 3 "WS _—— 1% #1 
* 8 K e (Sb, We A 
* 8 K rn 
N 4 3 45 EN 1 * 
4 # * 


* n . * 2 p "I = yo * ek 
4 R wat 42d 4 e AS... bus n = PR... Fs 2 a 
* ene * 2 9 * S ee r [3 23 Whos if 
GGG ON 377 ee RNs. "LE G 
W ; © ME REM "FP W 
k S, : . Y _7 : 5 > 8 . 5 1 
2 k : wg, 7 | 3 * Ys ; A 
160 © omerricat Dl ECD 
— * * © FF Y : 4 3 8 * 
* * ? 4 : 
bY hs * ” 
— ) G < * - 


2 ** 8 8 


—— — | — — — — 8 | 
CA TA. a. dat of thr ry  B- 
TTT 
1! te. 7 AE 
Ta TP TIETS 7 l 
9 


fr 
=< 

— 

— 


21 1 5, 6 


| 
ö met, ent T0 var 
© WHERFORE a ſtrait Line drawn through the 13; 
Interſections of theſe Hour- lines, with the Paral- 
lels of 8, 12, and 16 Hours, ſhall be the fir 
Hour after the Sun-riſing all the Year. long. | 
II like manner, if you would inſert the m T 
Hour after the Sun-Riſing: By the Table you ſee ing 
= that in the Parallel of VIII Hours for the Length 
= of the Day, the ſeventh Hour from Sun-rifing is 
zin the Afternoon; therefore obſerve where the 
Hour - line of 3 croſſeth the Parallel of VIII Hour, 
= which is at 4. —— Alſo by the Table you ſee that 
= in the Parallel of XII Hours, for the Length of 
= the Day, the ſeventh Hour from Sun-riſing is 1 it 
I the Afternoon; wherefore obſerve where the Hour- 
line of x croſſeth the EquizoF:al, which is at ô.— 
_ , Thirdly, By the Table you ſee, that in the Paral- 
lel of XVI Hours for the Length of the Day, the 
ſeventh Hour from the Sun's riſing is 11 in the 
Forenoon ; and therefore obſerve where the Hour- 
line of XI croſſeth the Paralle/ of XVI Hours for 
the Length of the Day, which is at c; ſo 8 75 


of : Y * 2 ** * g * p 
— > : * 2 LA 3 oY 
- A , 

* . " ths «<4 
1 1 ; 
Fe r 


enn 8 8 
2 _— 4 4 "Wl Wee EN” > de 15 ph #2 
o e > #5 
. 


, 4 neg . wy * m 4 . 5 
** © r 2 9 5 we » db a N 2 a 3 
CNRS FS a. 9 * _ * r — 4 r * * 
* 5 l — * 8 N * Fits I; - N 2 FO all J * 2 1 EI £20 

5 * N a 5 * „ 
N % : 89 3 

7 *%* ' « #0 ; W's * 
4 « * Ss SOS + SE 

_ - * 7 -» 


ight 7 N e through theſe . points 2 
b, c, be the ſeventh Hour after the Sun's Riſing 
throughout the Year: And thus by the Help of 
this litele Fable, may all the Hour-lines from the 


Sun's Rifing be drawn as you ſee them drawn and | 4 


numbred, as in Fig. 3. Plate 9. 
IN the ſame Manner, as the Hours from the 


Sun's Riſing (which are the Babylon;ſb Hours) were 


dawn, may the Hours from the Sun's ſetting, 
ference being only in numbering of them ; the 
Hours from Sun riſing being numbered from the 
Weſt End of the Horizontal Line, by 1, 2, 3, 4, 
5, 6, 7, 8, 9, 10: And the Hours from Sun ſetting 


fom the Eaſt End of the Horizontal-lize back=- . 


wards, by 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 


13; 1 which is evident i in the fore-named Fig. 5. | 


,, ok 


"a 


TAE Hour-lines from Sun riſng and San b. 


ting being deſcribed upon any Dial.plain, as is be- 
fore taught; there will by their correſpondent In- 
trſeQions one with another, be points produced, 


rough which if Lines be drawn with an even 


Hand, the ſame ſhall be the Parallels of the Length 


of the Day, and ſuch are the pricked Lines in Fig. 
3, numbred upon the Meridian-lihe of the Dial, 


by 8, 9, 70, 11, 12, 13, 14, 1, 16. 


! 


CHAP. 


(which are the Italian Hours) be drawn: The Dif- 8, 23 


28 s 
* are YA 
| -— 
£ T * 
1 3 
2 1 ad 2 


— 21, 
8 


#25 44 


8 p * TY 6 EE BN 
ö 8 ; TER Be. „ 5 RD 
42 1 1 ** gee vg. E « 4 1 > \ PR 4 3 1 * 
n 8 2 * . 4333 . D 

2 2 5 7 . 89 4 8 ww C4 8 8s av 45 77 by 24 l 3 ar 2 ** 1 4 1 Jy 

Y * 5 N 8988 FE. n , 2 PAY " 2 * d - 

of 5 r 2 * * 1 
. : IS FFF 


». a 
IX. 


. 


— ; * 2 __ 9 7 3 7 * I f * q r 
F 25 ak * R * A Baca” Ea bd "2 r e 
_ 8 — 9 PTY > tha 3 TH * 9 ON 4 * J * * 77 * 4 x2 PEE 25 5 
4 I , 77 ; mY EY 1 
. R . 4 . | | 
0 , 4 * 2 4 , ; 7 * b : 2 
2 4 * y x6" 3 4, . * 3 N 7 
* . % - ®. 3 83 "ths. * * 6 
= 4 * * 4 N 5 2 
i 4 . 72 
15 « 


I 4 N 
—_ f 2 88 85 78 9 7899er 


; Of the Jewiſh, or Ola Unequal, or Planetary- 
_ - hours, and how they may be mſcribed upon any 
SS Dial: plain. 5 . 


T HE Ancients Account of their Day, was 
from the Sun's Riſing in the Morning, till its 
ſetting in the Evening, which Space of Time they 
did divide into 12 equal Parts, were it long or 
Mort: So that in the Summer all that Time that 
the Sun hath North Declination, the Hours of their 
Hay were longer than a common equal Hour; 


aud in the Winter, when the Sun hath South De- f 


clination, the Hozrs of their Day were ſhorter then Hand 


nà⁊ common Hour; but when the Sun is in the E. Trof 


"I Bl 
hy 2 
8 
4 > 
I J 0 . 
* = 
x 
8 \ ga ' 
_ 


quinotial, their Hours are equal to our common ſilſj,, 


Tux Inſcription of theſe Hour · lines into alli, 
= forts of Plains, is very eaſy, being much like the 
= Inſcription of the Italian and Babyloniſp Hours, 
taught in the laſt Chapter. HA Ya 


Hav Ws. 


tary: 
y any 


f III 


1 
It. 


Jewiſh 
Hours. 


We 


-" 9 r * . N 
* TY eels * WI W- 1 rr 47 " 0 4 3 4a 4 5 8 * * g's N 8 "I - Nr FR * ada. |: - r 2 "wu 
NG ö 50 a & * ; ; ba. ba Roan ein IeE "ITE 
r EY 8 , " . r tees | 8 Y eng; 
15 + 4 
N 5 2 - ba : . 5 3 9 "=" 
3 : F* : , y ; % 
a 1 3 * 
f FIC ; | f ? 
7 : % p 4 * 
— 7 0 4 
* Ci oy 
=; * - 7 * 
„ 
* 1 5 5 : x "7 £ 8 „ 8 * 
4 2 2 
1 8 958 bc uk * 5 — . 8 8 - 


min. 


The Parallel Equi- 
of 15 Hours. noctial. 
ho. -: 


x5 
0 


— 30 


8 
9 


The Faralle f 


Ho. 


— 
4 9 


of 5 Hours. 4. - 


Min. 


O 


| 


Was 
ill its 
> they 
ig or 

that 
their 
lour; 
De- 
than 
je E- 
mon 


Dr 


XII 


7 narters; and alſo the Eguinoctial, the two 
ropic 


6, Plate 10. which is a South Dial declining Eaſt- 
ard 15 deg. you muſt make Choice of two Pa- 
allels of the Length of the Day, which muſt both 
of them be equidiſtant from the Equinoctial, 
which let be the Parallels of 9 Hours, and 15 
Hrs, for thoſe two Parallels are moſt convenient 
for this Purpoſe; becauſe the Jeuiſß Hours in 


) al 
> the 
ours, 


Havixe drawn your Dial with Hoxrs,' Hai, 


and Horizontal Line; and alſo the Pal. i 
klr of the Length of the Day, as is done in Hr. 


thoſe Parallels will juſtly-fall upon the even Hurt, 


Halfs, or Quarters: Now the Points thro' which | 

he Fews/p Hours are to be drawn, this Table wil _ | 

lire& to; wherein you ſee, that the firſt Jeu 

Hur is to be drawn through; Hours, 45, min. in 

the Parallel of 15 Hours, through 7 in the Equi»: 

noctial, and through 1 nd 15 min. the Fa- 
5 | &. | 


"ING 


ralleli ' 


„ 1 . N Py 
pa 4 * a with „„ 
YE 4 3 c IAEA F * 3» : c 
* 2 _ $ 4 " 8 e TL %. * 8 ” 5 at 2 nll 
wy * oo * * po — 0 
ies 1 e * 4 * * 2 N a 
of n A N N y * N 
A £ 2 ou Y 3 
r N F | y — 
1 U 4x; I" 2 p 4 . NY 0 
„ —— "> * , 
2: | _—_ Sn yu . : * LE 
1 *7 < * g 5 . . 4 . in 39 
3 4 3 5 5 — 8 
3 
4 


- rallel of 9 Hoxrs. =— In like manner the ſecond 
Fewiſh Hour muſt be drawn through the Interſec 
tion of the 7 Hours in the Parallel of 15 Hour: 
through 8 in the EquinoQial, and through 9 in tha 
Parallel of 9 Hour: And ſo muſt all the reſt o oſe 
them be deſcribed as the Table does direct, and 2 th 
you ſee done in Fg; c. And in this Manner, bye / 

help of this Table, may 0 ve deſcribed in all ſorisſhou n 
of Plains, whether Direct, Reclining or Declining. | 


asses 
3 EN 
x How the Azimnths or Vertical Circles are to be in- 
3 5 ſcribed upon Dial-plains. | 
Eo TH Azimuths are great Circles, and being 

= © projected upon all Plains, become ſtrait Lines; Mud i 
and they are variouſly deſcribed, according as the Huber 
= Plain is ſituated. Particulars of which follow: bowi 


£02920950900009600999 i, 1 


SECTIONAL :.;..: MM 
On an Horizontal Plain. . fron 


IN theſe Plains the Azimuths are moſt eaſily in- Wy 
> ſerted: For, your Dial being drawn, with the deu 
Tropicks and Equinodial thereupon, you have no de 
more to do, than upon the Foot of the Perpendi- Wan 
eular Stile at O (in Fig. 7.) as a Center, to de- and 
ſcribe a Circle, as & N, which n, - 3 


3 


R * 18 F » „ * L ; 6 
d. * _ Wes * * ALPS" Ts Hs WT. — rh. þ Nen 8 R N £4 * 2 TIES & q . og OT 125 VI * 
8 f : - * BR SSL let” EA. bas dd d » £2. 8 
* 5 . : MONEY YI = 2 e "MI 8 
, IS: 3 vr r 
* | 5 - 4 * © * C3 » N m 26 . by GK \ L 5 
A P * F > * * as 
Ce "£ ö 1 a 4 . *. F : \ 2 *, =y, 
5 4 * 2 "L508 
K p þ * D¹ 9 . * ay ; 2 I : 2 6 
7 : ; 2 1 


de into 32 equal Points (beginning at N) un- 
wering to the 32 Points of the Mariners Cam. 
, (or elſe you may divide it into 90 equal Parts, 
x Degrees) noted with & & &, Ce. and three 8 
hoſe Points draw ſtrait Lines from O, the Foot 

f the perpendicular Stile, and they ſhall be the, 
Ime Azimuths upon the Horizontal Plain; Which ei 
you may denominate by Souzh, $ by E, SS. E, K ü 
by S c. as you ſee done in Fg. 7. Plate 16. 


4 
— 1 — - CY - 5 
' ” k ft * \ F 
* > i - s * 


15 


. , 4 . ' 43 * 
N g IE 1 
A , 5 * , . E * 
„ SA CTT 
„ 4 I ASS 2) VS. W "I 
! ; 5 _ 
Upon an Erect, Dired Eaſt or. Welt Plan,, 
| ? 1 © 2 


%. 2 


Plate 9. Figure 1 


T AVING made an Eaſt Dial, and therein 
SO inſerted the Equinoctial, the two Tropicks,, f 
ines; And the Horizonta line, you may proceed to ine 
the nſeription of the Azimuths in the. manner fol- 
owing. „ ' 
Urox the Point E, of the Horizontal-line of the © "8 
on M, E, N, ere& the Perpendicular E Q, equal! 88 
9 o E G, (the Height of the Stile of your Dial). - 
. Wind upon O, as a Center, deſcribe the Quadrant 
OE L, and divide it into 8 equal Parts, repreſen-; 
ing one Quarter of the Mariner's Compaſs, and, 
om Q, through thoſe Points, draw Lines to the 8 
— Mirizozra-live-M, E, N, noting them with. W 
in- ee © ©; from which Points let fall Perpen”* 
the Näculars from the Horizontal- line, and they ſhall bs 
00 de Azimuths between the South and the Eaſt: mw 
1di- WF And for thoſe Points which fall between the Eaſt. 
oe ad the North; namely, E by N. E NEF, 
NE by N. the ſame Diſtances being ſet 
ide mud: DEM 75 H. 3 88 | | upon | 2 


_ 

"3 
... 

_ 


upon the Horizontal Line from E, towards the left 


des @ Died South apright Plain. Plate 9. Fig. 3. NA 


EL - Stile of your Dial A B, and ſet it upon the Me- 


Qual. Parts, (if you will) but I have here divided 
© tt but into 8, to ſhew the manner of the Work 


6 draw Lines perpendicular to the Horizontal-line 


S 
5 3 


A 
* 
- 


22 22 — E - F * 8 * v * "> 
e 
N v7 * 

* . 
Diallin | i 
© 
is g. : 


Hand, as the three firſt Azimuths, E by S, — 


ESE, — SE by E, were towards the Right 


Hand, ſhall give the three Points G © © on the 


Tes Hand of E; through which Points alſo Lines 


dran perpendicular to the Horizon, ſhall be the 


. = Azimuth or Points of the Compaſs between the dd 
= Eaſt and the North: As in Fig. 1. And as the 


Eaſt - Dial contains the Azimuths between the 


South and the Faſt : The Weſt Dial muſt contain 
thoſe between. the South and the Weſt, 10 


eee 


T HE Dial, with the EquinoQial, the two Tro- de 


picks, and the Horizontal Line deſcribed there - Ni R; 
on, the Azimuth may be inſerted thereon as fol- ne 


loweth : | „ 
Fit, Take the Length of the perpendicular egit 


wiian of your Dial from B to G. 
© Secondly, With the Diſtance G B, upon G de- 
Eribe the Semicircle E B F, which divide into 16 


it the Points * , dc. through which Points 
from G, draw obſcure Lines, extending thein till 
they touch the Horizontal Line of the Plain C B 
D; now. if from theſe Points of touching, you 


between. the Tropicks, or parallel to the Line 0 
L have 


* 


7 - 
ay 
. 
ths 1 
9 2 2 


F ro- 
jexe- 
fol 


ular 


Me- 


| de- 
0 16 
1ded 
"ork 
DLNtS 
1 till 
3 


-line 
e 0 


have 


21 have not drawn the Lines W in 7 
this Fig. 3. becauſe the — is full wo _ 
of Lines e 4 _ 


WI 


| X + 
[2 
_ 
- 4 \ 
7 x _— 
, : ., 
.- == 
1 
1 ©, 8 1 
IX - (oO 
76+ *"+,.f 1 
2 
9 
_— 
+28 
＋ 
» * 
+ c 
4 


SECTION. Iv. 
cher a South Declining Plain. Plate ro. Fig, 6. 


AN Example ſhall be of a South Plain, declin- — 
ing Eaſtward 15 dleg. 
SUCH a Dial being drawn, and the 


ect the Perpendicular BC, equal to BO, the pers 
xadicular Stile of your Dial; upon which point 
C deſcribe the Semicircle RB 8; which done, lay 


Ruler to C, and the point ©, where the Hout · 2» 
ne of 12 croſſeth the Horizoxral Line, and wheres 
te Ruler cuts the Semicircle R B'S, at that Point 


tin to divide it into 16 equal parts, at the Points 
*, Cc. and from the Center C draw Lines 


trough theſe Points, extending them till they ©. 1 
touch the Horizontal Line D E in the Points 6 


lefg hi and 1; through theſe Points right Lines 
King drawn parallel to the Meridian, ſhall be the 
Mimuths defired, which you muſt number accord»! i 


ug to the Situation of the Plain :: Namely, the 


Weſtern Azimuths on the Eaſt Side of the Merl. 
lan, and the Eaſt Azimuths on the Weſt Side of. 


he Meridian, as you ſee them numbered in 3 6. 0 
Plate 10. 4 | 1 


* 


— Ccnam 


Equizedlial = 
Tropicks, and the Horizontal Line inſcribed there-- 
on :: Upon the Point B of the Horizontal Line e-- i 


7 
* 


2 eee Di e 


= = 
=_ j 


| 2980444444444] 


; + „ HA P. VI. 


e to inſeride 6 the Circles 3 be Saw 4 Altitude into 


TH E OD or Circles of Al titude e, in 
* the Sphere, have the fame Habitude to the A- 
8 Amnths, or” Vertical Circles, as the Parallels of 
3 » Declination have to the Meridians, or Hour-cir- 
b dies: And therefore, the Eguinockial it ſelf, and 
Ali che Paralleh of Declination in a Polar-plain, 
are perfect Circles, and ſo are the Almicanters or 
* * 2 „ Circles of Altitude eben an Horizenzal Plain, us 
1 0 Place 0. Fig. 7. 
Herixontal Plains, which 1 patallel to the Ho- 
iron, have the Zenith for their Poles; ſo that for 
1 e Inſeription of them upon theſe Plains, the 
3 „ 39 * of the perpendicular Stile muſt be the Center 
Eon which to deſcribe them. 
8 _— the Numeration of theſe Circles, when 
£ ne deſerſded, there are two Ways molt in 
g The-one by Degrees and Minutes of the 
0 & Altitude ;. the other according to the Pro- 
in that the Height of any upright Object (as 
= 3 Houſe, Steeple, c.) bears to the Shadow of 
- it: The laſt of which I have here followed in this 
-- Figure 7. where the Circles of Altitude are equal, 
double, triple, and quadruple to the Altitude of 
3 2 2 perpendicular Stile. ä 
Tux Inſcription of theſe Circle} into all other 
Plains, ate, in a kind, the ſame with the Inſcrif- 


1 the Parallel of:Prglivation - 88880 where 


* 


8 of ».#; 
4 4 Is 1 
* 2 K * 
I" 0 
* n * 


7 
F K. 
a in. 
2 . a 


POP: 


N 
* * % 
E. 2 
* 337 


7 * * 
n 1 
ONO * 


9 $2. * «7 
. 
1 * 12 
W j I 1 3 

„ * * 


1 2 W 
. 
N 1 1 

e 


4 9; 


91 
aer xy 
3225 * * ö 


— r 1 


as * L HS 
4p ES ab 
\ « 8 1 


* 


W N 2 EN 


— — 

Att 6s 
* 
« — 


M 


r 
3 
* 


2 


ä — — — ͤ ů—ðèð;3« 


* 


2 => 5 
——— (v—ę— — — 


HJ 


: 
"Yi Ar Sy 3 


————— — — 


— 


„ « © © 
1 
Z. 


4 
of the 2 


22 


* 


5 


21 


. 


G * „ ö 


_ IS Ss a 
3 
. K 
12 +. * 
* 
— 
= 
* 
% 
* 
1 
4 
1 mn 


{South D: {1 
-—_ taltian Hours G4 


nn 


— 


enn 


* 


* 
ww 
7 

4 


Ay gw 


eng TT oF 


„ 1 4 
— = 
2 80 1 
Y * 
ol 12 
* 5 g 4 * 
£ * ea. 
2 — F 4 0 
* bd 4 
. 2 
£ . 8 
—— — — 
a 838 3 
f * . * * 
; +" 4 % 
Ki. 4 " 
| - f \ 
aw * 
| tet 5 A 
"x 
— 
Ke off , 
A * 
[ F 
| * . „ % 
pn ol - LY 
1 *. 
- a) Lit. 
4 
> 
. 1 y 
"” S 0 8 
. "JR = *S L - 
* . ® 
F- *Se : * 89 9593 
3 — "I on * * 
* . 
0 , . +» #<< 
2 *% «- 
* 
| Fes 2 * — 1 2 
| * 00 
„ * LEI Ss & * 
4 - 
6 * 
2 
1 2 
5 * 
43; 
f . CEE LEES * 
* hin — 0 fon” 
* of 820 32K << 
5 8 
—— <<< 
| „„ e, 
* 
8 ATE * — 
; £ " a” 
PE ke q 
| — n_—_ g 19 mg 
— 
4 
5 23 
1 , 2 4 
« . — 
44 23 Go 400 
. 
/ * — 
a7; 
g - 
. a” XN „ 
42 * 1 5 <> * s 
* 8 
. ay 
9 4 ” * - 
| I ot” 
4 
* 
»*®, ; 
* 
; 4 
> A . 0 
* 4.5 
* 
5 5 7 ; ; 
45 — 
ö | 
; 7 F 2 
N A 5 
oF 1 
| SW Id br : — 
4 — = a 
x E 4 
1 * * — 
* | a 
7 3 - ; * 
* FY 3 £ ”” Nc 
” » 3 3 * \ ay 
1 » = . . 92 
x . 5 F "4 * 8.” 
; * * * 8% 0 N e 
« > . 
9 4 5 S Sy 1 * F > 1 NS a 
ds "a2 6 {4 
vc ** - 
« * 
* * 
* ; 1 
z 2 f % — * 2 
* N 1 
0 1 5 
* 
£© \ I 0 
4 * CEE M%.- 
1 * F or & be Sh "IMS 
: 3 
* WY” 8 ol 8 1 ho 


— — 


2 5 
„ 


TOS, > 
Th en ep 


* yy; 


e 


5 = © ...38u 


wa _ : x 
4,99 £4,045 ame 


* 
2 p wi #$2; # 


we a ind” "IR 


1 


* a 
* « 4 
# * 
1 # 
4 
f 
* 
p 
. 
4 
* 
+. 
ace 
” 
wk 
« . 1 
+ 2 
3 . x 
I 1 
1 * 175 * 1 
REL 8 N. © ; 
5 s * r * 
9 * 
„ * - 
-_ 


/ 


2 | 9 Dialling. 


85 in SS the Trepicks, and other Paras Wl 
 lels of Declination, you take the Hoar-hines out M 
of the Dial-plain, and put them into a Trigen; ſo. 
in the Inſcription of theſe you muſt take the Azi= 1 3 
muth Circles out of your Plain, and put them in- 2 
to a Trigon, and from thence transfer them back 1 
again to your Plain, as in the other: And as the 8 
Hour-lines in the other muſt be firſt drawn upon . * 
the Plain; ſo in this muſt the Azimuths be fitſt in- 
ſcribed : And becauſe theſe Circles of Altitude are 1 
ſmaller Circles. of the Sphere, as the Tropicks and 
Parallels of Declination were, they will upon alt. "= | 
= (the Horizontal "I = m0 ho ade » IF 
ections. 1 3 


* 


— — 


* r 
= TE 


* 
i al atk . FS * * 
1 ** , . > 
r n # 
* => = I - 
| = 


CH A Pp. VII. wn 4 3 


4 3 and eaſy Way to project b Er 2 
all kind of & eee without any Regard bad 1 


their — , either in Reſpect of W 
Reclinatiom or Inclination. 15 


— 


11 


1 


4 5 
1 
* , ; PRs 
Ry * 5 1 hs 
4 4+ Wb 44 4 7 * * 1 5 
: Fs | WA | 
n ; i i TY ys ty I : 
_ w—_ 2 * 2 _ 4 
"a" * Te" Sh 
* FE F +9 


'> 


AY Fi 
! 


3 1 
Fr" 


Oy 


12 


2 
"EDS 


£08" \ 


17 a Point be aſſigned upon any Soest, , fa 1 5 
or curved, one or more, wherein the Hear A J 
lizes and: Axis ſhall concur:; ; how to project the 
Hours to that Point, and to ſet up an Ai. 3 8 7 
the ordinary Manner, to give Shadow to then £0 


15 


without any Knowledge how the Dial ſtandeth in: 
reſpect either of Reclination, Declination, or In- 2 I 
clination. i 
-- Fir, To the Point aſſigned (upon any Side ok | 

it) by the help of a Semicircle, or other Levely © Y 
3 out an Horizontal Thread, ae for the 1 


e . 
e Morn 
. * 


. 


„ . ” a 
* = * 1 4 - - aw © 
N . * } * 1 2 3 5 a A oy 
4 : = a2 HS Y : ; 1 I x 1 ” k 3 5 
A ˖˙ ⸗·—* A 467 27 N 5 
- * Py 22 OO ett ei SETS af 1 * wh r Gs * * 3 * A ; -_ 
S : * wp - py 4 "* E 
Y n= = 

« | ' — A 
. $8.44 2 


EN. q Y "oak which n deen fngle M_ 
x { Line, but may be turned at one or more Angles, 4-3 
= that it lie (all the parts of it) totally in the WF * 
IR © Superficies of the Hort OA. | 
l 1 Secondly, With a perpendicular Thread held up, 
en the Sun upon the aſſigned Point, and in- 
1 x0: the Horizontal Thread, and ſtick in a Pin, or 
e Mark upon the ſame Horizontal-line,” thro! 
4 E bien the Shadow cutteth, and at the ſame In- 
1 Z | + Gant alſo take the Sun's Altitude. 
erh., By the Altitude taken find out the 
= Sun's Azimuth; this Azimuth, whatever it be, is 
—— reed by the Mark formerly made i in the 22 
Z * rzontal-line or Thread. 
= Foerbly, Apply a Paſt-board to As aff gned 
1 Poiat, and hold it Ig that it may anſwer to the 
= Horizontal Thread alſo ; and upon this Paſt-board 
poor Azimuth by a Thread extended from 
thc Point affigned for the Center to the Mark upon 
2 Ee Horizontal Thread. Which done, 
I , By help of that Azimuth upon the Pa/i- 
= protract the Metidian : line, obſerving the 
one Coaſt and Quantity of the Angle from the 
Anh; and to the Meridian thus found, de- 
8 22 an Horizontal Dia] for the place. 
43 A :Sexthly, Apply the Poſt-board to. its place again, 
.. er ſtanding rigtn as before; project all the 
Hours int into the *Horizowzal:Thread from off the 
bora, and ſet Marks upon the ſame Line, 
tor: the point of each ſeveral Hour, which Marks 
[= _—_ Iitle Knots to Wy to and fro upon r ſame 
3 45 -Seventhly, Project the Meridian Point by a per- 
pendiculat Thread upon ſome Object into that 
* ace whereabouts you imagine the Axis of the 
oxld would paſs, above of Oy from the 
1 for the Center. e 
l : 5 Eighth, 


* 
1 


— 
"3 


1 +0 2 
__ . 


es 


| VT 


* 


7 


{ 
} 


00 | 


SY V 


* 


8 


p av 


SS 


fi 
E 


lh 


( 


/ 


4 
vw F — 
SR Do Te >. 


T 


it Mi FH n 52 « 
Hit 1%“ iy A 
Wl 


l 


| 
WA RS 
WIRD IT 


- - 


P 
4 N 
"hy 
- 
. » 


1 
» 


SV PS 


7 25 f 
I r . ; 


1 2 * 
- 


© 2 V0 4 


* 


PW, * — 


— 


we 


* 


* 


att ret — ů — 


gn DE TOAST 
1 + 
r 


— „ , a 
ot 8 „ Ce 
28 * 


* 
« 2 (EPL 
* SI Qs * 


x 


7 * 


— by of ., | a 
8 = 2 CA 


" 4 : 8 
. 2 8 4 * 
lane” 
2 , 
* "4; ”Y ens 
* . 
þ 
- 
- 
* 
” 
* 
"Ou 
* 
„ 
* 5 
r 
« 
* 95 
- 
- 
, 
7 « 
P 
* 
* 
oy 
* 
x — 9 
9 
1 
.* 


0 
(FE 1 nn * a 2 £5 Owe MAb 
* 3 8 83 e 1 


r 7 
: os 2.1 5 75 
5 ; 
* s | ; 
7 5 
s IS 
: „ 5 
* * 5 * ; 
? >< 4 
wo. $ F 
1 = 5 
8 . 
* w 
7 0 , 
bh * * 
* * 
* 0 
f - 
+ 
: i 5 
. » ” 5 
-” £ N 
1 og < ; 
F * 
0 pp 
1 % * : 
- = 
7 
4 * 
* * : 
2 
* & "Is / 
1 p 
8 
Pg 
8 3 
EF” 0 
1 3 
* 
w 5 
s ' 
* — + 
Ss 3 Le L 4 
. * 
Z 8 7 
. 
* 


. VVT 


o 


_ » 


2 Is 

* rn 

r 
. N 


ehubly, With your ee (ot a 8 | wi 
and Quadrant) elevated or depreſſed, (as it ſhall 1 
required) from the point aſſigned for the 
according to your Latitude, project the Pole * | 
Nintbly, Extend. a Thread from the Point a. 1 
ſigned for the Center to the Poles of the Word, 4 
which ſhall repreſent the Ait. _— 4 
'  Tenthly, By the Point upon the Horizontal 
Thread, and this Axis, (either by your Eye, — 
ing the Axis to the Hour- points, or laying ng 7 il 
Hour-knots to the Axis,) you may project all the” Y 
Hours, and draw them: Or elſc you may. 
let the Axir alone, and content your {elf WW 4 oy 
Pole- point projected into the Meridian: For if frags "I 
the Pojuz aſſigned to be the Center, or Meeting = 
the Hoars and Axis you extend a Thread to each 7M 
Hoar-point in the Horizontal-line, and do repoſe- 5 34 q 
(with your Eye) the ſame Thread upon the Polos 
points; then ſhall the Shadow of the Thread bu 1 bel 
,708 that Hour-line ; and do fo in all the reſt. Wh = 
| Eleventbiy, Your Thread or Axis lying in 100 : AY 
196 Situation, you may eaſily fit an Axis t@ the 1 
ſame Poſture. If your Dial be deſcribed up a. M0 
plain Superficies, you may then (by one ſide:oF a2 
Square, applied to the Thread or Axis, and ws! 
ther fide lying upon the Plain) find out the Fe 
- and meaſure- from. it the Elevation of the = 
 ——— But if the Dial be deſcribed upon a C, 9 
ed Super ficies, you mult be content to ſet up vou. if 
_ Axis by the Direction of the Thread only. 4 
' . Twelfthly, This Point aſſigned for the Cntr, 85 3 
being a Poter. of the Axis, is, as it were, the * 5 1 
ber of the Euomon, unto which all. the Work is. : Y E | 
projected: But if it be required to ſet-up an Jan 
to ſuch a Superficies,,. upon which the Hours and "I 
Ki wb nat meet ew Dy tolerable. mary be- 9 


Ne 


2 bo 


[EEE * 


27 


P 8 4 R , PR OO * TI * DES 4 * FO 9 * 4 7 * 
r 9 * : Fs ZOE LE PIT » 
ks v7 7 2. ri Sr a aun " > oF - c 
A , ; ' f ; 23 
5 | 7 a by | | 


= cauſe perhaps the Axit may be but of a · very ſinall 
Elevation above the Superficies, and yet an Axis 


= we.” e F 
5 5" of) 8 
8 


1 
1 . * 1 
1 * 
1 * „ * 1 
4 A 
< 25h BE IR X ; 


is required, in this Caſe ſet up any point (of wire, 
or ſuch like) of ſuch Diſtance from the Superf- 
= cies, as that the Hours and Axis may be diſting; 
and through that point let it be required to make 
the Aris paſs; you have no more to do but only 
co project to this point as before; by letting the 
Shadow of a perpendicular Thread paſs through 
that point, and noting the ſame upon the Horizon- 
tal Thread, and counting that End of the Wire as 


dat nes to project the Hours is a Pattern for the 
Tuis Way is general, ſerving to project the 
Hour- lines upon many Superficies, be they 


= plain or curved, and however ſſtuate, whe- 
| ther contiguous or ſeparate, and that with- 


- »* out any laborious. Inquiſition after any of 
= their Situations in reſpe& of Declination, Re- 
= -  :Glination or Inclination. „ 


8 4 - g * 5 


6 een * 
a r 8 
. Fx 


your Center, proceed as. before; for the Thread 


Gene Vans 


i 

1¹ 0 y 

8 eee aue n © 

1 onA vat. 3 

| Se. 

if thw Howl 4 2 Enriaintlly he fo pal, 2 

th Hurt apo any e flat ar IND] ove 3 

1 0 more. a Bon. : 2 

7 FL RST, The Glad dan bucel truly Hori 1. 

= 20ntal, obſerve the $pot'of Light that the Sun A 

calls; and make a Mark at it. E 

Secondly,” And obſerve immediately. the” Same "0 

Altitude, and find thie Azimuth.'- = 


y . Thirdly, Then' extend an Horizontal Thread in 38 
8 Room: ſame Leyel With the Glaſs, but within the 2 
a  Frarthly, Proje the Azimuth! into the Horidage .- 
-. WM Tbread, by holding up a Perpendicular Thread 1 
in ſuch a place, that tho it hang at Libert u 
may at once diſcern both the Mark of the Spot of 
Light, and the Glaſs likewiſe; and then obſerve 
where the perpendicular Thread ſeems to cut the 
Horizontal Thread; and at that apparent Interſec- 
tion make” a Mark mooſe the n Thread = 
for the Azimuth. YN 
Hiffibiy, Apply a Paſt eardt to the Glas, fo that. 22 
it may 2 ſtayed upon ſome Reſt, that after it is 
taken away, it may be reſtored into its place again 
with all Exactneſs: Let it be alſo placed Hor. 
Leah, ſo that it may have fall Relation to, the 4 
Horizontal Thread. - | 
$:*thly;- At the Glaſe's Center make a Point for! 1 
the Center upon the Paſt-board, and extending 


f. Tem. from the Center or the Paſt-board to the* © 
| Mark. - 


oe 


4 5 174 "Geometrical Dialling... 


= Mark of the Azimuth upon the Horizontal Threat 
. dra upon the Paſt board that Line, which the ex- 


unto the ſame Azimuth upon the Paſt- -board draw a 
Meridian Line, and to it an Horizontal Dial ; and 
applying the Paſt-board again to its firſt Situation, 
project the Hours thereon unto the Horizontal 
Thread, and there make Marks or Knots. 
"Seventhly, Then projet the Meridian (by a 
perpendicular Thread, covering in Appearance both 
the Knot at 12, and the Glaſs) unto the contrary 
Coaſt to that, wherein the Pole is elevated above 
the Horizon; that is to ſay, in our Northern Cl: 
mates, you muſt project the Meridian Southward 


= ed: And in the Meridian elevate your Semicircle, 


$ zouthwards, till the Plammet falls upon your La- 
dttude, ſo ſhall it point out upon ſome n ſet 
00 receive it, the North *. e 


indaws, which look towards the South, 


(and fo the Axis above the Glaſs extended to- 
Wards that Pole will be without alſo) you 
may in ſuch, Caſes. find out the oppoſite Pol 


= the Glaſs, and below it, would ſign out, and 
= that may be effected i in this Manner. : 


gin, Project „bonn 

1 the Pole that is elevated, that is with us, towards 
=— the North Pole; and then (becauſe the North Pole 
js elevated b Reflection towards the South, ſo, 
== Nr the e ane Reaſon, oy South Pole muſt be depref: 


. tended Thread Figures out thereupon; afterwards 


from the Glaſs, becauſe the North Pole is elevat- 


or extend a Thread and Quadrant from the Glaſs 


- On elſe, 7 this * not Fönen because in 


3 Ds the North Pole will be without the Room, 


to it, that is to ſay, that Pole which the for- 
mer reflected Axis being extended through 


"04 8 


3 * 


String and Quadrant, directed even with the Cen- 
irds ter of the Glaſs, expreſs. or project your Latitude 
wa downwards, (but towards the North) ſo ſhall tie 
ang Wl Semicircle or Thread point out the reflected South 
on, Pole in the Meridian. Now, whether you will, 
ntal Nor can (moit conveniently) uſe the reflected South 


Pole below it, you are to take your Choice, for 


«4 


y a boch the one and the other of them do repreſent 
oth Ml the reflected Axis of the World, © Te 


ary Ninthly, By this reflected Azis, and the nen 


ove MW points ſigned out upon the Horizontal Thread, 
Ci. you may eaſily project the reflected Hours, upon 
ard any kind of Superficies, one or more, whatever 
vat- Wl they be, that ſtand in the Way, xy. 


PL 


— 


laſs gt; 


_—_ 
- 


* a 4 * 
- . Ka 
2 F 5 . : 2 <> "a 
* 53 . . 
8 : 
— \ , 
4 * * 0 4 - * Y * 
* % 7 1 — 2 + $44 * 1 * — mg * 
7 ; 4 4 : ; * 
A Ks £ * - : > > * 7 * * — 
s 5 * J * 
: N 85 %'Y FI 


| ſet t 1 |; . 


2 
* 


x > ek * - RR 3 2 ” 8 2 

> *Y a 2208 ES 2 ,< F 

3 3 8 . 
8222 


n as 

32 N 
a —— 2 —— 
Kr. N 2 r: 


X.. 72 4 "SS. 
n 


<4 4 * 
- OE 
P34 1 
r 
EI 
5 N iv 
- bf 3 
2 NE LSE EEO 
7 4 Fe) > 
n — "= 


REP ca a * * 2 "IC" WWW a | 
V * eee ß ET en 
RR : | 0 J) I don ro do a bY oe N 
2 r > 0 : * ” * 8 n e e r 
. 3 wh . wy 4 e is wo od ERS 
3 7 N þ : r 
__ © "Ureometrical Dialiu g. "0 
8 5 . ** b 4 ho 5 % . x * og #3 
4 g 4 » 1 . A 4 E X 4 & 
* o 4 Ke ©. 
, ; 3 80 Mi * 
, P 25 9 £8 
89888 5 1 
ed the North) by your Semieirele or 
. bs 4 II n * : be. | . 
war. | 1 nicircle, or 
ins J 74 
8 


3 


* * 85 
d She 
2 2 
1 
— —— = 
„ Vo 8 
7 1 8 
3 


Bn EST? * PEEL 
— — EY 
1 


* 


TOY en 


a; 
3 


oY 
— 
28 * 


C 
n 


„ 
— ——» — — —— . nh. on. 
. —— ELD . nn EE = IR 4 
i,%\$> 6 LAT ASS 92 vie .o'g y P 
— — . 
=> — — —— - — . 
5 a — . p 


U 
11 
* 
4 
4 


os 


t 
» 
* 
Fd 
* ö 
1 
* 
LF Tad 
®, 
10 
's 
% 
Wo: 


— 8 e nds 


* ü rr rr. — 
„„ rr . 
— = 


- » —— — — — — 
— — — — 
_ at AMC ACA CEE EC Ar ee CC er Oe Ce err ee CO Oi re ala — -_ 2 — 4 


1 
1 


: Geometrical Dr I A LLI N 0 


* 
gue > 2 p « - F - d 
1 Y T4 . * N 5 7 
* N 4 Y 4 4 q 1 3 5 44 5 4 1 
455 er B of s 3 1 _ 8 . 
2 7 ” 4 i 
. 


. 5 . 8 5 c H A P: IX. 
2 7 e male. 4 plain Dial (either South or . 


et ſhall give you the Hour of the Day at any 
= a Race or Places aſſigned, as well as at the las 


TS 


— F2 - 


® wy A reckoning. 
* * * 2 MY; 
f . 5 I 
0 k 4 
ö 9 
* 


Sogth or Horizontal, as you would have your 


= -- the Hours ina CircularForm, as you ſee 
1 7 late 11. it done; then (beſides. the two Circles, 
| SA EF x between which the Hours are placed) 
—_ draw fo many Concentrick Circles as 
you would have Places i in the Dial, and behind 


of whoſe Hour it repreſents; then obſerve what Dif- 
=_.- ference of T.ongitude the Places propoſed have 
dom Ee guden, and by allowing 15 Degrees for an 
er. 8 the Hours with ſo much Difference 
the W of e . ah om 


br Dial is 8 r, — 8 the +" on Way 


by | TR $ T. Make 2 common. A Dia either 
Dial to be only in this "Caſe. i it is beſt to place 


the Stile in each Cirele put the Name of the Place 


the moſt correct Table of that Kind now extant, 


A Table of Latitude, and 17 


dom ſhall give the true Hour at any of the 3 1 
propoſed. But becauſe in this Caſe a Table of 


Latitude, &'c.. of Places is neceſſaty, I ſhall inſert + 


an Example of each of the nenn OE 
19 85 : 5 - — 1 n , 


* - 7 ® : * 
1 4 a ls * * 


A correct TABLE of the Latitudes and Dif- 4 4 


ference of Meridians from London, of the 3 1 


moſt eminent Places in the World, my 
e wy 6 Celeſtial, . 


a 
* i 


* 


* - 3 
5 I < 
% * So 8 * 
* 5 ? 5 2 PS => 
a, 4 . 
= Þ 8 * 5 * 7: 
J ; . 45 
* * 1 > 4 


£20 


x D. M. H. M. * 
bf JCapulea i in MS N .. AWE 
Agra, the Mogul's Court 128 
Aleppo in Syria * 3 137 
{Al . in Egypt: 34. 
Amſterdam i in Holland - 49 
Amiens in France _ 52 
Antwerp i in Brabant 51 
e in Frauce 
Babylon in Chaldea 
Barbadoes  _-- 
Barcelona 5 
Batavia in Sumarr 


Beugel in in ids : 7 2 

Bergen in N. orway 

Bonouia in Traly | 
Bofton in New-England 05 
Breft in F rauce | 


Bonr dean's in France. 


R K ; * < 
+ * 22 þ * * 8 2 © 
* + * Ss Yes by © 4 4 1 

= a 9 1 5 4 

n * 5 1 * * r* 


; Names of Places. © Latit Merid _ OO 


? . 7 12 + 
* * 9328 * =" — * $ 


* 1 
6 * * 4 Ws 
* x p 8 IE * 
Ps 8 y . 8 * b 8 Jos. +4 * 8 * \ . 
; Wal , y 0 8 "Ys 1 - E wy x ö x * : 
4. 8 124 & 1 = 9 } r R — 2 SEA n ' 1 12 O ; „ . 8 * 1 
6 8 ITS l 1 2 as: 2+ 6 1 8 N FEI SK: 8 2 : 1 1 5 1 N * l 2 hs EY > Be. 8 * 5 1 
- a - 2 2 $4 x37 * 442,508 . * „„er Nen IKE 3 k LI ION 2 * mats. 4 3 OR * — Cz — — — — — — 
— TEENY, ECT STINT er — ä — PP A 7˙ . E — AO) TA ATED Ge EEE oe TI ES 0 Lg ol 2 
— * : IJ ns CNS 3 _ I „ 7 *- 2+ 7 7 5 * * Fs _ 1 Ae SE 8 2 664 1 1 2 " a. 4 1 — 3 e 
2 8 8 — ; xe of Pl 2 © W ds a eas N 1 — 8 6. Yds N n 
v . a F g * li dts. AP i — — . = 3 7 2 


ers 
* 


6 


. 5 8 5 5 Bi 5 
| | * | Wain of Pons, | Latic. Merid | 
. DD. M. H. M. 2 
„ 0 Sl 1s 
2 *. TCamboia in Traly : 5 9 
= . Canea i - nal 


_ 
1 * « 
—_— 
_ ; 
* e Bon 
5 : As. IE 
. 5 „ 
2 wit 
- . 2 
ox N 
4. 4A» 4 
* * * 


he Comerin 


— 25 e , 4 i, I 
Cocks in the Eaſt Indies > 
Coimbra i in Fortagal . 
22 antinople 5 
7 Pr 1 3 
1 


1 Ie * * 
A * 4 4 * 


F FOOL 
NOT 7 
16 FX 2 


* 
1 * 


n 
nnen 
99 TS 3 


. 


9 , 

* 0 * . 3 'C; a 

* Is een Rt TY. — 
* 


z * 4 8 1 : 
% \s 6 S068 : r n 5 ee 
4 oy * By e 1 . Y E 47 bh, 3 Yoo a 7 
5F- ©.» Yagi, bY „ 4 * 1 3 rr. 
r M 7 5 BY S 233 „N Ab. te, $3 
TN „ f vp ns ) 7 ws 
7 5 5 
* 


3 
* 
ro + 5 * „ 
WY » 
* . * 6; 1 7 * 9 N 
$75 "4 


FC Cue i in Per 
il in Poland 
3 IP 2 # Dep | in Normandy 
22 4 Dabliz in g 
===> 3 in Flarders 


Des 


mY 
. 


% a * "pa 
Wy. Ft #4 


* hy 
* 2 * . Nr 4 


"A Table of aal "and | 


N eee een 


* 


; Names of Places. 


Goes in 2 ealand 
Guardalonpa : 
Greenoble © 
Hamburgh 
Hader. de grace 8 
Heydelbargh 1 
Hogignam in China 
Jamaica Fort Kt 
Jerufalem - 


K! — in rale a 
Leghorn * % 
Lege 5 5 
Lopfick I "3 
1 - Pere Fs 
mz in Auſtria 
Lins in France 
Libor in i 
LONDON” 
Macao in China * 
Malagaſcar 
Mazrid in Spain _ 
„„ 
Malacca . . 
gone; | 


* * 


„ : 


2 
3 


7 = * 


' 


F 


. 
7 7 
- 


OE] 


? 3% 
TORT 


a . 


1 
1 


54 55 % 
43 1 
350 420 24 | 
51 190 53 
12S 205 24]V 
16% . 


E 


* 


. 8 8 


1 , 
8 ö 


1 8 in lee. 
Nople i in aß 


= | Nie. | 
= 7 
— Ningpo, or Lions in d. 


e, 


* W 


'N ames Ry Places 


— 


OE INE BPG;  * 2 


a 
— in 1 | 
© md nnd 


Provence 


eig 
Olinda or Pern mb 


| in Japan | 4 


N 


— Pa in wow 


p Wu i in ey 


Paris in France | 


1 Feet dar © 5 Ge: bo” 
Salamanca i in Sow 


Selle 85 : 
Siam in Tudia 1 . 
Smyrna e 


" — 


1  Spahan in Perſia | Fa 
=_ - UN in Ju ker 
1 ng in Sicily | 


+ M. H. M. 


Diff 
Ties” Merid 


* e 4-5, 
y — 


. e 4 
"794 in 
y + 
? 5 X | | 
1 : Y | . 
2 1 
' i” 
' 5 2 l 
4 we 
hay 5 x p 
f — — ETD, f 2 . 
- - ” * r WA 
Y 
__— — EE . 
8 . 2 43 a x rl : 5 — — 
3 5 p - Wages e 46 
5 E : _ * rn „eee ee 3 » Athy 2 
8 % ; ; 
NS 4 x s 13 7 : 
P 5 1 . 
1 — 
L 
— ” S » 
a 


4 4 * * 2 5 14 8 


* " Geometrical T Dialling. | 


— -v 


Names of Places. 


Taere vl Gon . 8 Re 6 37 
Toledo in ain 111839 ᷣ4 600 14 
Toulon in France „ 
Tripoly in Barbary 3% -14 64 Wt 34 
7 ing in Germany . „ 340 : 
Valencia in Spain 9 3000 8 
Venice, 504 3 203539800 : 
Nins „ ee eee 
| alin Sweden | | re 
ee bs = „ 27 P83) 23008: 7; 
Wittenburg) in e $ax0; 3 511 5 


w Sv 


No ke. " by 4 : & # <: * 

2 4 2 2 gk 2 of 1 4 £3 — % 2 * 0 „ 54 . * & 

EN ** * * K * f 
I 811 +7? P : 1 151 8 } } 4 74 

* N Fn 5 
2 Has . ; 
* 3 5 

"= > * . 1 * 1 ; N 


| Nor, In the Sand: of Bandes where 
f $ 281 is placed it is South Latitude, es alt e 
reſt a are North. £5 


oY * * 
1 1 

FI of 3 BY wy 
— «4% p 9 . 0 1 

7 , 1. ; n 

! Y * 7 * a a 
of Roe * % 5 * 1 1 * 8 
a 4 d * * * = * * + by 6. 

a ; * 1 » 5 6 55 1 1 3 - 

E 2 ao 4% , * p $ a 15 . "WP a 3" > 2 
ry my « * . 5 LE *» ! 1 
. 8 
+ 
3 
* 

1 


8. 


1 ſhall now 1 to SES che kosch Di- a 1 
ections to Practice, and ſhall inſtance frſt in 1 . 8 
iontal Plain Dial, which ſhould be requited © © 


STi gs 
* 
2 


jth 4 2 . 


ive the Hour of the Dy at Landis, Mexico, wn. 1 A 
Yeruſalem. Sa. | 8 4 
Nit; Draw a Horivoutuh Dial by the Directions : 1 


ven Chap. 3. Of Geometrical Diall e 37. 
hich reduced to a Circular TY 
A Plate 11. Fig. 1. where the middle Circle 
* 4 a + 4g for the "ROWS nm 


ee gee” ISAS ARDEN So DEF OP TIE RL 


” x 9 


" Gromerrical Diallmg. 


then within that Circle of Figures FOE: 


= Tabs, 
=. the Concentrick Circle a b c d for Mextceo.. Alſo 
1 "with? it draw the Circle e f g h for Jeruſalem, (ot 
= dtaty them both within or both without, 
1 72 — thetis more proper, becauſe one Meridian 
1 —— the other Weſt from Londan) then behind 
te tile in the jnner Circle write or engtave 
eco) in the Middle (London) in the nter 
moſt (Jeraalem); then haying'Retourſe to you 
| Table, Hou find that Mexico is Weſt from Ln 
en s Hows 49 Minutes, (or Which is the flme 
wer it fs 12 a Glock or Noon at Mexico, it is 
= 1491 Minutes * paſt Afternoon at London; ther- 
EZ ifotehy a Scaleeftbm Q, the Center ef tte Dial 
neh in this Caſe is not confined to ne Center 
3 85 fof! the Girele) to 49 Minutes paſt 6 in the mid 
3 dle Oircle fer London, and there Make a Stroke 
1 . np! : ky{thin the inner Circle, which ſhall*bexheHour- 
=: Moeof At Mexico: Likewiſe lay a: Scale from 
=* «>. the Center Q to 49 Minutes paſt 3 in the Circle 
bier London, and there in the inner Circle for 


4 of + + 


*Þ + 9 5 "Mexico, *place thei\-Hoursline of 1, and {0 pro- 
3 . 5 red round the Diabto ly the Scale t0-49 Min- 
=» 5 antes paſt every Hour backwards fromed, you hare 
| * the Hours from 12 to IT, 10, 9, 8, c. at 
Mexico, and the fame Shadow that gives the Hour 
IR * At paton-inthe'middie Girbte,>givesrat the ſame 
$ MH me e, (Hoe bt Aerte rin the ner 
e | ' 8 ; . bet «Bo HTC 


f - 
S 5 * * 61 A ENT 


EXAMPLE. 


” 2.0 „Sberoßr hgo ne be e aches, and 

nud the Shadow of the Stile inthe Line DI 1 
* 5 Is Audit is half Ann Hour paſt. 9 at: Amon, and in 
the inner Circle it is not. quite three Quatters of 
an eee 5 e 
TY EM - ; 7 EE WH pi 


2 wp. oy 3 


9 
* a 
+ 927, —— nba 


be. 


vs 
« 


* 


o * - — 4 
* + T7 . 
; Xo Sk 
3 
- 


ther Dial, Whether Direct, Declining, Inelining. 


* * ä N 'Y 
8 Ke 4, r erm 
1 „ en 
* * * pt * ay TE" br oof = 
s 4 * WW 
2 5 K q 
* : 1 
ical ia alling. 4 oh * 2 
61 # : 
8 * "8 : 5 


piſh 2; and f 5 70 100 at 6 in the Mornitg,-it is 
a Mexico but 11 Minutes (vx. not a Cuner ol | 
an Hopr) paſt 11 at Night. 

By the ſame Rule you may. inſert as many Pla- 
ces in your Dial as it will contain Concentrick Cir 
cles, and thereby give at one View the Hour at al! 
the _ remarkable or remote Places in the | - 3 
World. | | 

Tn. ſame Method is to be obſerved. in-any. o- 


or Reclining, by placing 'the Hours at ſo much 
Difference, as is the Difference of Meridians be: 
tween London, (or any other Place that the Dial i: 
made for) and the Place afligned ; but that the...” 


Learner may not be at a Loſs, I have © 8 "i 
likewiſe drawn a Specimen of a South Plare 11 1 
Dial for London, Jeruſalem and Mex . 2. 1 


ico, by vhich any Perſon may do te 
like for any other Places, and the Method 65 6 88 
and intelligible, that it is not. neceſf 


ay more ime in Directions about it. e 5 


Note, You may by theſe Tables. find the 2 = 5 5 
at any Place afſigned, without having it R 45] 
-upon u Dial, by, ſubrraing the Difference. of - 


Meridians ffom the Time at Losdon, if he 85 2 = 
Place be. Welt from London, or adding TE:it-+ 
'be'Exft, and thereby having." the Time of af | 9 81 
'Eclipſe;,. new or full Moon, ec. at Lows RA 5 = 


may know at what Hour and Minute it is, Fo 
* e the 2 2 


SECTION: I. 


| mob "TRY 10 draw the Hour-lines upon any Plain 
45 Be 5 95 Line of N "ay 


HE 8 E Lines may 28 inſcribed on 
d the Side of any Dialling Scale, edu 
or any other Inſtrument of Braſs o 
Wood, and they are common 
known by the Name of the Lined 
| Hours, Inclination, and Latitude, and if you 
have them upon any plain Scale, vou ought . 
have Chords to ſeveral Radius's; but in this Cf 
I would rather recommend a Sector, becauſe then 
you may take Chords, Sines, or Tangents u 
What Radius you pleaſG. 
I ux firſt of theſe Lines is the Line of Hour 
commonly known by the Word (Hours) at tit 
ee of the Line; it contains 6 Hours, anc 
is. . e with — — — from I to Vl 
- FA. R$ | £ 


is 4 


*. 3 
Fe 
5. y 


Wenn 0 * 
* eee * 
* EL 4.0 N N 
* 4 e N 
- id 3 . 4. 
. 1 .- 1 Rm 
"FN, — f. 1 
*.. 2 1 1 
2 ® oF g . 4 3 
| - - Sy 4 
i 1 
? 5; 
5 


2 Tux next to that, and cloſe to it, is the Line 
8 Inclination, known by this (Incli.) at the 
505 zinning of it, and is 90 Degrees, divided in the 

fame roportion as the 6 Hours are, ſo that every 
15 Degrees in one is an Hour in the other, to 
ew how many Hours and Minutes of Time an- 
ſmers to any given Number of 1 mm en 
nutes of the EquinoQial. | . 


EXAMPLE. 


1 7 SEO: 8 * : * Y 83 * pul 7 N at ed he IDS 4 WE dba 8 
ok * — 7 CAN # A 8 * 
5 C 75 - 7 n 
2 þ * 4 , 7 K. 2 . 
” * 
* 4 * * 
b o „ 7 
ha 1 4 . . 4 * N * 
F \ 


— 1 would RO how many Degrees and Minutes: 
of the Equinoctial is contained in an Hour and a 
half of Time. Look againſt an Hour and a half 
on the Line of Hours, and under that on the Line 
of Inelination you find 22 deg. 30 min. and ſo 

much is contained in an Hour and a half of Times 2 

Tn next is the Line of Latitage, * marked 
(Lat.) at the Beginning. 

Sour have two Lines mote, one marked G 
Pol.) and the other (L Pol.) but by a Sector 3 2 
Lines may be more commodiouſly ſupplied fromm 
the Tangent; but I ſhall ſhew the Uſe of both, 
and to avoid Prolixity, I ſhall fall directly upon 5 | 
Examples of the Uſe of theſe Lines in wee 
Vine 34 ay mw Plain.” r | * 5 24 


F 
7; WEST $52 . 


* 
3 

"Ms 3 

— — 


. 
3 
Wn 


3 4 35 
8 1 : * p > 
2 4 2 PR Bet 5 . * * 3 8 We 
FCC 


* 2 1 * pe { 3 : 
Y * — * - 4 - > < 
fs ; 2 wy, © 55 » hg þ 4 5 © 
b 7 ? 1 * L = * > 4 1 & * * * * 5 "IS 2 
4 To ? ES. — * „„ © > 

2 i : 1 ; 4 7 "Te 1 9 5 D 

$ | | EEE £ 1 SE ; 
; ; * „ 


* 
* 


AN 
4 L 
.* 
1 
q 4 
ES, 
"cM 4 
4 
=. 
* RP 
_ 
'Y 
3 
Bet - 
_— -- 
© A 
"0 
_ 
a 
2 
+ 
_ * 
* "z 
q L 
"> 
3 ; 
47 
et 
5 — 
=. 
= 
A * — 
vg . 
en. 
EY 
bc” 7 
Wn . 
= 
3 
* 
* 2 
1 
* 
* 
. 20 
A * 
* 
+ 


» 
r 


n 
Dd, 
"4 I „ 


7. „ 


n x 
n 


*; 


. 
* 
J 
- 
_n 
" 
"— 
* 
* * 
. 
Ws 
4 
.. 
- 
"oF 
2 * 
* — 
Ro 
- 


- '» * 
. 7 n . 4 bY * 
2 . 


* a a os 6 * 3 
; 75 . e 7 6 
BAK. : 2 * Dp. 
ns i © SECTION 
1 bl _ CEE 4 11. 
* 


Is; 70 ow the ee ni o a Horizontal Dial, 
for Latitude 51 deg. 32 min. 


Figs? Draw the Line E W for the ſix 4 


Clock. Line, and7at right. Angles.thereto dray 
the Line N S for the 12 a. Clock: Line to biſſed 


7 the former, where. you- intend to have the Centet 
S: vour Dial as at A. | 
Iuxx fixing one Foot. of! HOME. Compaſſes in the, 


ing of your Line of Latitude, extend the 


ED —— to 51-deg, 32 min. the Latitude of the Place, 
and ſet that Extent from A to E, and. from A to 
3 W. then take in your Compaſſes the whole Scale 
of Hours, and with that Extent and one Foot is 
E or W, wiel the other Foot cnoſs the Meridian, 
or 12 4 Clock Line. i in 8, and draw the Lines L 
3 Ke 
ux take in your Compaſſes the Diſtance upon 
WE: the Line of Hours from the Beginning of the Line 
to I, and ſet that Diſtance from 8 to 1 and 11, 
and alſo from E to 5,fand from Wto ; take allo 


the Diſtance from the Beginning of the Line to ll 
on the Scale of Hours, and ſet from S to 2 and 
10, and alſo from W to 8, and E to 4: Alſo the 


Diſtance from the Beginning of the Line to 11), 


and ſet from 8 to 9 and 3, Which will alſo be e⸗ 
qual to the Diſtance W 9, or E 3. Now Lines 


drawn from tne Center A 7 theſe Figures, 


7. 9, Ex. to the Limb af the Dial (which may 
be * or Round in what Form you pleaſe) at 


— 


53 SSS Wm] 


N ; " 
eine OT" ON? 5 
. * 
s 
17 nth Dicks 
m 


the he Hour-tines of that Dial my for the Hoare 1 
before 6 in the Morning, vis. 4 and 1 and: He- 7 
wife 7 and 8 at Night, they. muſt be Ces 
through the Center from their oppoſite Ho! 
then are your Hour-lines finiſhed ; and . 
Sile, it muſt be a Plate of Braſs, or the like, to- 
make an Angle of 51 3z, (the Eatitude of the: 
Place) with.the Plain, the. Angular Point: being; 
fixed juſt at the Center A, and the Stile ſtanding: 
upon the Meridian Line at right Angles with a 
Phin of the Dial, and then. is your Dial, Hinjhods- 5 


8 E 2 1 1 0 125 UI. 
lw 70 draw Hur: iner upon, a a red South Dal 5 


T HE fame Directions, that ſerve for a Et. 
$ontal; Nia may vxith . a title; Alteration; fery 

for draming the Hout⸗lines upon 2 South Dial, 
ik inſtead of taking the- Latitude of the Place off: 
itom the Saale of 1 — you take the Complen: 
ment, proceed. in all RoſpeGts as before, onby nume 
der the Hours the Contrary: it will produce ai 
South Dial. Fhe Neaſbm i is; decauſe as the Nortk 
Pole is vlevated above the Plain of the Horizontal 
Dial, equal to the Eatitude of the Place, fo the 
South Pole is elevated above the Plain of the South 
Dial, equal to the Complement of the Eatitude o 
the Plaue. Therefore if you would make a Son 
Dial for Latitude 51 degt 32 min. take 38 deg. 2 i 
min. the Complement: of the ſaid" Latitude, (or it 
you work for any other Latitude, 'take arr 
hos Complement of the ade you rovk: for; 
8 out 


© > o 


out of your Scale of: Latitude, . , 3 . in all at 
eſpects as you did before, only accounting the le 
Meridian- line for the Hour of 12, number the Pi. 4 

gures the contrary Way, viz. to the right Hand tv 

of the Meridian, as Practice and even Reaſon it Ml yo 

ſelf will inform you; and as in the other, the Stile def 
made an Angle With the Plain of the Dial equal Ml 24 
tothe Latitude of the Place, ſo the Stile in NY He 
2 . muſt make an Angle with the Plain of the Dial e- tha 
© qual to the Complement, of -the Latitude, and. the 


both ſtand at right Ae . or en 
B to the Plain. 


8 * 0 T I 0 N wv. 
of a Dire North Dial. 3 


NA 701 Sv 1; Prog” 7 1 
"A? North Dial is the lanai in all Reſpegs with Q 
South Dial, only in a North Dial the Stile 
points upwards towards the North Pole, becauſe 
the North Pole is elevated above the Plain of that 
Dial equal to the Complement of Latitude; for 
I it-is-anuniverfat Rule in all Dialt that ſhew the 
Hour of the Day by a ſtrait lined Stile, to have 
tkat ſtraĩt Side of the Stile, whoſe Shadow gives 
the Hour, to lie parallel to the Axis of the World, 
and to point directly to that Pole which is elevated 
above the Plats! of the Dial: And the Diviſions 
for the Hour-lines are the ame, as in a South Dial, 
if they were to be inſerted; hut as it Would be 
EF ſuperfluous to deſcribe Hours which could never 
de ſhew'd by the Sun, it is proper t© omit the 
MM i hg — vix. , ä 12, 4 55 hk 


783 


Shy wy, ww 

-- * 1 N 
* N , 
, GE. 


Jang MI tude, you muſt put on more Hours; as ſuppoſe 


>n it you ſhould make a North Dial for Latitude '64 


Stile {MI deg. oo min. the longeſt Day there is 20 Hours 
qual 24 Minutes, its Complement to 24 Hours is 3 
this Hours 36 Minutes, the Length of the Night at 


al e- that Time; half the Length of the Night is ai ways 


and the Time of the Sun's Riſing, which in the fore - 


-vlar mentioned Latitude 64 deg. is 1 Hour 48 min. 5 3 


for the Time of Sun's Riſing in the Morning, and 

half of 20 Hours 24 min. 07/2. . 10 HGurs: 12 min. 

n the Time of Sun's ſetting at the longeſt Day in 
178 Wl that Latitude: But that the Artiſt need not be put 


to the Trouble of Calculation, I have inſerted a - 


* * * TYM n ” * 
ä 82 N wen een Pe Ot EO * am 
K , . r , a : i 
Fu” * 1 1 > \ x * * 33 46. 2 18 * 9 n 
A 7 4 * N eee FETT 
©, * . 2 F : : 1 a | 
50 ' : 8 9 22 g | 
o * = : 
p . 83 ” 7 fl 8 | 
: "IS os. 
N 1 4 8 « 
. F g : 
* 3 » * 4 
\. 41 1 : af , ” 
*. mor ( 4 * * ; +8 q 
1 , 7 5 r 6) Fay N * > #4 E. : 


at which Hours the Sun is under the Horizon, e- 
the ven at the longeſt Day, in the Latitude of Lon- 
» Fj. an, but if you work for a more Northerly Lati- 


Table, which ſhews the Length of the longeſt Daß of 
in all Latitudes, either North or South, 18. from 
Pole to Pole; and although the ſame Table extend>+ 


ed from the EquinoQial to the Polar 1 


might have ſerved in common Uſes, yet for be 
h 2 Stsfaction of the Curious, I have inſerted the * I 


LY : 


whole as 


E 
* $4. 4 * % 
* * 


} 


. . 8 - 3 1 8 : _ 

* A3 £253 0 2 I H y 7 no „ N WH 
: Ec : , — 5 + "3% "2 

i > 7 ; : , 2 ? ed We. 7 3 
v * 7 ? * 5 x . + 9 
= * * * - * : 4 * 
5 * 8 : * : 7 8 Þ 

* % * 1 * x . A 17 -* p * 


© 3 a * 4 0 p 


1 


* end > 2K; ab «EC oath * 
A Rn N — 4 beat af; hs 
nn * N * F S * 20 17 
L arr ”m—_ GE P oh 
* * > <1 . 1 
{3 
1 
i 
= 
% 
* 
5 x " 
4 x ? 


— % 
Wo 


5 A TanhtE ſhewing the Leigh of the Wen Ar- 
tificial Days, in all Places from the Equinoctial 


1 
E  - . tothe Poles of the World. 
* 1 / : g b i 8 


8 


— — 


| 
166 11 23 
171 21. 4) 
176 5 29 


187 6 39 


* 
— - 


Tux Uſe of this Table is very eaſy, for in the 
4 firſt Columns you have the Length of the long: 
eit Day in any given Eatitude-in Hours and Mi- 

nntes, and in the two laſt. Columns you have the 


- 


91 21 30 


Length 


e [ 
r 


a8 1 m_—_— * 4 M * 2 E. 


any Erea, Direct, North 


Length of the longeſt Day i in Days, Hours, an 15 I 
Minutes, the Sun in theſe Latitudes zemais 24 
tore the Herizow diving > many Days, wile je 


is near his,greateſt Declination, of the ſame Den | 


mination With the Latitude of the Place, whether 4 
South or North, and when the Declination is con- 


ry, the longeſt Night. i is the fame I Le 


R e Length. 1 


"3p Is 60 deg. Norah, the Ons 1 
15 Hours 30 Minutes, which Happens when the 2 
San entets Cancer, and hath,z3 Ceg. 30 min, N 1 
Declmation; but in 60 deg. South, he. Day is t f 7 
fame length, when the Sun enters 7 . 
bo in the ret, but Beyond: Latitude '66 deg. 
the du un contfnues above the Horizon feverat D ws, | 
15 of 'W 7 is before the W and Wa A* 


* ” Ms 
3 3 $7 = oy -f 
Ur. aft ; 5 | : : 
, * * * 4 F 
1 $ 8 2 6. * -. 8 
” 
* 
* 
* 
* 7 
1 


* 322 113 * 1 E 8 


 Thckre 5 know the Longet D: in 135 de 5 
dB. os min. and I find it in the Table 54, Day 
viz. 37 Days before the Tropic, and as many af 
ter it, which is from the 4th of May to the Wo 
of Pauly. „ in all which Time the Sun never ſets in 
that Laziewde. 

By this Table the Artiſts may know by Inſpec. 
tion how many Hours. are Roy to be put upon 

ial, or any Tir 
tal Diet, in anx ' Latirade whatſoever. 


3% aw 4 * * „ 
*. ; 5 5 . 1 , 2 4 y os les vi = 
74 # et ws Fs "BUSY £- f : at i 25 x ; A 

. 3 $5 4%; «hh E 4 « A By... 

l 5 + "4 
7 , 1 * 2 

> + * '2 N ; N . 2 55 
53 3 1 : : 7 ge e's oo . \ ; 4 © 4% _ OF FA — c +5 : 
: . „„ : * > ba 75 * 3 #44 '. 42 * * * N 5 L ; 4 * 2 « £ ” 
8 K ; =  & 0 

ie: + 3 | 8 1 

S. 2 " Y £ 4 — 
2 5 N * A N W a * 5, p 1 4 + 4 % : : 2 D. 2 
LS 2 s © af. 4 * £ d 3 l 0 ' pt 
l 69 $ 2:32 L 4 3 2 6 w +44 * 336-2 hd 4 > 3 — — 

a * 5 0 4 = * 5 7 5 24 * fe” 
v3, 2 ny; i 8 8 £ 
* hs — LA 
2 : n ba wy 
* 9 


0 * „ o 
1 £ =... e 1 I * 8 . 
74 8 {© nn 5 

« & 
TT x 5 , * 2 D 
4 « js "_ - 8 * f - * e Py N 
> 5 
1 as * ® 
1 8 1 1 — 1 2 1 7 I 
a 5 1 % 2 4 14 1 4 % R £ 
o 7 8 - & © 1 * 9 W * 8 


1 1 
1 


_ Of South or North Reclining Dial. un 


N a Dire& North or South Reclining Dial, 
there need be no Directions given, but what are Ne 
already laid down, for all ſuch Dialt are South the 
Dial, or Horizontal Dials, in ſome other Lati- 2 
tude; fora Horixontal Dial in Latitude 51 32 or is 
any other Latitude, is only a Soxth Dial Reclin - thi 
ing 90 deg. for in an Erect Saath Dial, the South the 
Pole is elevated above the Plain of the Dial, equal wt 
tothe Complement of the Latitude; therefore if be 
2 North Dial in South Latitude, or a South Dial pre 
in North Latitude, recline equal to the Comple- or 
ment of the Latitude, the Plain of the Dial be- 
comes parallel to the Axis of the World, and g 
Stile of the Dial, and then that becomes a Hiri. * 
Soma] Dial under the Equinoctial, and hence theſe W Nt 
= general Rules may be dedu cee. 
I. IF a South Dial reclines leſs than the Com- Ml fro 
1 | 9242 of Latitude, it becomes a Vertical Dial the 


for a Latitude, fo much more than the given La. is 
tirade as the Reclination is. Or more plain, Add WW ing 
the Reclination to the Latitude, the Sum is the . 
Latitude, where that is an Ere& or Vertical Dial. 30 
VV ; Val 


1 '  Suyeos I would make a South Dial for Lat. 
| tude 51, 32. North Reclining 22 deg. Add 22 d. for 
to 51 deg.” 32 min. the Sum is 73 deg. 32 "ne all 

tr- il 


01 


* 2 a 8 4. a 22 
RG 8 N n * =” has wi * N | 
a 9 * ö R * * * Es ia xs "— F 2 

* : * * 'y enn FTI "7. L 

| : wo © ©, "—_ 

4 * 1 c 
FS 55 * 

1 N 
» b = 3 I 
z | 
. ; . 3 ey 

2 . 4 * 
k \ 

* 

a 

; 

<F 

1 

2 

y 


therefore A an erect dired South Dial, for 1 
titude 73 deg. 32 min. North, the ſame wall be a 
direct South Dial reclining 22 deg. for Latitude 31 
32, and the Rules for making it are the ſame in all 
Reſpects. 

2. IF the Reclination be equal to the Conipls 
ment of Latitude, it becomes a Horizontal: Dial 


under the Equinoctial, for Reaſons before given. 


— Therefor, 

Ir a South Dial in North Latitude (or a 
Non Dial in South Latitude) recline more than 
the Complement of Latitude, it will be a Hori 
20ntal Dial for ſuch a Latitude, as the Reclination 
is more than the Complement of Latitude: Or 
thus, ſubſtract the Complement of Latitude from 
the Reclination, the Remainder is a Latitude; for 
gs if you make a Horixontal Dial, it ſhall:alſo - 


be the N for the TOO: and. NINE 721 3 


=o EXAMPLE. =: Berne 
Tr reg F ; 

11defire- to wake- a Dial 2 Latitude 60 de. | 

North, to. recline 40 deg. 223 on 8 


SUBTRACT. 30 the 6 166 Latimde 
from 40 the Reclination, the Remainder is 10 


therefore a Horizontal Dial for Latitude 10 Nor 


is the ſame in all Reſpects as a South Dial reclin- 
ing 40 deg. for Latitude go deg. North. 1 Ef 1 
Fon it is plain, that if the Dial had raclined but 


zo deg. the Plain had been parallel to the Axis of 


the World, but. reclining 10 Degrees more, ele: 
vates the contrary Pole 10 Degrees, and becomes - ſl 
a Horizontal Dial for that Latitude. © 4 
Ueox the ſame Ground we may deduce: Rule 
for Incliners, for if we conſider, that the Stile of 
all a ſhould lie parallel to the Axis 5 — 
orld, 


* 


4 2 * * * R * 8 \ 
* A ITY WW * R TY * 4 
n ** CCC 5 PS nen r 
8 4 W N FT AN PRE . . 5 ? 
4 KEE I 9 * No 
7 < . 
; — 5 . * - * 6. 
4 A f . 2x 
4 5 , , V 
5 0 a 
& 3 
2&3 
4 
* 
& 
1 
8 


5 and confder how much the Angle, that 


the Stile males with the Plain of che · Dial, is aug · 
mented or diminiſtied by the Inelination of the 
Plain, it gives you the Latitude for which a Ver. 
ical Dial being made, it will be a North or South 
Dial wich the givem Inclination, andi for the given 
| - _ apr 4 5 _ one 2 ſuf. 


& 20) ** AMPLE: 


eee « South Dial for Latitude 57. 32 


North, to. incline 10 dog. . 
Ix is evident, that this Dial that ineknes 10 d. 
would be vertical; or perpendicular to the Hori- 


20n in a Latitude 10 Degrees leſs, therefore for a 


South Inclining- Dial in North Latitude, or 

North in South LatitadeCQQ. 

1. Ir the Latitude be more than the Inet;etion, 

fabtraQ the Inclination from the Latitude, the Re- 

mainder is the 'Lazizmide: where the fame Dial is 
| Vertical. a 


„ Ip the Inelination be equal-to the Latitude, 


ä i is an Eguinoctial Dial under the  Equinodiial.. 
3. Ivthe Inclination be more than the Latitude, 
fabtraS tho! Latitude from the Inelination, the re- 
mainder is the Latitude, where the Dial is Verti- 
cal;- but of a contrary Dlonointantion; wiv. if the 
Dial is to be made for North L it ĩs ors; a 
eee 8 centre. 5 5271 


4 * > Gr 423 24 
* K Stnr TOE 4 


— Eo mee Recliner | 


_ IF 
L 2910 . Fe- 4] 


Bf 1611 16} TITS) wn N 
291 [oF a n bn 201 185 iE 90% 2 
10 $113: is 2 11 II. 5 Ou 6 JI 173 i : 12 


ny LY : En 265: odd 122 B38J 11. bluod ser. 


* 


— 
r N 


eee gere g SRS SKS. - 


I; 


SECTION ky 


Hh to draw lug I ea ; 


Erle begin with an TER of an Ext. Dulfer, - 
Latitude 51, 32 North. —_ 
Tak in your Compaſſes tha Chord = 
of 60, and with one Fer in rg "Place. 1 1 = 
the Arch: A B, and ſet aff. the Com- . Hg. 2... Þ 
plement of Latitude from A 8 and. 
through B draw the Lines; C, B,. E, then re 
where towards the upper End of the Line C E ag. 
2 R, draw & R F, perpendicular to C E for the - 
Subftile: and Hour-line of 6,.aud dram H 1. 
6 E C; and at any competent Diſfance from. it, 1 
men from one of the Lines, marked. (Pe ap: 3 
your Seale take the Diſtance, from the. Begigaing © 
of you Scale to. L, and; ſet; that Extent-fram R,m 1 
55 and from R to 7; then take the Diſtance from 2 
the End of -your-Scale to H, and ſet from Rto , 
and ta 8. t alſp the Diſtance, from the Beginning 


al the Scale;to III, and. ſet from R to 9, and 10 


proceed-to. find the Hours of 9 and. 11 b bent 3 - 
es III, and V, upen the Scale and f 
ines 4. 4½ 4.5, 1 7 e. ae n 

ſtalb be the Hour: lines required. 
Tux Diſtance from the Beginning g ol the 

to III, is the Height of the Stile, 1 5 muſt 

upon. 'the -Hour-line of 64 and perpendicular 0 

the F hin of. the en i your, Dial fi- 


19 , 4 — 
38 . it ; iN 3: A 18350 203 


PWV 
1 
hs 4 | 


« WF. 


9 


; 
2 
„ ; . HE 
* 
- > ; 5 


A, 


Kao "= 5 x . Sn co 9 r 5 A F 27 W 
a 3 N "FS » 5 * 9 WY 9 * 8 Fr OY 1 3 — Fans, St < 
_— 7 * Rh 9 E A 9 4 
r 182 
= r AF p 
* * 8 2 a 0 * 4 
= N P: 
2 4 N 
ff ö 4X « 4 * 
8 ö . . 7 
j . * 5 ” L e $ 1 — / 
1 < * f 
F » 8 „ 
* N % ; 
7 
A 
1 


Tux making of a Weſt Dial is all the ſame, 
only as the Eaſt Dial is elevated towards the left 

Hand equal to the Complement of Latitude, the 
, and 


E take the n 75, they give the 


kected, gives the Hour · lines required. 
in ; S652, . $6 2:41 j ; . ; 


* 


: . . 
"1 $#7 143. AS45098 4 


bs © 44 2 
i... * WW3s ti - 


3 1 
E 4. + 


» — ON 5 o ; 9 


9 e = K 4 A m_ F- 

\ 12 * 77A 4 = K ; 
FI * 9 9 * 3 I. 2 IM e '. 

ad; * p l 2 bo OI IR © 4,08 

* p 5 
- F 4 
N 
4 „ ts 6 

. 98 , 7 1 * 

z | b 

: 4 

. | b 

% _ 's 

: 

x 

. 

1 


4 * above 45, you muſt make Rs 43 
Radius, which is at the Beginning of the re. 
maining Tangents, (which-is alſo BRL * 

And — as before. EE | ory 


veces c 


1 3 * 4 wo 9 


| SECTION . Gs” 


tw to Auen. Heter-lewes upon direct Eaſt or wet | 
Keclining Plains, 5 : 


n 3 * 
n IJ, hs 2 3 
Wn 


OP not trouble my ſelf to Sow any DireQi« | 
ons for drawing Hour-lines upon Eaſt or Weſt 
Reclining Dials, conſidered as ſuch; for as in 
Seck. 5. you have Directions how to znd in 1 — 
Latitude ay North or South Reclinet becomes a 
Vertical Dial or an Horizontal Dial, and it is alſo 4 
ſhew'd in P. 12 3 hom do reduce any Eall yy” eſt”. 


reclining Plain to an erect declining Plain 
ther Laritude, or in what Latitude the given P, 
ſhall be an erect Plain, and how much it declines; 
it will therefore be.ſufficient:to/ſhew how to draw 
Hour-lines upon all ere& declining Plains, be- 
caufe in them all I and Weſt Recliners"are 


included, | 
F = 1 

e . : I N 
0 * . 3 1 . : : - 1 : * 7 


. * a 


p 1 7 . * * A - 4 * 
8 „ ˙· Ede at ret rn yt ni OLE 7 * 
Eq G34 GANT 23 Javz” 2% 4 * A RK * 1 r 
£ * 1 * : 4 ” 


13 8E N 0 N. VI. 3 5 
| | 7 draw $ . 0 a North o or "South 4 


N *7 880 rr Plain. | 
i ſhall er in a South Ere& Plain declining 
Weſtward aa. deg. 20 min. fon rhe Nati tnde of 
8 don, 51 deg. 32. min. North. (See Chap. 7: 
- e 46 and 47.) —_ | 
: erer tv alen, dy required b A 
Et Ty: 91 2 2055 41K 2 N 
I e! N 38 Se 
; Se e | 


5 y E 2 # : $2 1 —_ 8 . e 1 5 z 4 
k : 1 a 4 4 3 : 
8 { ; 2 7 y } 5 pn 
_ dal. Eight « ef aber Seis above the 


The Inclintiowal: Meridian. 155 ob 


: en . Sallilen Dic haun ther dias. n 
Foray . e 10 000000 5 

o the Sine of the Plain' 8 Decli- 7 | PI 
nation 24 206. 99614944 a 

9 Tang. Comp. of Latitude 38 28 9. 900086 : 


To Tang. of Subſtile's | Diſtance . 
from the Meridian ene * 9.51 5030 


. Ps oo | : J : 4 2. For 


8 & mee $9. te Fd a6. 4 ES TD OT EEE TI ID ITE 
n 9 SY ** 8 e 


| For the Hei be of the Pole (ox Stile] above 


3 As eee, 

To Sine Complement-of” Latitude 
38 pr ene 

80 Sine Complement- of Dectination 

le- 65 deg. 40 min. * 7-3 


A * 
* g 2h *. | +25, % 4 — 


12 Si Sine of the Stile's Height. a- 
ing L Fe dove the Plain 34 deg: 32 min. 


. hs 3. Nr kreis of mu, | pa 1 7 


rd rd e eee 
ere of Deals 
5 65 min, 


0 * 


3” „ 4 


* _— — — _ 


7 - 


23 5 8 Fo X 0 n xc? 8 998. == 125 
N arm 7 — 


! e, the ny” be: | 
upon the” Sers Scale thus: Os 


1 
14 42 * +, \& {#5 n 


x, For the Subſtile's Diffanet” Fen the Meridian. ” 


Tus Extent from Radius: to the Sitte of the! 
Plain's Declination: : 24. 20, will react from the! 
Tangent Complement of Latitude 30. deg. 29 m. 
to he Tangent of the Subſtile's'Diſtance- from. the, : 
Meridian 18 *. e eee Led 


„ eri  EEESSES 3 703 
8 1 = . 4 SP a # a e * 


be RAS | £7 5 
* is CE a 


a bs alt "EE PPT DON I * 88 ** 9 
2 " 22 188 * 8 . * " K * ; * en 5 
A * * n 8 W 9 "TI" hs, __—_ 
7 * . Cy * 
8 N J. — 
* "V $ 1 — 


200 Hifrumemal Dialling. 


2. For the Height of the Stile. 


3 from Radius to the Sine Complement 
of Latitude 38 28, the ſame Extent will reach 
from the Sine Complement of Declination 6; 40, 
to the Sine of the Stile's Height, 34 33. . 5 


TS * : "© : 
: i 


i. For the Tnclination of the Meridian. N 5 


Tar: Extent 6 Radius to the Sine of Lati- 


tude 51 32, will reach from the Co- Tangent of | 
Declination-65 40, to the Co- Tangent of the In- MW 
elination of Meridians 30 oo. 4 
J Tux Requiſites thus found, draw the Horizon- | 
B -  zgak-lime HO; and in ſome convenient | 
© Plate 11. Part of that Line, as in C, fix the Cen- 5 
Fg. 3. ter of. your Dial, and from thence : 
een perpendicular to H O, then t 
with 60 deg. of the Chord, and one Foot in C, ˖ 
malte the Arch y 2, u n which ſet off 18 deg. 9 a 
min. the Subſlile's Diſtance from the Meridian j 
from AW x, and draw C x F, for the Subſtile. | 
The Subſtile muſt be on the right Hand ; 
| of 5 * Meridian, becaufe the Plain declines to the c 
= Weſtward, and ſhould have been on the left Hand, 1 
if it had declined Eaſtwarxlt. 4 
* THEN through C, and at right Angles with the 'þ 
Subſtile, draw the Line A B, and from the Scale 8 
of Latitudes take 34 deg.. 33 min. (the Height of cf 
the Stile) and ſet from Eo to A, and from C to B. J 
E Take. in Our, Compaſles the whole Scale of 6 Þ 
1 Tours, and with one Foot in A or , turn the o- I 
| ther about, till it touch the Subſtile, as in 15 and 5 
2 draw the Lines A F and BF. | fi 
ft 


hw 


Y "EM 9 A 9% > r 
. 2 - N 1 2 — [Os ier 
REELS P 8 $0 3+ od 8 883 an 


nt 
ch 


juſt 30 deg. the Szb/ti/e falls. juſt upon the Haar-. 
line of a, but if it had been any other odd Num- 
ber, as ſuppoſe 35 deg. this found in the Line f 
Inclination, there is againſt it in the Line of Hours, 3 
2 Hours, 20 Minutes, then you muſt have "ſet: ot ; 


 " Iiſirumemal” Dialing. "vor + 


Fr ND the Inclination of Meridians. wh jak: in 
this Example is 30 deg.) in the Scale. of 1 Elina- 5 
tions, and againſt that in the Line of Hours you 
find 2. Therefore take 2 Hours in your Scale, 
and ſet from F to 12, and from B to 6. Take 
alſo 1 Hour off the Scale of Hours, and ſet from 
F to 1, and from B to 7. In the ſame manner 


take 3 Hours off the Scale, and ſet from F to 11, 


and from B to 5. Likewiſe ſet 4 Hours off the 
Scale, from F to 10, and from B to 4. Allo ſet 
5 Hours off the Scale, from F to 9, and from B 
to 3, and for the 2 a Clock Line it happens to fall 
juſt in the Suhſtile, becauſe the Inclination of the 
Meridian is juſt 30 deg. which at 15 deg. to an 


Hour, makes two Hours: And for the Hour 
of 8 in the Morning, continue the Hour-line- of i 


8, which falls above the Horizontal line on the I 


right Hand, quite chrough the Center to the Edge 


of the Dial, and it ſhall be the Hour - line of 8 in 


| the Morning, and for the reſt, draw Lines — 4 


the Center C through the Marks Li 82 5 75 = 


Se. to the Edge of the Dial, they ſball be he N "4 b 


Hour-lines for that Dial. 


Tre Stile muſt ſtand upon the Sabſtile, * per- 9 IF 


pendicular to the Plain of the Dial, the back Part I 
of the Stile that gives the Hour by the Shadow, 4 


making an Angle of 34 deg. 33 min. with the "i 
Plain of the Dial equal to the Height of the Stils 
| before found. 1 


Note, The de of. the Meridian. being 


from the Line of Latitudes 2 Hours 20 Minutes, 1 


tom F to 1a, and from B to 6, and o Hours 28 4 


1 
9 
min < 
* Fs... 
, ; 
> "2A 1 
g — 
: ; 1 
9 ef 1 
* 


— 


_— Pf mm etal Dialling, 


win. from F tõ a, und from B to 8, and pi in {any 
other Caſe. © 
Ix drawing this Dial, vou have likewiſe made 


| 8 : 3 more, for Which to avoĩd Repetitions, J ſhall re- 


er you to Page 50 in the 7th Chapter, and to the 
es of them W 3. 3 Fig. 4. 


3 vo nnn, ene ave 
c Met oY = SECTION: . 


IF . Hou fo. * Honr- Lues upon 4 Dial has. decline 
Fw far, that the Gs * not be 
„Hblicient. 


= 1 Peſi ey he: Hourlines upon an ered 


5 Plain, "declining from the South Eaſtward, 80 
eg. Lat. 51 __ 

=_— Ser the ſame Chap. 8 Page 5 
Tov ae already taught in the laſt 'Se&ion, b 

E und the *Requffites, which are by, thoſe Ry 
= found | to he as koftoweth. 


Aeeg. min. 
2 Bobble Dhance fem the Meridian. 38 2 
echt of the Strife. 6 3 
= © Inclifation'of Meridians. 82 


* 


KH 


Dew the Line H I, and with the Chord of 
= .. _. 60, and one Foot in H, deſcribe the 
A Plate 11. Arch AI N, and from M ſet off the 
3 R. 4. Subſtile and Stile to mike their reſpe- 
AY Qive Angles with the Line H I, vis. 
JH Me Subſite to make an'Angle.of 38 deg. 2 min. 


ae Scile to make with'the Subſtite an Angle of 


. os L min, or with the Line H I an, Angle of 
Ti eee Stile. 


Tux 


7 and draw HC B for the Sußſtile, and 


err Fr 


wa? 
+ * G 
£ 


'Trxx in any convenient Place towards the low- 1 
er End of the Subſtile, as at B, draw a Line at 
right Angles with the Subſtile, as the Line FB DL, 


inen wird one Foot of your Compaſſes at the Be- 


ginning of your longer Polar Scale, extend the 
other 20-che Hourrof da, ſet that Extent from Bt 
P, and D draw. re. Ee PE parattet to . 
the Stile H K L, then is D E the augmented Ss. 
Then with one Foot of your Compaſſes in the Af 
Beginning of your leſſer Polar Scale, extend ne 
other to 3 Hours, and vrith that Extent pls E - 
Foot in the Szb/izle.B CH. carry. it along ih 1 
Heile, till the other Foot juſt touch the Line D E,* 
which will be when the other Foot is in C, then 
make. a Mask, -and-through: C draw 2 Liner paral- 
le! to ther Line FD, as the. Line G hen 
find the Iaclimntion Ca. de. 9 min. in the- j þ 
Inclinmtion, and Againſt it in the Scale» of ions Þ 
W Hdurs a9. Minutes, -whichi hews AAüBt 
the Supftrle bh eee ee nd zin 1 


— 5 — Stand. 6 — \Aftrencon if fe E 


had been? Weſterly. 


'Now:if, the -lowwdline of 12 be :5 Heuss 
Minutes from-the Swiftile, the Hoursline: of Ex 


muſtibe. 4 Hours: 9 Minutes from it, Fc. ande 
Hour-line of e Homs 29 Minutes! 3 
and if ſo,» chel Hou line of & muſt. be o Hm,, 
31. Minutes on! the. Contrary Side, beenuſt oJ 
Minutes and 31 Minutes make ut am- Four, S. 
eee, in dle — 
e 255 ty: 33% VEE - $413 * * 03-0 OL 
t ie l l bats 8 0 it 06 1 20 in in 

n $113 01 291 nr, n 008 


3 


* 9 
h RF, n 
. 3 
OY 


* — — WY. OSTER In ” 1 D * 2 : ; a 
— * * p * ; N - 
204 INfIrHnenta falling. 
k ? 3 a * 8 
4 I 7 5 . * x G - "EF... © 2 ” * 2 5 i 


7 From B towards F. : 4 From B towards 1 ron 
Hour on'the- | | | Hour on the 
JH. M. Plain. fl. M.] Plain. 
in at 4 55 3 | + Hon 

, - apo 

2 31B. 

93 31B 

VVV ter b 


| 


© ww .Þ ww 
ed. 
2 
5 


„ * 
4 * 
1 Er. 
\ * 


Tux Uſe of this Table is very eaſily underſtood, M 
for, take (according to the Table) 6 Hours 29 207 
Minutes from the greater Polar Scale, and ſet from 
B towards F, it ſhall fall at the firſt in the Line 
BF. Take likewiſe 1 Hour 29 Minutes, 2 Hours 
29 Minutes, 3 Hours 29 Minutes, c. from the = 
aid greater Polar Scale, and - ſet them upon the 07 4 
Line DBF, from B towards F, to the ſeveral MW - 
Points & * * c. and the contrary Way, et 7 
the Diſtances o Hours 31 Minutes; 1 Hour 31 A! 
Minutes, c. upwards: from B upon the ſame 2 
Tine, to the Points & & & c. it finds the Points 15 
for the Hours of 6, 3, 4, c. do the ſame by the | 
leſſer Polar Scale from the fame Table, and find 
the Marks * & & in the Line ECG; then lay- 
ning a Ruler over the two Marks next below the 8. 5 
Saule, a Line ruled thereby ſhall be the Hour - 
line of 7, and by the two next Marks, a Line 
ruled ſhall be the Hour-line of $8; and ſo in all the 


© reſt, as you ſee inthe Figure. Ir 


une Dialing, 


Tax Seile i in this, as in all others, "a 0 
direQty 0 over the Subſtile, and muſt de a Plate of 3 
ton ot and in the F orm of the Figure © 
CED. 1 
Ix the making of this Dial, you have alſo made Ro 
2 South Dial er Weſt 80 deg. only for tjye 
"Os 6 9, 10, 11, you muſt put 1, 2, 3, 4 4 
ifs LE You have Ne a North Dial te. „ 
aug 8 Laſt So deg. and a North Dial declin 7 4 
Weſt do deg. with only inverting the Stiles and Fi- 7 2 ö 
gures, as you are taught Page 30, in the 7th 838 
tet before · mentioned, and the Figure Plate z. By. #; 
+) 5 ä y uftrace this n LE 


| os 


aue aduaruuse we 


SECTION x. 


of Deckining Reclining Plains, aud how ey - ” A 9 7 
lines my be deſcribed on them. ä 


AL: THOUGH we have elſewhere. in this Book + | 

laid down ſeveral Methods for effecting this, 
jet in order to reduce the whole into as narrow aa 2 
Compaſs as poſſible, we ſhall in this Section aqua .- 1 
how thoſe Declining Reclining Plains may be re 
duced to new Latitudes, and new Declinations, +: 
and may be made by the Directions given in An — 
d, a; the Lines on the Scale. . 1 


EXAMPLE. 


Tri is ned to make a South Plain for Lati- wo 
tude 51 deg. 32 min. North, to decline from the lt 
South-weſtward 24 deg. 20 min. and to recling ry 
ſrom the auth 54 . | i _ 


% 
®, 


"200 Inſtrumental 1 Dialing. 


The Cette ” the new Latitude i is, : | T 


there 
ie Radius Re 10 000000 Wtitud 


To Sine Compl. Dovits. 24 20 9.959596 Welt 
80 Tang. Compl. of Reclin. wo. 9.861261 2 
+ To Tengent 33 30 9. 82085 metr, 
Ix South Reclining Plains, as our Example is, 129, 
the Difference between the Tangent laſt found tude 
* _ Gwhich here is 33 30) and the Latitude of the Place Mdeg. 
* 9 Complement: of the new Latitude ſought, new 


vey. min. the T 
Latieude of the Place i 3s 
e „ 33 30 
w/e „ : 4 "21S = whole 


ne 71 58 is the new Latitude ſought, 
Only obſerve, that if the Tangent be more than 

the Latitude, the ſame Pole is elevated; if leſs, az 
here it is, the contrary Pole is elevated, and con- 
_ ſequently, if they be equal, neither Pole is —_ 
bes but it is an Equinoctial Plain. 

5 But for North Reclinesr, 

Ir the Tangent laſt found be equal to the Com 
piement of Latitude, the Plain is a Polar declining 
Plain; but if greater or leſſer than the Complement 
of f Latitade, the Difference i is the new Laticude. 


- The Canon 70 find th the new Detlination. 


a 
1 


4 Radius | | LO.CO00C09 
To Sine Compl: Reclin. 0 9.769219 
80 Sine of Declination oY 20 - 9.614944 
t SY 

ro Sine of 1 14 geg 1 min. 8 9.3 84403 


Tais 


RR W 
. R 


WG 0 ˙·¹ ne ae 1 r 
- ve en - 12 i : » * 
- bd Ps * 0 bY, neo N 1 
5 1 Þ XK: k = 
| h 7. ſt | I Di 12 | | 
Aſtrumenid Ia mg : 


therefore if it be required to make a Dial for La- 
titude 51 deg. 32 min. to decline from the Sonth= 


weſtward 24 deg. 20 min. and to recline from 


the Zenith 54 deg. oo min. you may proceed (by 
— te Directions given, Chap. 7. Page 46. of Geo- 


51 WY arical Dialling, or Part 3. Sect. 3 and 8. in Pag. 
b, 129, and 14 1.) to make an upright Dial for Lati- 
ing MW tude 71 58 (the new Latitude) and to decline 14 
ace deg. 1 min. from the South, (according to the 


- 


. new Declination found) that Dial ſhall ſerve for 


the Dial required. 


Note; The Declination thus found, 18 always 


leſs than the old Declination was, but is always 


the ſame Way, vir. Eaſt or Well, as the old De- 


joſe Nelination was. 


ght. . Bur to apply this new Dial to the Plain propo- 3 
chan WI'ed, you muſt not place the Meridian or Hour= | 


„ line of 12 perpendicular to the Horizon, but it 


-on- muſt make a certain Angle with the Horizontal. 
line of the Reclining Plain, which we call the | 


Meridian Aſcenſion or Deſcenſion, which is found 
C | 1 


om- „„ 
ning . To Sine of Reclination 54 o 9.907938 
neat {Wo Tang. of old Declinat. 24 20 9.655348 
To Tang: of 20 deg. 6 min. 9.563306. 

hoſe Complement 69 deg. 54 min. is the Angle 

that the Meridian makes with the Horizon. 
5000 WM  Havine thus obtained the Meridian, Aſcenſion 
9219 r Deſcenſion, viz. the Angle that the Meridian 
4944 Nrakes with the Horizon, your next Work is to 
id the Poſition of the Meridian-line and Sub- 
4163 Nile, for which ſee the three following Pages. 2 
Tus 5 | K 2 N inn 


0 "I F 

« ” ” 9 8 - ere 
2 5 is OR Ibex, IR . g 9 
* OC ROY mme FEI TEAN n 
* * * e K * 

4 WT Ou iY 

* * * — 2 Z 

— Y - A. 

Ly * * — 

8 


Tais 14 deg. 1 min. is the new Declination, 


i 


2 


A N * 21 
en19j2da3 80e % | 3 
ut. Umrap Sy}. urfp ro sin,. 75 > of ung 39 3 : 
>, pry —— noheumpPag $uIgqQ - 8 b pam ueIp1aJN 2un $1201aY. 
3. Jo peo 2h yyua NME pi $354 957 ne 
Sulej ay S$FOO1 Jeu uf mw TE 
: 


. oh $ aid 2 nog == E "nip 2q yn 


. 


ö 
C — TOEOTITST OY 
p „ 
] * 
4 
. 


* CY r 2 
: 
rh 9 


5 


* PTY 


00 30 prog dn un im) mir 22 jen 
daun on senf yolya u jv 
ore et JO PU "IG 1 _ 5 


PF 
* 
3 


> N "uo" 2 


+ & 
* 


_—_ 
128 


3 7 s. upelg ain 30 30 peog 2y3 07 auen q n 
E d&xnuo? gall nn u ry OE Uvy3 E 


* 


I» =D n ah 30 pad I. Cop 


2 „ e dae. 8 . 
-— x Jo vol ai MEIP 01 JV 


$1- u suff ymog| |  Varipaq 
un puy — Yong _ yum ure 243 
sufeld o 30 ro am | 
oi Axe11009 $211 yolya | 

ur. re2u0210F 3} 
3 4⁰ FR 1 ni. puy ole 


» { ; - 1 
+ p = 8 * * £ q < 3%; 9 * * 
* I * 4 


3235 

| 00 35 I) n 
+: pur uopruſloꝰ Jo. yeo*) amn o Anu 81 
8 YoTym pug 1811 ir u imo zh¹õuỹ 23 αν,],ẽtte 


, 
* 


* 
4 w 


x 
* 
Xs IE 


| 


- day 0191qr221a2a £100 VVV 


wiod e vey} % 


„ LP 2q you ur!PH2IN I Od & 02 bg.) 


$1901 


ul mog (ur 
Sus 


N quoN 


„„ 


. ot r 
— * F 
» 
* * 
8 _ 
"IK 2 . 
4 2 
5 75 22 
£ f 
* + 
no . 
20 
- 1 * BO 
* ' i 2 N 
« me * wy | 3 
3 
5 
5 $55 b * 
- > * = 
; 8 
1 
3 N G 
F — % 
EA 7 : 
3d * 
5 ö « * 
- 
* - 
— 
1 * 
* * 
* * ＋ 
4 _ 
34 by 
* We * 
« 
*A 
1 n 
o * 1 
Pl 
3 { 
Fe 8 8 
As ; 
— 3 * 
1 oc ? : 
* 7 2 
2 * 
Was b 6 
- EY Lo 
"ETON * _ 
Bat 5 
# 
9 Y 
' 2 FR : : 
mw , 
* 4 © 
* 
4 J 
W 
— * 
AS * 2 
* * * 
* — "4 * 
— 
* 


CES 
% » 


- 
: * 4 2 — 4 "I / a 1 „ ö 
* R A . ä y * N 8 ö . 8 * r . 
4 n * E * A n 0 
. 8 0 » N ts 7 AF; * vy e 
[ - 
o 1 4 4 , . & 
= ; * 
8 5 ö — . r ts 
— 1 © 2 8 
* i Py 2 1 £ * 4 
1 
&Q 
"61 
Y 


1. To know which Way the Subſtilar Line of 
any Dial muſt ſtand from the Vertical Line of the 
FM. a6, 7. 

2. How to order your Work in the Southern 
Hemiſphere. 3% RS 
For the Firſt. 
1 5 . Upon all Plains whereon the 
North Pole „ Sonth Pole 
3 | "TY | 1 . 3 Fe 3 


is elevated, the Subſtilar muſt 
J, ĩ np — 


— 


Koper 1 Lower End, E 


8 


— 
— 


. 


=: of the Vertical Line 

: \ toward the fun!! 
—ů— Gö6—Z8•—ͥU : 

3 n - 


„ . For the Sechiid 


Arx the Rules, Precepts and Examples given in 
= this Caſe, do ſuppoſe you to be in the Northern 
Hemiſphere of the World ; therefore if you 
mould be in a Southern Hemiſphere, theſe Pre- 
cepts will ſerve there alſo, by only changing the 
Words North and South one into the other, as for 
South read North, and for North read South, and 

- ſo Northern for Southern, and the contrary. 
Fon placing your Dial, draw an Horizontal 
Line upon your Plain, and ſet off ſo many De- 
om by the Help of your Line of Chords, as the 
iſtance of the Meridian and Horizon is found 


ne of 
f the 


thern 


n in 
zern 
vou. 
Pre- 
the 
for 
and 


ntal 
Dez 
the 
ind 


* ö : 
ad MEAS tage ron ir a0 te 5 3 * * r 3 © 
y \ des. . . Eg. ite oh it gh * e TIN 
: \ AVE c þ 3) 8 n 2 
* * 5 n NR 33 +, 8 Rn 
; 225 ; Cs af? EL ans ; 
5 4 5 #5 5 7 SY 1 
5 'F 2 > * 4 1 #1; 8 1 
# * 5 * * 
i RES. 4 4 
AE 
3 | : 18 
- wt. 2. 
3 
* 
4 * 
n 


to be, and to the right Coaſt ; there draw ae 


Meridian- line, then apply your Paper Draught to 


your Plain, laying the Meridian- line of your Pa- 


per Draught exactiy upon the Meridian · line (now: 
found) upon your Plain, and take Care that the 


Subſtile lie according to the Directions now given, 
and that the Stile do always point towards the 


pole, that is elevated above your Plain, and then 


by prick ing through your Paper, or any other con- 


venient Means, you may transfer the Hour- lines, 


c. to your new Plain, and drawing the Hour- | 


lines you have the Dia! required. | 


As for Eaſt or Weſt Recliners or knen the 


reducing them to erect Decliners in other Lati- 


tudes,- and the Meridian - line in theſe Co- inciding 


with the Horizontal- line, and having no Eleva» 5 4 


tion or Depreſſion, there is no Ditficulty i in. 115 
ing them, when rightly made. 


Aso North and South Incliners or Reet I 4 
teing.ere&t direct Dials in other Latitudes, are to 
be made as ſuch and then placed in the Latitude 


propoſed, with the given Reclination or Inclina- 


# 


tion, c. Which is cally og Ig to every 


N 5 | „ 


* 
19m, 


.-* 15 
vB p 
* fy 
Vo 


1 
— 
Fe 
2 N 
14 
* 
* 
* 


* d 
— 
2 


eee a 


SECTION xl. 


Fw to make a Polar Dial. 


15 N making a Polar Plain, you have no more to 
do but draw a Circle, and divide it into 24 e. 


qual Parts for the Hours, and draw Lines from 


the Center of the Dial through theſe Diviſions to 
the Edge of the Dial, which may be round, ſquare 
or what Form you pleaſe, and placing 12 on that 
- fide towards the elevated Pole, put IT, IO, 9, Ce. 
of the Forenoon Hours, and 1, 2, 3, Ec. of the 
Afternoon Hours ſo far as you have Oecaſion, will 
e the true Hour- lines of a Polar Dici. er 


e of a Polar Dial for Latitade 77 4 32 n. 


Lr the Square AB C D be your Plain; biſſec 
A B in e, and C D in y, and draw ef. 

. 11. Alſo biſſect B Cin g, and A D in b, 
Tr. 5- and draw g 5 perpendicular to e /; 


to cut each other in Q; then upon Q. 


as a Cenetr, deſcribe The Circle r tu, and begin- 
ning at r, divide the Quadrant r ſ into ſix equal 
= Parts, and each of the Quadrants in the Points * 
„ X, Sc. Lines drawn from the Center Q thro 


_ theſe Marks, are the true Hour- lines in ſuch a 


© "Note, A Polar Dial. 8 be placed 5 9 the Pol, 
9 to have all the 24 Hours upon it; but be 
cauſe a Polar Dial to be placed in any other Lati- 
tude is only a North Dial reclining equal to the 
j. Facade 6 of the np and becauſe in Latitude $1 


3 


9 5 
5 


, Doſtrumental Dialing. 213 

deg. 32 min. the Sun never riſeth till after 3 in the 

& Morning and always ſetteth before 9 at Night, it 
will be ſufficient in this to inſert the Hours from 


= 
7 
9 
4 
* 
5 


4 in the Morning to $ in the Evening. „ 
Tux Stile is only a Pin of Braſs, Iron, or the 
like, fixed in the Center Q, and placed perpendi- 
Anne 277 


rom: i =: 15+ E C TION Xl. - 1 A 
are Of an Equinedial Dial. Pl. 11. Fig. 6- 


eye. A N Equinoctial Dial is a South Recliner in 
the North Latitude, or a North Recliner in South 
will Latitude, equal to the Complement of Latitude, 
55 is moſt properly done upon an oblong Plain, 
tus; ” | „ 
m. Arx a convenient Diſtance from the Edge of 
, your Plain, draw the Line B C, and parallel there- i 
Th to near the other Edge draw the Line DE, ang 
5 through the Middle of theſe draw F G perpendi> 3 
n 4, cular to them, for the Hour-line of 22. 
F; Tukx upon either of the Polar- Scales marked 
1e.) take the Diſtance from the Beginning of the 
zin⸗ Scale to I, and ſet that Extent from FE, and alſo 
ual W from G, both Ways to 11 and x, on the Lines 3 
1 C and DE. Again, Extend your Compaſſes from 
iro' MW the Beginning of your Scale to II, and ſer that 
h a from F and G, both Ways upon the Lines 80 
- and DE to 10 and 2; take alſo the Diſtance from ⁵ 
o', the Beginning of the Scale to III, and ſet from F 
„ud G to 9 and 3, and in like manner take the i 
ati- W Diſtance from the Beginning of the Scale to III, 
the and ſet from F and G to 4 and 8. And laſtiy, Y 
1 take. the Diſtance from the Beginning of the Scale 
5 S 25a 


* 


nnn 

to V, and ſet from F and G to 7 and 5, (the Hour 
of 6 can neyer come into an Equinoctial Plain) 
| hen draw the Lines 7.7, 88, 99, &. theſe are 


the true Hour-lines on that Plain. . 
E - Tux Stile may be a thin Plate of Braſs, Iron, 
e. and muſt ſtand upon the Honr-line of 12, per- 
= 1 to the Plain of the Dial, its Top ot 
Hage that caſts the Shadow muſt be parallel to the 
Hour-line of 12, and its Height muſt be the Di- 

ſtance between the Hour- lines of 12 and 3, and 


5X 


** 


IS Fo the 6 a Clock Line to the Hours of 7 and 
, 8 and 4, Se. which i 


ie or Gnomon, you maſt allow for the 


A 1 
— * 


= a 
* 
* 


3 Thickneſs of the Stile, imagiuing the Dial to be cut 


22 72 
52 
7 - 
2 Mx 
BY 
* 
E * 
. * 
* N 
3 
*_X 


* #4 \ 4 


"x 
- 


W 


* * * % : 
* . * —_ 4 8 , 
- * , p # 
* ; 53 : N 7 8 . 7 * 
"Xs ö : - of: Bo Fo . Iv 7 5? 5-2 1 2 > 
3 * P x * — * [ 5 * - . * 4 x - w by . 25 E 8 
2 £ N 9 n * 58 2 — 4 . % * b 
- 1 5 — i — 
* > of > © S * bl . e ® 1 4 4 * J 4 5 =! 
- OS 55 35 + $75 132 M $3 2.5.8 4 "38 
s 4-0...» v.44 6-4 . e o 4 
hs "== 4 - $5 FE”, 26 A 
= * 3 * 4 C 8 5 4 4 > N 
a Wow. " BY 4 FOR j * x 3 S +. - 4 
W * * 3 wiv 4 * 1 w 4.3 — 9 
* ® P 9 * "A 


, 8 
1 
8 


Fa 


vs xXx 


—— — ood 
x d 


TY 


2 
, 
2 


9 
9 


” 


* 


— 
——g—ͤ— — — — 


WIA 7 


vi 
C 


{5 


i 


— 


* 


8 


r 
a 
. + 


4 Y 


pr eu e mY 
"_" © 


= 


CHAP. x. 


of Mechanick Da | 


Teaching how to . any Plain Dial ads dies, 
declining, &c. without the Help of Matheminti- i 
cal Calculation, or any Inſtrument, 1 575 405 i 
Plain Ruler, and a Pair of C ompaſſee. 5 | 


Abr HOUGH the Varieties of Dialli 118 efare: 
treated of (viz. Geometrical, Arithmetteal, 2 7 75 
Inſtrument al) might be thought ſufficient, Vel . <p 
cauſe this Book max come into the Hands of ſome - WO I 
that have not-learned ſo much Geometry or 1 9 1 
wometry, as to be capable to put thoſe Direct N 
in Practice, ar cannot procure a Ruler with the 

Dialling Scales upon it (which is the Caſe of 1 

Maſons, Carpenters, &c. in the Country.) Fot the 

Sake of ſuch I have added this Chapter, whereby: 3: 

any Perſon that can but read and write, will be 4. 
ble to draw a Dial upon any Plain, provided he = 
can raiſe or let fall a Perpendicular, and draw a © 
Line parallel to a Line given, Oc. which is e 23 


& 
EY 


a the Deglaniog of this Book. 
. = * 6 | _ 8 ren 
1 2 
8 1 : | 
a 7 AR 


SECTION 1 2 


. to s dſerit the . pon a 22 
"Ia 


* Shall, to avoid needleſs 1 forbeat to 
give any general Direct ons, and fall directly 
upon an Example. Let it therefore be required to 
an a Horizovtal Dial for Latirude 51 deg. 30 
min. 
Fiksr, Through the Middle of your Plain 
draw the Line A B for the Meridian, or 12 a 
Clock Line, and ſome where near the Middle of 
- it, as at Q, croſs it at right Angles 
Plate Iz. With the Line 66, then with any Ex- 
. 1. tent of your Compaſſes, and one Foot 
in the Center Q, with the other de- 
ſeribe the eee E B, which divide into 90 
Parts thus; Hrſt, With the ſame Extent of your 
Compaſſes, with which you ſwept the Quadrant, 
- and one Foot in B, ſet. the other towards E, and 
there make a Mark, for that is 60 deg. then with 
- the fame Extent and one Foot in E, ſet the other 
towards B, making alſo a Mark, thus is the Qua- 
_ drant divided into three equal Parts, each contain- 
_ Ing 30 deg. Divide each of theſe Parts again into 


three equal Parts, then each of theſe laſt Divi- 


Fons into two equal Parts, each of which will be 
5 deg. And laſtly, divide each of theſe laſt into 

5 Parts, ſo will the mn be divided into 90 
70 Parts or FOES. > 


Now 


8 5 a — 4 Oo ww} — = HQ 


"Mechanick Dialling, 7 ty - 


Now becauſe the Latitude propoſed is 513 de- 
tees, count 313 of thoſe 90 deg. from B 33 i 'Y 
A which will reach to Z; then from the Center 1 

Q draw the Line Q Z for the Stile; aſſume a 
Point any Where at Pleaſure, in the 12 a Clock | 
line, as at C, through which draw the Line EF | 
parallel to the Line 6 6; this laſt Line we Will for 
Diſtinction call the Tangent-line. Place one Ft 
of your Compaſſes in the Interſection of the Me- 

ridian and Tangent-line, as at C, and with the o- 
ther take the neareſt Diſtance to the Stile QZ, and 
keeping one Foot ſtill in C, turn the other about 0 
till it cut the Meridian-line in D; then upon Das 
a Center, with the ſame Extent D C, draw the > 
| Semicircle H C G, and draw the Diameter I B 1 
G parallel to L F, then with the ſame Extent, 
with. which you draw the Semicircle, and one 
Foot in C, turn the other Foot both Ways to-. 
wards H and G, and there make Marks, alſo with 
the ſan.e Extent, and one Foot in G, turn the other 
towards C, and where it falls upon the 'Semicir- 
cle make a Mark ; then with the ſame Extent, of 
and one Foot in H, turn the other towards C, and i 
there alſo make a Mark, then is the Semicircle di- 
vided into 6 equal Parts; divide each of tes 
Parts into two, and then it will be divided inte 12 
equal Parts; lay a Ruler from D, the Center f 
the Semicircle, over every one of "theſe Diviſſons, 
it will cut the Tangent- line in the Marks *,*, "8 
c. And Laſtly, From the Center Q draw © 
Lines through the Marks * *, &c. in the Lan- 
; e they ſhall be the true Hour-lines of the oY 


Ir you defire to have hs half Hours and Quar- 1 
ters, you muſt divide each of the 12 Piviſions f 
your Semicircle into Halfs and Quarters, and 
£ mt them to the THEE) and from thence 8 


. 


Is 
_ 
S rom 
8 1 _ - * : 9 
* 1 
8 N 75 5 | * „ + 1 
* ** 7225 e $ 6 5 7 © - 
3 5 þ * 5 
—_ > 
* 5 "4 
A 45 5 x 
1 8 8 FRF mo * 


\ A CL * 
b _ 6 _— Y * MA 
ll Lakes on} nb e 5 „ * 
bs 5d 1 ** wt Le R 4 
4 PIE TY l * ke x 2 g 9 
« . ' 1 © 46 oe * , 
* 8 £ 2 : / J 
&+ 
. 


. 
. - 


from the Center to the Dial, as you did the Hour. 
Tux Lines being thus drawn, place 12 at the 


Middle or Meridian-line, and proceed towards the 


right Hand with 1, 2, 3, 4, 5, Sc. and towards 
the left with 11, 10, 9, 8, Cc. and for the Hours 


1 of 4 and 5 in the Morning, and 7 and 8 at Night, 
= they are found by continuing the Hours of 4 and 
zm che Afternoon, and 7 and 8 in the Morning, 


quite through the Center, as you ſee in the Fi- 


i 3 Tx Stile is to be a thin Plate of Braſs, or the 


tike, made in the Form of the Triangle B Q Z, 
to be erected perpendicularly upon the Line QB, 
the Side Q B of the Stile, upon the Line Q B, 


= and the Angular Point at Q, and then is your 


4A 4 wt 7 
1 5 
* 
_ E 4 7 
4 1 4 * 2 * ; : - * 
3 85 Ko 8 ** N | at 2 
3 hn , { OP, 9 ; 
x 232 i 
1 : 4 a] oy) 9 A 
_—- . 
ER. WJ * U 
P. ; « 5 5 LN ; _ o : ; 5 * a : 
p : 3 . \ = : 
7 * - ” * * 
af — " , 
i f 
* 


©... SECTION: IL 


Heu to deſcribe Hour-liues upon an Ere& Direct 


L IT it be required to deſcribe a South Dial for 


a Soxth Dial. Plate 12. Fig. 2. 
— Latitude 51 deg. 30 min. 


Fit, Through the middle of the Plain draw 


= the Line. A B, and at the upper End thereof, as 


= at A, croſs it at right Angles, with the Line 6 A 


for 6 a Clock, or an Eaſt and Weſt Line; then 


With as large an Extent of your Compaſſes as your 
Plain will admit of, and one Foot in A, deſcribe 


® the Quadrant B C, which divide into 90 Parts or 


<= 
2 ! ” 
"208 
* : 1 
— 
3 

8 - 
I 

> 


Degrees, as you were taught SeR. 1. of ah ſet 


8 een a ak of. 
. EN FR TR e 
22 - 
1 
* 
N = 


ur- 4 zo the eee of the 3 from 1 to 
WE, and draw A E for the Stile, then aſſume a 
he Point at Pleaſure in the Line A B, as at F, thro 
the MW which draw the Line O F H, perpendicular to A 
rds B for a Tangent-line ; , with one Foot of your > 
urs Compaſſes in F, with the other take the neareſt * > 
he, I Diſtance to the Stile A E, and keeping that Foot 3 
nd aun in F, turn the other till it cut the Meridian 
g, line A B in G, then letting that Foot reſt in G, 
Fi. vich the other deſcribe the Semicircle I F L i 
which divide into 12 equal Parts, as you were 
he WY targht to divide the like Semicircle in Seck. 1. f 
Z, mis Chapter. Lay a Ruler from G, over the e- 
B, dual Diviſions in the Semicircle, and it will cut 
B, the Tangent- line O F H in the Marks * *, ,, MN 
ur Liftly, Draw Lines from the Center A through = 
the Marks * *, c. in the Tangent-line, gt 1 
ſhall be the true eee e of the Dial. ee, 
HAviNG thus finiſhed the Hour - lines, place 12 1 
at the End of the Line A B, and (ſppoſi ing the ' 
Dial to face the South, and your Face towards it) 
proceed with 1, 2, 3, &c. towards the tighe' i 
Hand, and with 11, 10, 9, Sc. towards the leſt 
| Hand, always obſerving that a South Dial can ne 
7 rer contain any more Hours than thoſe from 6 in we 
the Morning, to 6 in the Evening. '* = 
Tu Stile may be a Plate of Braſs, or the like, 3 
in Form of the Triangle, B A E, the. ſide Bx 
to de ſet upon the Line B A perpendicular to the © 
Plain of the Dial, the Angle of the Stile ren Mo 
juſt at the Center or Point A of the Dial, and 4 7 J 
they. is ror opt dnimen 1 


"= 


7 
_ 


, * E 
9 n 5 2 
j p W os. 4 
9 FRE, DO * R 
N. due TT. by. 


; | 225 20 ** "Mechanick Diallng, 


ee Ti 
E . . s E 0 T 1 0 * II. 5 
$ |. 2 Of 6 1 . . 


Fr E Erect Dired North Dial is made by the 
- ſame Rules as a South Dial is made, the Hour- 
"Ss and Stile being the ſame, only in a North 
Dial the Stile points upwards, making alſo an An- 
gle with the Plain of the Dial, equal to the Com- 
HIER of Latitude; and for the reſt obſerve. 
I. Fo put no more Hours than are of Ute, as 
at TO, 4, 5, 6, 7, 8, in the Morning, and 4, 
3, 6, 7,8, in the Evening, the Sun never ſhining 
on a North Plain at any other Hours. 
2. TaaT. (though the Diviſions are the ſame) 
- the Hobrs, which on the South Dial are marked 6, 
| 75, 8, in the EC muſt on the North Dial be 
| marked 4, 5, 6, in the Morning; and the Hours 
3 - of 4, 5, 6, in the Afternoon, muſt be 6, 7,8, in 
= the Evening. | 


any Hour before 6 in the Morning, or after 6 
the Evening; but the North Dial (at London) ate 
in 4 and 5 in the Morning, and 5 and 8 in the E- 
vening: Therefore to ſupply that on the North 
n, you need but continue the Hour- lines of 4 
and 5 in the Afternoon quite through the Center, 
 - and that gives you the Hour-lines of 4 and 5 in 
the Morning on the oppoſite Side, and the Hour- 
lines of 7 and 8 alſo continued, __ you the 
Hours of 7 and 81 in Tie Evening. 1 
7 | 4. As 


, 's 
af 4 * > 8 * 1 4 * * . 1 
3 * 4 4 8 2. * 1 . 
5 IG r 20 1 4 1 

9% * \ 2 ve em 


„ ed . 2 OE" 
* £ d fend ts TEINS IE BS YR 7-1 np PE” TIEN” 2 
2 n F r . 
[ha * T 5 I: COTE oe A n R 3 2 N 
BW OA Ex EO: 9 1 
5 22 LY : 
dts = 
, * F * 


3. BECAUSE upon a South Dial you never Gran | 


any further Explanation. 


4. As for what Hours are neceſſary to be put - 
upon a North Dial in any other Latitude, I fal! 
refer you to the Table (Page 190.) with its Ex- 

planation immediately following; there you have 
the Length of the Longeſt Day in all : 
whereby you may find the Sun's Riting and Set: 
ting in all Latitudes, and conſequently know 
what Hours in the Morning or Evening are pros; 


atitudes, 


- 


per to be put upon a North Dial, it being ſuper- 


n 


fuous to put on the Hours before Sun riſe, or af. 


5. Ir a North Dial for, wy given Latitude'be 1 
required to be made, take a Sheet of oyl'd-Paper, 


and proceed in all Reſpects by the foregoing Di- 
regions to make a South Dial for the Latitude 


propoſed, (only you may ſave the Labour O 
working for the Hours that you know will be f 


no uſe) which done, turn the Paper over, taking 


that End towards you which was fartheſt from i 


you, and you will ſee through the Paper the true - 


North Dial required, which 


55 


K * 1 
1 1 
; : _ 
7 » * 1 A 
2 : 4 : & 5 4568 
. * " : 7 > 7 Fd | 3 % if 
4 8 * 1 1 * 4 Fa . ©2Y 
1 Py „ 
7 5 7 13 wh 
-y-* e ; BE ad 
; \ .. : $4 "Th e : 
. Z ” - 7 Ll * * * x LF £ 1 
5 : EE. — 
j N 5 * | : 4 : 4 48 4 
* 3 + be 3 ng 4 
1 N 3-245 
1 7 4% 
+> ©K 


deſcribe an Erec Direct | 


How to 
FE %% 


Pave prepared your Plain WX V Z, whe- 5 9 
ther Wood, Braſs, c. Draw towards one 
Side of it the Line A B parallel co WZ, and 


in that Line chuſe a convenient Point towards the 


think will not need 


; > 
8 2 _—_— 
4 2% , 
r 1 
© 4 1 5 5 - , ,_— 
7 * . 
* ; 
4 


upper End thereof, as C, upon which as a Center, 


with any Extent of your Compaſſes wa 0 


—— 


e 
8 8 by 
« — o 


4 LH ; N 
2 IS SOT * 4 N N 
n . er tx; 
” bl] N e * 2 
5 R N 7 
* fa 71 28 — IB 5 
a * + - 3 = : 
. * 8 ) k 
ax ” : * 
7 " * "> o 6 2 \ [1 
$ Pg 7 
1 ; 4 N 
: 7 5 
ov 6 * 
= "2M 
5 + 
. * 
- « 
* 1 


4 * c A 2 oY _ 
1 4 ire AT * * — wit \ Od Ba TOE WITS pla So. ods ALS A xs «42 7 0 * a - — LY 
= * al * 9 * e a 4 * Cds n 3 (Fo a 5 4 
I I IF 7 * 4 A* 2 * Y = EIS; : . | 
4 : \ r % * Ss 
" 7 - 74 
„* Ls v 9 " 4 — * 
»; , - N 9 7 * 
: all. Þ ü , { | 0 
» Bo 5 » k LL 2 1 . : z \ 7 
$ LH * N | % * 4 ; 
* 
@ 
5 


plement of Latitude, which in this Example we 


4M | plement to 90 is 36, ſet off therefore 36 deg. from 


I lel to CD for the Spbſtile and Hour-line of 6, 


; you drew the Semicircle, 


Arch D E, upon which from E, ſet off the Com- 
Will ſuppoſe to be Latitude 54 deg. whoſe Com- 


E to D, and draw D C for the Axis of the World, 
then croſs this Line at right Angles with the Line 
F, drawing C F both Ways to the Edges of the 
Plain; chuſe any convenient Point in the Line C 
F, as at 6, from which draw the Line 6 6 paral- 


. -- (which in Eaſt or Weſt Dials are always the ſame) WM 0: 
© Continue the Line 6 6 at Pleaſure, as to G, with 
the Extent from G to the Line C F, keeping one Ml H. 
= Foot of the Compaſſes in &, with the other de- Ki 
= ſcribe the Semicircle Q R, which divide into be- thi 
1 2 Parts both Ways from the Line G 6, and i the 
FE laying a Ruler from G over theſe Diviſions, it 
iii cut the Tangent-line C F in the Points * „vo 
ee. from every one of which Marks draw Lines do 
parallel to C D, they ſhall be the Hour-lines re- D, 
E quired, which (beginning at 6) muſt be numbred I br: 

- upwards with 5 4, and downwards with 7, 8, 9, M 4 
210, 11, the Hour of 12 can never come into an int 
= Eaſt Plain, becauſe at that Hour the Sun being up- 

don the Meridian, is juſt upon the Edge of the Plans. 
TDux Stile is a thin Plate to be fixed upon the il 2 
_ Hour-line of 6 perpendicular to the Plain of the =» 


Dial, being from End to End, equally of the 
Height of the Line G 6, the Extent with which 


F ̃ͤͤ—elnuu.¹.. IU INIT ITT OT We EC RO . a 9 ä , 
* 3 © * 8 2 R 5 4 9 * R/ ABI. . N 2 
1 6 N 4 2 ö . "RE"; GONE . 4 8 We Buy 0G EA FEM PT 
n . * 4 > * T 
* * LI s 2 
, * 3 - 
- F 47 X < : 2 
. 3 > 4:1 : > 
1 : , x v : . a * 
. 5 80 4 , = 
* . : 2 N 0 5 N * 
93 2 3 # 3 2 
= 
a > 2: "bd * - £ 
#:* . _ "= 
F £ 1 
» 5 4» 
1 


Favs EY 


from Br 

ord, | 

Line HY SECTION v. 
ol . of an ered rect V. ft Dial 


aral - ANer ere dire& Weſt Dial is deſcribed in all re- 
ſpects by the Rules given for the Eaſt Dial | 
oaly appear differently in two Particulars. 5 

1. TEñE Eaſt Dia! is elevated towards the Left 
Hand, but the Jeſt Dial is elevated towards the 
Right Hand, as the Eat Dial would appear, if ſeen 
Gn the Paper, the Diviſions being alſo exatly 

me. 

2. WHEREAS the Eaſt Dial contains the Fore» | 
noon Hours, and is numbred from the upper Part 
downwards, with 4, 5, 6, J, 8, 9, 10, 11, the en 


ing upon the Hour line of 6 in both. 


* the Figare * a W, ** Dial, ſee Plate 3- And 2. 3 10 i 


sa AAAa4a. 


SECTION VI. 


Dial contains the Afternoon Hours, and is num. 26 
bred from the lower End upwards, with 1, 2 © 34 4 
4, 5, 6, 7, 8, the Stile being the ſame, and ſtands . 4 


How to Geſcribe the Hoar-lines, &c. upon an Ered = 4 


South (or North Dial) dechning Eaſt. 


. ALrnoven we have given. DireQions (Chap. 4 
EC- Page 34.) for finding the Declination of au NY 


Plain, yet theſe Directions requiring ſome Know- 


ledge i in Aſtronomy previous to the Practice of 2 
F : 5 ene. Ng 4 


: . 5 : dle of the Top of the 
= _ the Circles as before, and then you are ſure 


4 bs OT 4 "Mechanick Dialling. 


that have not acquired a ſufficient Knowledge, i in 


chem, and this being 4 tom for the Uſe of thoſ 
the Mathematicks, I ſhall give a Method, where: 


by (mechanically) to take the Declination of any 


Plain, as followeth, 
T axe a fine Board of Wainſcot, or the like, of 


about a Foot ſquare, or more or leſs at Pleaſure, 


and plain it very Fine, or elfe paſte a Sheet ot 
ſtrong white Paper yery ſmooth, on one Side of 

it, as oo ſee-in the Figure, the Board repreſented 
2 by ABCD. From the middle of the 


> Is Plate 12. Side A B, erect the Perpendicular x y 


| . 88 2, and in 'the middle thereof, as at y, 
N place one Foot of your Compaſſes, and 
with the other point at ſeveral different Extent, 


dra the Concentrick Circles, as you ſee in the Fi- 
|. - gure, (it matters not what Diſtance they are from 
beach other, or whether they be equally diſtant a- 
mong themſetves bs done, erect a ſmall Pin of 
8 or Inches in 

E the Center of the Circles, and then is your Inſtru- 
ment ready for uſe. | 


ngth, exactly perpendicular in 


Wote, If you are doubtful of your e 


. 8 5 4 in erecting the Pin exactly perpendicular, you may 
place the Pin before you make the Circles, and 


then with one Foot of * Compaſſes in the mid- 


that the Middle of the Top of the Pin, where 


= x. you placed your Compaſſes, is perpendicular to 
de (ſuppoſed) Center of the Circles, whether the 
Pin be perpendicular to the Plain, or no, and then 
draw aLine perpendicular to the Side A B, and to 
cut each Czrcle exactly in two Parts, 1 to 


$3 . make uſe of we Far Wont, as followeth. 


in, with the other deſeribe 


ms Pract ; 


9 


| Prace the Inſtrument exactly parallel to the 


Horizon, with the fide A B againſt the Wall or 


Plain, whoſe Declination you defire to know, ane 


then about 7, 8 or 9, in the Morning, (when the 
Sun is clear of the Refraction of the Horizon, 
and before 10 or 11 a Clock, becauſe then the 
Sun riſes but ſlowly) obſerve which of the Concen- 
trick Circles the Top of the Shadow of the Pin 
cuts, and where it cuts it, and there make a Mark. 
This done, let your Inſtrument ſtand un-removed 
till the Afternoon, and then wait till the Top of 


A \ 
* 
* : 
dC 
Pl - "26 
1 
. o 
l _— 8 
& 


1 

: - $2 

- 28 
XY 


-.+ 41 


. 9 P * 
* ! + 
* * 


— - 1 * 


oY 
=J 
2 


2286 
exactly upon a Circle, wait till it doth; for 28 


_— 


* I * 
1 
a go 
E. 0 F 


 "Mechanik Dialling. 


the Sun riſes the Shadow paſſeth from one Circ: 
to another, viz. from the greater to the leſſer, and 
; the contrary at his falling in the Afternoon. 

Havine- thus found the Declination of the 
=, Oi your next Work is to proceed to make the 
Dial, which for an Example, ſhall be a South 
Dial, declining Eaſt 40 deg: for Latitude 54 deg, 
yy min. 

-In performing the Work of this one Dial, you 
_ hive: alſo made three more, as is farther demon- 


32 rated Page 50 and 51, and Plate 3. Eg. 4. to 
Which 1 ſhall refer the Learner for farther Inſtruc- 


tion in that Variety: But of theſe four the South 
a Eaſt is that in the lower Part of the 
© ProjeQion, for making of which, firſt, towards 
the upper part of your Plain, draw the Line E 
W for the Eaſt and Weſt, or Horizontal-line, in 
Which chuſe a Point, as at A, for the Center of 
your ur Dial, upon which deſcribe the Se- 
Pb, La; micircle 2 ME. Through the Point 
Hig 5. A, in the Horizontal- line EA W, and 
a Right Angles to it draw the Line A 
M. which divides the Sernicircle Z M E into two 
Quadrants, of which that towards the left Hand, 
iz. the Quadrant A Z M, ſerves for our preſent 
Purpoſe, becauſe the Dial Geclines Faſt, and con- 
ſequently the Subſtile, c. falls in that Quadrant: 
_ Therefore, ſet 40 deg. (the Plain's Declination) 
from M towards Z, upon the Arch MZ, and 
e the Point where that falls, and from the 
9 A, draw. A D the Line of Declination, 
then ſet the Complement of Latitude, 22. 36 
(becauſe the. Latitude is 54, and its Complement 


E - to 90 is 36) from M the ſame Way upon the 
ſame Arch, and thro' the Mark where that falls, 


and ym the * A, draw the polar Line oh b, 
then 


then aſſume a Point at pleaſure in the Horizontal- 
line W A E, at a convenient Diftance from A, 
as at B, and from thence draw a Line paral- 


From P draw a Line parallel to the Horizontal- 
line WA E, as the Line PC. Take the Di- 
the i tance A B upon the Horixomtal- line, and ſet on 
uth WF the Line A D from A to D, and through D 
geg. dezwea Line parallel to A M, to-come- into the 
Horixontal-line at R, and continue it through 
ju D till it cut the Line P C in 8, a Ruler lai, 
on from A to 8, and the Line A S drawn there 
'0 is the Suhſtile of the Dial. Then at the Pbint 
'UC- WE erect a Perpendicular to the Line A 8, as the Line 


the WF draw the Line A T, fo ſhall the Triangle 8 A F 
repreſent the Stile of the Dial ; for a Triangular 
Plate in that Form, erected perpendicularly upon 
m the Subſtile A 8, ſhall by its upper fide A T caſt 
ef Shadow to the Hour of the Day, when the 
Se. Hour-lines are drawn, which. is the next Thing 
JJ... ae We es "ot 


M 


and Fox drawing the Hour-lines, aſſume a Point inn 7 
e Ade Sabſtile at pleaſure, through which, and rx i 
two Right Angles with the Sz4/Z:/e, draw the Tan; 
and, I vent-line F F as long as you can, and ſetting. 

lent one Foot of your Compaſſes, where the Tan- 

On- gent- line cuts the Subſtilar „ take with the other 

nt: dhe neareſt Diſtance to the Stile, or Line A , 

ion) ¶ and with the fame Extent; one Foot remaining in 

- the Point of Interſe&ion, with the other find the 


Point Z in in the Sz4/#i/e, and with the ſame Ex- 


— . "PREY ren Au 8 2 N LEN) — ” : * x 2 $ t \ N 1 . 1 
* G . - bs 77 9 25 CE INN — 7 5 r FER x 
Se, ox 7 n - + a 5 7 3 
; ' * . s 9 : : 3 £24 9 N 
5 N * 4 l % JS 
5 N 7 — : f 
* - F . * — * 
£ A ” x N ” 
: : $A * — : 5 9 
- x 7 . 8 
" ” b, Py - 
* 
Y 
: 


and f jet o A N, 40 cut the polar Line AP in P. 


. bod 4 
: d 14-2 


$T. Set the Diſtance R D from 8 to T, and + 5 


"ons tent (one Foot reſting in ) deſcribe. the Semicir- 
2 ele min; this done, lay a Ruler from , (te 
a % 


Center of the Semrcircle) to the Point where the 

the Tangent-line E F cuts the Meridian A M, as at 

O; begin at O to divide the Semicircle into 12 
„ „ equal 


en ß; — 


I Dialling. 54s 


equal parts, at every one of which make a Mark. 
Phen lay a Scale from E, the Center of the &. 
anicircle, over the ſaid Marks, it will cut the 
Tang ent- line in the Marks * *. „ec. And laſt 


| | ly: ** a Scale from A, the Center of the Dial, 


over theſe Marks * , e. in the Tangent- line, 
and Lines drawn thereby will be the true Hour- 
* of that Dial. 

Ix this, as in a South Dial, the our of 12 
is at the Meridian, or middle Line of the Dial, 
and the reſt numbred forwards with 1 2, and back- 
Tons — the left Had with I. 105 95 5 7, 


SECTION vll. 


er Dial arching from the dun b We Pars. Pla 
5 1328 . 12. Ag. * 7 


8 


1 5 * Draw the Horizental-line W A E, and 
upon the Point A in the middle of it, as a Cen 
ter, deſcribe the Semicircle Z M E, as you ſee 
taught i in the laſt Section for Dials declining from 


1 * the South Eaſtward, and draw A M perpendicular 


to WE, which will divide the Semicircle Z M 
E into two Quadrants; and as in the South Faſt 
declining Dial, the Quadrant A Zz M was of uſe, 
| ſo in this the Quadrant A E M muſt be made uſe 
- of, becauſe in it the Szb/##le and other Parts of the 
Work neceſſarily fall, and there is no Difference 
in the. Operation, only inſtead of ſetting from A 
or hs Sc. to the left Hand in the laſt, you fe 


= ; from 


rk, from A or M, ec. to the right Hand in this; ſo 
K. hat if the laſt had been drawn upon oyl'd Paper, 


| } 
: 4 77 ä * N 2 * 9 cc N ann * * 
9 * N Fl N a * . * 1 e 6 mg 
G a Ss AS oY e ths pf * 9 * * 0 s KEYS 'r 1 8 N 
o 2 * : e, 5 a : , 2 4 "7 XY 
Frys 2 8 * * * off 8 : r LN, 
; p Y d] 2 -. . : : I 
- 5 2 + 4 4 [308 x 
% 5 4 * 
ö | * | 5 
7 — 8 * 
. * - 
: - . 
A 
< 


the or any other tranſparent Thing, fo as to be ſeen 


alt. Mthrough on the back fide of the Paper, it would 
ial, de exactly a South Dial declining Weſt, as far 
ine :s the other did Eaſt, and for the ſame Latitude 
vu. only, the 11 muſt be 1, and the 10 muſt be 2, 
nnd ſo in the reſt, and the North Decliners are al- 
1 bo deduced therefrom, as is taught at large Page 
Yal, WY 50 and 51, before mentioned. 5 


ack» 6297 . . ens + - 
essesssesesessssseees 

1 SECTION vn. 
2 5 


Of Eaft or Weſt Reclining or Inclining Dialr. N 


Arnoven we have given Directions (Page 

125, for reducing Eaſt and Weſt Recliners 
for any given Latitude to new Latitudes and 
new Declinations, and ſo may be performed by 
he Directions given in Se&. 6 and 7. of Mecha- 
ick Dialling, yet I ſhall here, for the Learner's 


mprovement, ſhew how they may be done Me- 
Cen- bazically, without any ſuch Alteration, whether 
: 4 ey be Eaſt or Weſt, Reclining or Inclining. + 
r 


Ir will be neceſſary firſt to premiſe, that Eaſt 
and Weſt Recliners have their Centers near the 


ZM Bottom, and in this the Incliners of both Sorts 
Eat we their Centers near the Top: The Weſt Re- 
; * liner and Eaſt Incliner ſnould have their Centers 
e 


£ oward the right Hand, and the Weſt Incliners 
f the ad Eaſt Recliners have their Centers moſt com- 
rence Anodiouſly towards the left Hand: Therefore, 
SUPPOSE I would make an Eaſt Dial to recline 
ou {tt i deg. for Latitude 54 deg. ” | | 


HAI NS 


RN '4 5 
Tal AGE "+" 3 
4 N "x 

: 


* ran Ham. 
: Harm prepared my ſquare Pra W XYZ 


. T confider by the foregoing Rus be 

Plate 12. where I may moſt conveniently chu id 

Fig: . 6. my Center; and I find firſt, that au in 

. Recliners both - Eaſt and Welt, have dr 

"their Centers at or near the Bottom ; and ſecond- A 

"1y, I find that Eaſt Recliners ſhould have thtil pe 

Centers moſt towards the left Hand; therefole x St 

= * the Bottom of the Square W X Y Z, draw the its 
Line SN for the Meridian, in which, not at t of 
4 Middle, but rather towards the left Hand, as at A, 
I chuſe the Center, and from A perpendicular to ple 

the Line S N, draw A E; alſo with one Foot a "1B 

your Compaſles i in A, deſcribe the Quadrant TUM ® 

and ſet off 45 Degrees (the Rechnation of the ſes 
Plain) from T towards U, and through that Poinqi de 

in the Quadrant where the 45 Deprees end, and Di 
from the Center A draw the Line AO. Alſo the 

off upon the ſame Quadrant from T, the Com r. 
plement of Latitude 36 Degrees, and thro theliſ 9 

Point where that reaches upon the Quadrant, audi eth 

BH from the Center A draw the Line AP; then ii dra 

F *'the Meridian Line NS chuſe a point at pleaſure i 2. 

1 as B, and from that Point draw a Line parallel Per 

to A E, which will cut the Line A P in P. From Ce 

that ImerſcRion at P, draw a Line parallel to thay PN" 

Meridian-line 8 N, to come to the Perpendicun May 

: A E in C; and alſo from the Line A O in 0 2 

. take the Diſtance A O, and ſet upon the Perpen W 

 _4dicular AE, from A to E, and draw E G par x Al 

el to 8 N, which will cut BP continued in G Tay 


Met alſo the Diſtance C O from A to Q, upon ths 99 
Line A O, and draw the Line QR parallel to © 
P; take Ale in Four Compaſſes the Diſtance / x 
R (from the Line 8 N) and ſer it off upon the ”* | 
Line G B, from G to 8, a Line drawn from in tf 


o 8 ſhall be the ma of the Dial. "Fav 1 ke 
pe wer 


: 5 
* 0 K-52 N , 
Ss . » * F4 a 4 5 * 


. 6 . * W *** r Sta, a Shes as th. | 
r e : y c R 
8 n * * * * ys A K > > * * 7 REV  —_— 
| | . - 7 n | _ 
; L C f oy ey Pd, 
> Rx , 4 5 ? 4 
l ; , | 5 * "= 
6 a 2 47 ; p14 * Z "73 

I, . » * ? - = 

q of - 1 

5 


perpendicular to A 8, and take in your Compaſſes 

the Diſtance 8 and ſet from S to M, and lay- 

ing a Ruler from the Center A to M, a Line 
drawn by it ſhall be the ſtilar Line, the Triangle 
ASM repreſenting the Stile, which being erected | 
perpendicular to the Plain of the Dial upon the | 
Fubſtile A*S, ſhall give the Hour by the Shadow orf 


„ +l its upper Edge, which will be parallel to the Axis | 
it till of the World: : te Par 520 rut 4 ly 
at l Fox drawing the Hour- lines, chuſe a Point at 


pleaſure in the Subſtile A S, and through that at 
night Angles draw the Tangent-line I K as long 


ot | 
TU as you can, and with one Foot of your Compal- 

F the fes in the Point where the T'angent-line IK crofſes 
Poindll the Subſtile A8, take with the other the neareſt 


Diſtance to the Stile A M, which done, (keeping i 
Io lf the other Foot yet in the aforeſaid Interſection?) 
Com farn the Compaſſes about, till it cuts the Ste KA 
” digen 9, as in ZE, and fixing that Point in E, with the 
ande other at the ſame Extent deſcribe the Smicircle ln; 


„ and 5 | J le i 
den u draw 2 Line from M the Center of the Semicircle, 


to the point where the Tangent - line I K, cuts the ® © 
arbeit Perpendicular, and obſerve here it cuts the Semi- 
From circle, and there begin to divide it into 12 equal! 
to t Parts A Ruler laid from Æ over the equal Di. 
zicua Viſions of the Semicircle, will cut the Fangent- 3 
in O line K unequally in the points *'*, c. And 26 
erpet Laftly, a Ruler laid from the Center A to theſe 


2aſure, 


 paral Ma ks ** * c. in the Tangent line, and Lines 
in G e thereby, ſhall be the true Hour- lines re- 1 
On the qure BOY . k | 3 - ; | : : „ : 
e to . Tur Line 8 N being the Meridian and Hour- 


line of T2, you muſt place 12 at the End of it, 


ance ! 1 pt | 3 Wages | 
on th and the reft 1 1, 10, 9, 8, 7, 6, 5, 4, as you fee 
"Ts 220 91.7 25 oops 


w SM 


Ix drawing this, you have in Effect drawn three 
per . | 1 


more; as, | „ 
| ; 1. 2 5 i 1. Ip > 0 


F * 1 * Youu N — * 6 „ * i ds, * e * * 
N „ ö N 0 bn” 7 Ne 7 
, Sy Sp”. — 3 
* - . , A x p 5 Li 8 = 2 
a 4 * 6 5 
* 8 "i "> = |; l 8 8 * : 
hy" ; as. * p „ © 8. 
8 F Z . 
* 
+ 
4 


2 


I. Ir it was turned upfide down, the fame 
ſide is a Weſt Dial inclining 45 deg. only the 
Hours are for the Afternoon, as for 17 put 1, for 
10 2, and then the Subſtile will conſequently be 
as much on the right Hand- of the Perpcndicy- 
lar, as now it is on the left. | 

2. If it was drawn on oyl'd Paper, the back. 
. fide would be a Welt Dial reclining 45 deg. only 
the Figures inſtead of 12, 11, 10, 9, Sc. muſt be 
12, I, 2, 3, 006. 4h 

3. Ir the Meridian-line 8 Nbe turned upwards, 
the Back- ſide will be an Eaſt Dial inclining 45 d. 
and the Figures, as: they are, only the Subſtile 
muſt be as far to the left Hand of the Perpendicu- 
lar A E, as now it is on the Right. 


Scrion. 
To Of Direct South or North Plains Inclining or Re. 


clining. 


TT is needleſs to give any Directions about di- 
rect North or South Reclining or Inclining 
Dials, becauſe they are erect direct North or South 
Dials in ſome other Latitude; and how to reduce 
them to ſuch, you are fully taught in Sect. 5. of 
Iuſtrumental Dialling, Page 192, 193, 194, and 
when they are reduced to direct North Dials in an- 
other Latitude, they are made by the Directions 
given, page 218, and 220, to which (to avoid Re- 
petitions) I ſhall refer the Learner in this Caſe. 


— 


er 


en 4 Dialing. 


EX EEE EEE; 


SECTION ©. 


7 Alen the Howr-lines. upon 4 South or N. = 


Inclining, Declining, or Reclining Plain.- Ws 


| TH ESE Dials, though different in Situation, 


are the ſame as to the Method of Projection; 

for the South Inclining Declining, and North In- 

lining Declining, as alſo the South Reclining De- 
lining, and likewiſe the North Reclining Decli- 
ning, are the ſame, only differently placed, and 

ae to be projected by the following Ruſes. 
Nor, You are taught in Seck. 10. of [ftira- 


| mental Dialling, Pag. 205. how to reduce (Plase 


12. Fg. 7.) any Declining Reclining Dial, for any 
given Latitude, to a new Latitude and new Decli- 


nation, where it will be anſupright declining Plain; 1 


which being done, you may proceed according to 
the Directions given in Sec. 6. of Mechanic Dial. 
ling Pag. 223 to 228; but becauſe that requires Tri- 5 05 
gongmetrical Cllonlarins for finding the new Lati- 
tude and new Declination, (which we ſuppoſe 
ſome Mechanicks are not capable of) I ſhall ſhew'-- 
how it may be done without ay Trig ovometrical 
Operation whatſoever. F 
I ſhall inſtance in a Sonth Dial declining Eaſt 
26 deg. and inclining 36 deg. for Latitude 5x 4. 2 
30 min. 1 
'Dxaw a Line on the upper Aide: of your Plain 
parallel to the Horizon, which mark with E Wi: | 


diz. (becauſe the Dial faceth to the 'Southward)? 


We 5 at the. _ Hand for Eaſt, and Wat the 
E-3 left 


EF left Hand for Weſt ; aſſume a Point in the Line 


E W, as at A, for a Center, upon which, with 
any Extent of your Compaſſes, (the longer the 
better) draw the Quadrant x y, and through x draw 
the Line A x X perpendicular to WE; divide the 
Quadrant into 90 Degrees, as you are taught in 
Seck. 1. of this Chapter, Page 216. or by a Line 
of Chords (the making of which I ſhall ſhew her 
after) which is much more expeditious, and 550 
theſe Degrees of the Quadrant, ſet from x the 
Complement of Latitude 38 4 deg. the Declina- 
tion 26 deg. and the Inclination 36 deg.” making 
Marks in the Quadrant where theſe Degrees ſhall 
fall, and through theſe Points in the 3 
and from the Center A, draw the Lines A b, A 
e; and Ad. Then chuſe a Point in the Line E. 
W, towards the Quadrant, as at B, from which 
draw a ſtrait Line perpendicular to E W, or pa 
rallel to A X, as the Line B P, to cut the Line 
Ad (the Line drawn from the Center A through 


the point where the Complement of Latitude 


reaches in the Quadrant) in the point P, and thro' 
that Inter ſection at P draw the Line P C parallel 
to WE, which will cut the Line of Inclinat ion 
Ae in O. Take in your Compaſſes the Extent 


» | AO, and ſet on the Line A x from A to F, and 
through F draw F G parallel to P C; then take 


in your Compaſſes the Extent C O, and ſet it on 
the Line A X, from A to L, and draw L D pa- 


' rallel to W E, to cut the Line of Declination A 


bin D. Set the Diſtance A B from A to V, up- 


* on the Line of Declination A b, and from V draw 
VV K parallel to WE, to cut the Line A X in K. 
Take in your Compaſſes the Extent V K, and ſet 


off upon the Line G F, (but on the contrary Side 
of the Perpendicular) from F to M, and draw MN 
_ Parallel to A X, to cut the Line W E in the point 


N. Then 


Line 
With 
the 
draw 
e the 
ht in 
Line 


ner 

500 
C the 
lina- 
king 
{hall 
rant, 
„A 
je E 


ler ents the Eq 


Mlierbanickł Bias, | 235 


N. Then becauſe the Plain is a South Feiliver® 


(or if it had been a North Recliner it had been e 
lame) rake in your Compaſſes the Diſtance L D, 
ind ſet upon the Line FG, from F to H, for 4 
Meridian-line, or the Hour-line of 123 take in 
your Com aſſes the Diſtance A L, and placing 
fo Foot 
men take the whole Diſtance A X, and ſet upon 
the Line of Incliuation A e, from A to Q, and 
from Q draw For parallel to B G, to cut the Ho- 
montal line in R; take in your Compaſſes 
the Extent A R, and with one Foot in M, ROT 
the other in the Line M N to the Point 8, and 
draw the Line A S for the Subſtile, aud N 
T perpendicular to A 8, and upon the Line 3 
M ſet the Diſtance QR from 8 to T, and draw 
the Line A T for the Stile, fo ſhall the Triangle 
AST repreſent the Stile to be erected perpendi- 
culat to the Line A S, and to ſtand upon that 
Line, the Side A T being 17 1 to the Axis of 
the World, and its Shado upon the Hour. lines 
determining the Eout gf the Day. e 


Fox drawing tde Tour lines upon this Pil, | 


chuſe a Point in the Subſtite A'S, and through that 
Point, and perpendfcular to A 8, draw the Tan- 
tene ie E g to cut the Subſtite AS in the Point 
h, take the neareſt Diſlance from the Poitit — In- 
terſeckon at h to the Stile A T, and keepfn 4 
Foot in h, tufn the Other about to che Rant 
in the Subſfite A 8; then keeping that Foot in A 
with "the other” draw the Equinoctial Circle 
touch the Tangent - line; 
E the Center of the Equino&tal: Ie, to the Pol 
where'the Fangent-line cuts the Meridian- line 
H, as in the Point O, and obſerve where that Ru- 
guinocta Circte, and fron ee. 


8 diride the Semitirete into 11 


li 3 - as 


7 


K, extend the other to "the Point X; 


then lay a Ruler ben 
n 


equal Parts,” 


* 
4 —— = 
= 4 <A 

12 

: : 

. — 


<< 
7M 
f _ 
1 
: 
; 


> . 
65 og 
4 * 


>. 


and 11, 10, 


; MI ä * 
7 % pu A a. N 4 * 2 * * "I 9 % 
6 * 1 * $6261 oh * R : - 9 y , 
* . N * N . 5 * - ö 5 
1 » o et CC 8 1 >. o ” * 
R n ä 
* l of 7 2 * FR RES. 8 þ OR * 

I * . * . * 
_—— — x © BANC U 4 
"= . 3 599 : ; 4 | S a 
ST * « , 


a5 you were taught, Page 217. and then, as you 
bave been formerly taught, lay a Ruler from the 


Center of the Equinoctial at over the equal 
Diviſions in the\Circle, and obſerve, where it cuts 
the Tangent-line, as in the Points & & &, ce. 
And laſtly, Lines drawn from the Center A thro! 
the Marks * & &, Sc. ſhall be the true Hour- 
i! 
Fon numbring the Hours, place 12 at the Me. 
tidian-line at H, and 1, z towards the right Hand, 
| o, 9, Cc. towards the left Hand as far 
as the Hours extend. Nh 
| Note, It is beſt in drawing this or any other 
Dial, to draw all the preparative Lines with Char- 


Coal, or Black Lead, or the like, that they may be 


taken clean out, when you have put on the Hour- 


© lines, and ſuch other Furniture, as you think fit 
dd put upon your Dial. 


1x might proceed to ſhew the Method of mak- 
ing Inclining Dials declining from the South-wett- 
Ward, as alſo North Recliners declining Eaſt and 


Weſt, but they being all, (with a little Conſide- 


ter) inclyded in_this, 1 ſhall only, for the mak- 


d 


1. AN Incliner declining from the South-Eaſt 


* ; . 1 


. N 


Ward, is what we have juſt now ſpoke of. 
2. Tas Incliner declining to the South-welt- 
Ward, is done by the ſame, Directions, only the 


Quadrant which in the Eaſt Decliners is on the 


right Hand Quarter below the Horizon, muſt in 


the Weſt Decliners, or thoſe that decline from the 


'South-weſtward, and alſo incline, be in the left 
Hand Quarter below the Horizon or Line WE, 
Which may be beſt conceived by ſuppoſing this 
Dial to be drawn on oyl'd Paper, and looking 
through the Paper, that which on the right Side of 


ien Dial declining from 
5 r . 7 . a n 3 50 85 t e 


- 


£24 * 4 
t * 


* 


. 2 
A 


EFT ůwüün ß FIG I 45 N unn 1 * 
LN SI FRET We 5 OE RO I ARES > * 9 82 . 
7 Ms. . [2 * A 2 o 7 n CMP R 
N 4 - f % N * 
1 * 7 4 = 
. * o 1 
: 1 fs 
. 
| f Me Ba 7 * ] D all Ng. 
: 25 s & © JE 7 *. nit 


the South-Eaſtward, will, (looking thro' the Pa- 
pet) be an inclining Dial declining from the South 
3. A North declining Eaſt Recliner is the ſame 


of a South declining Eaſt Recliner, only the Ho- 
rizontal-line W E muſt be at the Bottom of the 
Dial, and the Quadrarit deſcribed thereon upon the- 


Center. A, muſt be above the Line E W, and to? 


wards the left Hand, and may be repreſented by a 


South declining Eaſt Recliner turn'd Bottom up- 
wards with the fame Side towards you as before. 


4. A North declining Weſtreclining, is the ſame - 
with a South declining Weſt inclining, only s 
before) the Horizontal Line EW muſt be at the 


Bottom, together with the Center of the Dial, and 


the Quadrant muſt. be above the Line; and towards 
the right Hand, and may be, repreſent 


an oyl'd Paper, and ſeen through being turned } 
Bottom upwards ; but of this ſee more, Chap, 27. 
Fe ii and. zi. l 

oe, The Hours on the North, Dials muſt be. 


8 


numbred the contrary Way to thoſe of the Saut i 


North 


Dials, and for what Hours to put upon any 


Dial, whether declining, reclining, Sc. See Ch. 


). 6 2 et rr 
. Thave not drawn. the Hour-lines in the Dial now 


deſcribed; leſt. it ſhould too much confuſe. the; 


Scheme, it being eaſy to imagine, Where they will, 
fall, when drawn from the Center A. thro? the 


Marks & K *, Ge. in the Tangent line. 


6 ian odd a dS. 
. n AE mg 
9 % 
1 ps 1 
* * 7 
2 é "ll 
» + 
. * 1 — 1 
. bs N wy © 
. 8 


. 


ed bythe 
Dial already deſcribed, if imagined:to be done up-. |} 


: 
1 5 
72 4M 

* s A 

* x} # * 


. 
© £ 
* AY. * 
E 
*. 
* 
2 8 - * 
1 
3 * * 
12 : 1 


5 


ä 8 : f ö * „ ee Rs I r : ; « bo D 
* * — 9 r W 2 N R = 9 * A 4 * © 9 — 7 * f 
9” n * , 7 a 5 - K * 
—_— 4 7 
75 ; - ; 5 
+8 * —_— Tx. 4 * 2 * A 
— * e 4 A 
K . . * p a 
\ | ; : 
* * R ” © * 
* 2 * 
4 5 5 
- 
* 4 75 » * 7 7 0 7 1 2 
3 \ : 4 n+ - M F 


eee e dee 


mor 1 ON XL. 


Abe plain and caſy Way to make a Dial, that ſtall 


give the true Hour by Reflection ou a Cieling, 
' . where the direct Beams of the Sun can never come, 
and fall repreſent the Sun's Motion as true and 
regular within the Houſe, as his natural Motion is 
_ without, provided the Window open to the South- 


* # 


three Quarters of an Inch broad, and fx it in 
a Window that looks to the Southward, (the near- 
er the Out- ſide of the Window that it ſtands, the 


IB longer the Sun will ſhine upon it, and therefore 
it would be better to make ſome Conveniency to 
E place it upon, quite without the Window, that 
= the Sun may fhine upon the Glaſs as long as it 


Mines upon the Wall) and take care to place your 


3 5 Glaſs very exactly parallel to the Horizon, for if 


you miſtake in that, you throw alt the Work amils. 


This done, hold a Thread with a Plummet exactly 


over. the Glaſs, and obſerve where the Shadow of 
the Thread falls upon the Floor exactly at Noon, 
and there draw a Line quite croſs the Floer as far 
as you. can, for this will be a true Meridian, or 
North and South Line; but if you have the Op- 


portunity of a good Clock, Watch, or Dial, you 


mey find the true North by the Directions given, 
Page 224, and 225. and having by any Means 
found the true North from the Glaſs, and thereby 
deſcribed a Line upon the Floor, or (which 8 5 
8 | = 8 ame 


4 y . _ 
. 
. 4 Y K 


Ward, or ſo that the San may ſhine in or wear ii. 
AK E a piece of clear Looking-glaſs, about 


= 3% +5 


| Mohit "Ding 1 © i 


met 1 its Seck Pat e tos a. 1 ad 
holding your Hand up again 

the Thread in your Hand, and the 1 8 ON lay- 
ing freely, move your Hand to and fro, ill the 
Point of the Plummet reſt over or upon the 2 
or Meridian-line before found, and there Where 
the upper End of the Thread toucheth the Jeelingz, 
make a Mark. Do the ſame at the other End Of 

the Thread or Meridian-line upon the Floor, and 
make another Mark upon the Cieling; then With a 
Carpenter's' Line, or a ſtrait Ruler, draw a Right- 
line between thoſe two Points, Which will be a 
ae Meridian, ot North and South Line, n 
the Cieling, Then becauſe the Sun's Meri 
Altitude, When in the Equinoctial, is equal to the 
Compleinent of Latitude of. the Place, and be» 
cauſe the Angle of Reflection is always. equal to 

the Angle of Incidence, viz. a Line imagined tc 

be drawn from the reflected Spot upon the Ciel- 
ing, to the middle of the Glaſs, makes always, the 
ſame” Angle with the Plain of the Glaſs, that 4 
Line drawn from the Sun to the ſame would da, 

| will follow, that the Equinoctial muff croſs. the 
Meridian juſt in that Point that makes an Angle 
with the Plain of the Glaſs equal to the Comple- 
ment of Latitude of the Place, which, Point in che 
Meridian may be thus found. 

-Cavst' one Perſon to hold a Thread exaly. 
upon the Middle of the Glaſs, and ſtretching 1 
tight, hold the other End up to the Meridian „ 
on the Cieling, to make (as near as you can guels) 
an Angle with the Horizon equal to the Comple- 
ment of Latitude; and holding it there, apply the. 
vide OE a Gunter's * to it, if it 2 too 


" 9 K * PEE K 9 6 nn 
, 4 6 ** „ > 1 * 8 * * 1 * 1 
— 2 — 9 1 
na 44 9 * N 7 Ti 

PEI WI Rue — * f * a 4: 

renne N p ; 
* 1 2 . PÞ - - 
we . 4 =... ” % On . 1 $4 Slat F 
27 5 


5 Freat an An le, (keep that End faſt upon the Glaſs, 
Aud) flip a little more of the Thread out of your 
Hand, and ſo moving gently to and fro, find where 


itmakes juſt the required Angle (as ſuppoſe of 387, 
1 if it be for Latitude $12 deg.) there make a Mark in 
AJ the Meridian. * the Cieling, for there the E. 
- quinoQiat muſt ' croſs it; therefore through that 
Mark draw a Line croſs the Cieling at right An. 


2 48. 


geles, With (or perpendicular to) the Meridian, to 
© - repreſent the Equimoctial. 

Wore, It may be as well to put the Thread thro! 
3 the. Hotes in the Sights of the Gunter's Quadrants, 
© | and letting the Plummet play freely, proceed as 


* 


ore, r ae . 
= Keey your Thread till faſt, one End in the 
middle of the Glaſs, and the other End in the 
| Folge, where the EquinoQial cuts OE in 
= the Cicling, turn your Quadrant with its Center 
0 the Center of the Glaſs, and its Side or Semi- 
diameter exaQly along by the Thread, propping ot 
atherwiſe fecuring it that it may not ſtir, then (be. 
'caule eyery 15 Degrees of the EquinoQial is an 
pur of Time) temove the String 15 Degrees of 
"the Quadrant; and obſerve where it cuts the Equi 
. "noaQial, when ſtretched to it, and there. make a 
Mark do the like for the next Hour, removing 
the Fhread to 30 Degrees, and ſtretching it to the 
© FyquinoQial, make a Mark, where it cuts it; do 
= "tie like at 45 deg. 60, c. as far as you can, 
3 which done, remove your Quadrant to the other 
Side of the Meridian, and ſetting of 15, 30, 45, 
© - 69; Se. Degrees, make Marks on the other 
Y alf of the Equinoctial, and ſo you have the. 
& Points where the Hour-lines interſect the Equino- Wh «+ 
Jia which are to be numbred. with 12, where. 
5 the. Meridian cuts. the. EquinoQial „ and from 4 


Om, ALAS YA 


* 


py — 


= 2 

"bg * 

11 * 
1 

1 Pl 
ROY 


. „ e . _ Xx, put 


© thence 


” * 2 2 25) BTR 
r a wow + x 
va 


5 


© Mechanick: Diullng: | bes 


la, 8 thence Eaſl ward with 1; 2, 3, Se. and Weſts . 
your ward with 11, 10, 9 He. as far as the Room ij 


here extends. 420 - 7 
3915 Noe, You may continue the EquinoQiat i 
tk in down by the Sides or Walls of the Room, as 
e L. well as upon the Cieling over it; if you conti 


on * 


that i nue the Quadrant at the aforeſaid Elevation, and 
An- continue the Equinoctial down the Wall, ſo as 
, to that it may juſt coincide with the Plain of ths i 

Quadrant, which may be done by continuing tbe 
thro! Thread parallel to the Plain of the Quadrant tilt 
ants, it touch the Wall; and though the Wall be never - 
1 a WM fo irregular, the Equinoctial may be by this means 
: continued, and the Hours upon the Wall as well 
the as the Cieling may be found by ta I 5 Ot re- 
the moving the Thread. 


nin W As for the Hour- lines, 8 are to paſs theo theſe. 6 J 
nter ſeveral Points found in the Eguinoctial by the . 
mi- foreſaid Means, but they mult not cut the Equzi- 


g or Wl modal at right "Angles. To find the Center, o. # 
(be. Point of Interſection of the Hour-lines will be 9 


an difficult, becauſe it falls without the Raom.in- the 
$ of Air; for as the EquinoQial is elevated equal to- 
qui- the Complement of Latitude, ſo the Pole is ele- 
de a vated equal to the Latitude; and as the elevated 


ing pole is to the Northward from us, and a Line ſup- 
the pos'd to be drawn from it to the Center of the 4 


do Glaſs, will make with the Horizon an Angle e- 
can, qual to the Latitude of the Place, ſo the reflected 
ther. Axis of the World ſhall deſcribe an infinite Line 


45 
ther 
the. 
no- 
ere 
Olm. 
nce 


in the Air to the Southward, making with the 
Horizon the ſame Angle. : 

Bor becauſe the Pole or Center of the E- "= 
_ quinoRial falls without in the Air, it is not ſo 
eaſily acceſſible for drawing the Hour-lines ; there i 
fore to remedy that Inconveniency, obſerve „ 


ok Ss he Aden 
IO ER Ts 
* * 
8 


the Direction ven, (Sect. 1.) For drawing a 

what Angle every Hout-line 
makes with the Meridian, and in this Caſe, they 
mult make an Angle equal to the Complement of 
the fame Angle with the Equinoctial. As for Ex- 


* — 


Sorrosx I would make an Horizontal Dial for 
Latitude 51 Degrees, 32 Minutes North. I 
Mall find by the Directions given, Sect. 1. that 
the Hour- lines make Ang les with the Meridian, 


591 * 4 
* " 
% wy 7 ** F F ” 
* he 
{8 1 * 
* * 
6 N 
« 2 * 
4 * * 
% * \ * 
P Ls ts F [1 
2 4 1 
"IA 0 U * 
= . = : y 4 I < 1 * 
> * 4 2 > 
8 ; - ; f 
8 : « | | 7 
. r * $ ” : 
* 5 5 * * 
TY s a ; 
73 7 8 # 22 i * * 
/ 8 x : ; . 
* * Z A 6 
1 3 Fl 4 — * * 
* 3 
— * \ $ - 
„ 
#5. * , 7 , N 
ff * 1 
2 7 „ * WW ; Ee N ; « 
as ** & * > * 0 2 4 7 $5; £ i 8. £ +2. £ 2 1 3.+ 5 
5 > HAT + my > » a 4 1 * 


: 2 are the Angles that each Hour- line 


8 
1 _— dach eee 3 el 9 9 9 to a 
— + o + * 3 E ? 25 : 1 * 
15 A 5 2 5 by "4 1 5 7 oy . # 
v * PE: * 4 
0 wy 
* ” 
* y * ol # * # 5 
* 8 — — q 4 7 | 
W . » — 1 4 d 
E 2 N - £ N 7 
{ . 31 1 5 * 3 # - oe * © 2 . 
: ; 
Fy ” F-, 82 * 1 * . : o a 
KS 4 * 1 3 4 . * £ 2 4 1 * 5 1 : 
: * . 
7 1 F- 
> 
x £ 1 7 —— 
: 3 
- 
F x "A 9 * . 1 * 
C 7 r — * % * 
* 2 4 1 IJ * s ; OE 8.” # 8 N 
ö 5 | 2 4 43 * 
, 
4 p . < Or. 7 
* 0 1 1 N : 
25 * 4 4 * By 
« > * 2 ; 5 
\ A 
2% 1 — . * 2 ” * E ' 5 
5 1 : 3 7 e 8 2 f 
* + a 5 
: 5 Ne N 5 2 3 
1 l "Be. n i * 7 * 
& **  - * E335 # 4 1 2 * * Ke 4. 23 0: %- g 
„ * * : | 
* 
*% A pe 
WS | N 
4 : : 
% 
, 
— 
— * > 
J - 
* 
y - 
8 8 : A M2; H 2 
T 8 8 ſy the 5 et 3 of 1 
Y 9 > 


* 


The Angle with 
on * 


yn Fo 


' THEREFORE, if through the ſeveral Points 
found in the Equinoctial for the Hours, you 
draw Lines to make the laſt before- mentioned 
Angles with the Equinoctial, they ſhalt be the ſe- 
veral Hour-lines required, and the Sun ſhining 
upon the Glaſs ' ſhall reflect the Light at an 4 45 
Time of the i _ the Hour of the Day: me | 


Now „Wust is ſaid here of” the 


"which the Hour-lines make with the E. 
quinoctial, is meant while the eee 
al is continued upon the Cieling parallel to 
the Horizon, and not with Reſpect to 

© doing continued down the Watt. FE 


o 


M 4 AS Ins n * „ a a . 
k o rann j ˙ 1 ERS en 92 
N "ye * ig he at. gh PRES N nnn "I R Yr pode 4 
4 ö R * aer S 8 
* * T 7 Y * * n * ? A ö 
8 * "Roc — oy * « * » * a y © » 4 
5 4 | Cc ; | 14 #21 q 
A ; * : 
” 3 5 1 7 £ 
- — 4 5 + ; | 


* 
* * 
* r 
_ N 
n 
4 85 
q 3 1 
= WS * Y 
* * * „ Ll 
_ . 
_ 22 Pg 
_., 5 
+ _ 
* o *. 
"= * 
K * 


3 % 
þ: 


a 
4 
* N 


Br - 
. 
1 
xo 
s * 
7 
2 
= 
"8 
3 
* 


S eee 
2 Z 6 CE 5 . 5 fy 5 | : 


— — — 


VV 


= How to male a Line ef Chords, whereby any Nun- WM th 
ber Degrees may eaſily be. ſet off upon any WM uf 
Circle, without the fore-mentioned Trouble of di. 20 
viding it or Toad | be 


— 


4 PDescaunr a Semicircle, . and divide. the Circum-- ne 
= —- ference of it exactly into two equal Parts. y 
At c, then divide either of the Quadrants (as ſup- C 
pose b c) into go equal Parts, as you are direc- 
dei in the firſt Section of Mechanick Dialling, and M ee 
=: -- +27 may draw. the Line- b c. Then upon the F 
din where. you intend! to make your Line of WW tt 
Chords (whether upon a Ruler, a Paper, or Board) is 
dta a handſome double Line and a ſingle Line c 
competent Diſtance. from it, ſo as to leave 
Nom between them for the Figures, as you ſee 
and Jet theſe Lines be exactly the Length 
the Line be, from A to B, which done, and 
tdtbe Quadrant very carefully divided 
Fe 12. into 90 equal Parts, as before dired- 
n.8. ed, take a Pair of Compaſſes, and: 
E '- placing one Foot in the Point b, ex- 
& tend the other to the End of the firſt Degree, and 
& Keeping that Extent, place one Foot im the End 
of the double Line at A, and make a Mark where 
tte other falls in the ſaid Line; then again placing 
one Foot in b, as before, extend the other to the 
End of the ſecond Degree, and ſet the ſume Et- 
tent on the Line A B from A towards B, and 


* * 

8 2 1 * 
* it „ 

6 5 


3 


3 4 NG . 266 = 


o n * : 
ä 9 , le. a 9 * * 

ö p CO FL LIP IE ROE IO IY x R W , , ' = = 

- Rs 228 * ral 1 g p , 1 9 N N 8 . "70 $4 0 , * « Nr * 
* * F” N N 3 N #8 
; » 0 .. a a 5 

a : 2 s : 1 : *. 9 <A 

; =_ a W 

: =» * 5 2 5 3 1 , _ bo 

- 7 5 . : - * Is: 
A * 

2 

, 8 *. 

a 1 


* 3 
where that falls make another Mark. Proceed- 
in the ſame Manner with the third, fourth, or 


1 


mw . It is always obſerved, that the Chord of d? - 


* 
— 
= 
4, 
* 1 
7 


* Fas, 
ton 


be, $7 
* 25 
4 2 
4 


Chords, it muſt always be a Circle of the lame 1 
Bigneſs of that, by which your Line of Chords 


— 


n 
* Ss 4 


+ hers l order Point falls upon the ite, and I ©? 
make a Mark; "Fora that is the e Numer of Degree 
required. 


= - . Wit 
_— ral 


E - * lr is eee to ſet 35 rees upon the uar- 
5 % drant d c, from d ae Place one the. of 
"your "Compaſſes in the Beginning of the Line of 
Chords at A, and extend the other to 437 De- 
. = (vez. to ſeven finall Divifions beyond the 

mber 36) then with that Extent applied to Mi; 
the Citele, one Foot in the given Point d, the o- 
ther Will reach to n, the "Quantity of 37 deg. ON 85 


* . be 
- @©Fo meaſtre -4 given Arch of a Circle,” is juſt the p 
= Revs of "5 for, take the given Arch, or the be 
Diſtance between the two given Points in a Ci W 
dee in your Compaſſes, and apply that Extent up». s; 
=. on your Line of Chotds, (always purting one 9 
Foot upon the Beginnin of the Line) the moves · p 
8 ble Foc cot t falls upon the J gree required.” — R. 
= er ot; l 5 * 4 a Þ E E. 1 5 


* | A e Sen to winiſtte the Py "IP in the Se. m 
mieirele de b. Place one Foot of ' your Compaſ- N 
ſees in q, and the other in n, that Exterit apply'd | 
tee the Chords, gives 37 deg. . ec 
bor no Line of Chords will mesfure any Cir- Ml © 
=* ele, but theſe of the ſame Diameter wich that WI 
* from whom the Line i is projected; therefore it may R 
be proper to make or have Lines of ſeveral Ra- ; 
= dies's,; but if you have not ſuch Variety, that dj 
3 — 957 Swag be in bee ee remedied * 


a bee 7 - 8 


7” 


rve 
and 
es 


to be meaſured, draw a Circle which: will be pa- 


5 * " R : 9 N 

9 , oY 2 CNV I ON FOR N 
ru 1 3 e 9 

2. . I 

"oj ft : $2 Ho "= 

Wo "= = 

+ « K 

* 


10 3 any part on any Cirele, (thether: | 
it be to a larger or leſſer Radius than your Chords 
are made for, it matters not) take in your Com ='Y 
paſſes the Chord of 60 deg. from your Scale, and 
with one Foot in the Center of the Circle that is 


heh” . 
br 


rallel to the. Circle to be meaſured, but Whether 
within; or. without, it is the ame; but in this: 
Caſe, we will ſuppoſe it falls without the Cir- 
cle that you would meaſure. Lay a ſtrait Ruler: 1 
from the Center to the Point, from whence your i 
Number of Degrees is to be ſet off, and obſerve. 3 
where it cuts the Circle laſt drawn, and make a 
Mark, from which ſet the given Number of Deo 
grees, and where the Degrees end, and from the 
Center, lay a Ruler, and 2 where it cuts 
the firſt Circle ; for. between that Point, and the 
Point firſt propoſed, is abe eee of pa, tee 


th 
wu to be ſet 0 b +255 x08} 
* 
| n PINE Y- i IT 3 
by | | . 
# E Xx 4 M P 2 E. | © 24 
7 = | £ 75 1 8 2 5 8 > — 


1s the Semieifele K. y 2, it is re- 8 SD 3 
quired to ſet off 37 deg. — x to- Plas 88 0 
wards y, but having no Chord to Fig. 8. 4 
that Radius, take the common Chord, © - - 
and with the Sweep of 60, draw the Circle d e b 
upon Which ſer 3 deg... from d to n, and N 
Ruler from the Center to n, it cuts the inner {8 
ele in o, and the Arch X o in the leſſer Circle, as: 
equal to d n in the greater, viz. 37 deg. as required. 

I ſpeak of meaſuring or ering off promiſcuouſly, - 
one being the Reverſe of the other, and fader 
Repetitions would be needleſs. 5 

Bur the beſt Way of dealing wih Circles of: 
different Radius's, is 7 a Sector, whereon or 1 
have. the: "Chords: commonly marked C, which, I 


A 
Love pro- 
2 — * . * 3 , 1 * * 1 " : 4 - 

* 85 2 CH * on * 2 N 8 1 : 4 : PF; ; *%, 


""Mechanick Dialing, 


-., from the Center to (near) the End of the 
ſame Side of both Legs, being exactly graduated 
alike ; and in Order therewith to, meaſure any 

Fart of any Circle of what Diameter ſoever, Fitſf, 

Take in your Compaſſes the Radius or Semidi:. 

meter of the Circle, then open your Sector to 

= that Wideneſs, that the Compaſſes (kept as they 
were) may reach from the Braſs-point at 60 on 
dne Leg of the Sector, to the Braſ-pin or Point 


would ſet off any Number of Degrees (ſuppoſe 
45) from any Point in the Periphery of the faid 
Circle, keeping your Sector at the ſame Opening, 
extend your Compaſſes from 45 on one Leg to 45 
on the other, that Extent contains 45 Degrees of 


4 | in the other will find the Point where they end; 
= and the ſame Method is to be uſed for Circles to 
23 k 8 — or Arches containing 0 Number of 


1 


How awake: 4 | Dial = 3s ball give 1 Wine . i 
- the Day, "without a Stile or Gnomon, only by the 


erden eee 
"HH ER E is. one ** this Sort of Dias near 


3 > and i in ſome other Places in Losdon; but for the 
making of them, you need have no Regard to 


| the Latinue of he Fee for that is to be Lee 
Ft . 1255 ET 


at 60 on the other Leg thereof; then if yo 


that Circle, and placing one Foot where the Leg 


© Shadow f one Part oy it PINE _ prada | 


the South Jeſt Corner of Middle Moor-fielas, 


ess Seer 


# , MY | 
p, R 9 5 _—_— a 
11 28 nnn 15 */ * 4 4 * . 
Mee Ale 1 114 S NE wo N a. > «a Ke FE 
* 7 ö <q} Ss N 1 * 5 * , l 
— e's Y 
4 — ſ 
LE 


| Fl in the placing, oF not in the making of 
the W them; in order to which, prepare a Piece f 
ated W Wood, Braſs, or Iron, of Bigneſs at en, 
any in the Form of a Croſs, having one of _ w-_ 
irſt, WM the Four-ends longer than any of the Plate 12. : 
diz. other three, and let the Thickneſs of Fg. S J 
to it be about equal to the Length of 
hey I one of the ſhorteſt Ends, as you ſee in the Fi. 
on WM gure a bedef g hi k I m, where be and 
dint cd and 1 m are ſuppoſed equal, and fg equal | 
you-W to hi, is longer than any of them; then for | 
oſe WM finding the Hours, take a Piece of plain Plank, | 
ſaid W or Wainſcot, as long as the Line f g, and as ñ⁶ 
ing, W broad as the Length of the Line cd is intended. 
45 to be in your Dial; ſuch a Piece is exactly re- 
; of preſented by Parallellogram, or long Square, f 
Leg b i, and which indeed N ſerve for the "WF 
ad; following. 


of Faxe the Extent fi, or h g, - are BY 
in your Compaſſes, and with one Foot in i, the 

very Interſection of the Side k e with the Side” 

| a h, and draw the Qudrant f n, which divide iu. 

bY to 6 equal Parts for 6 Hours, becauſe it is a Quar- 4 3 
ter of a Circle; and where theſe equal Diviſions |: 

fall, make the Marks * *, &c. A Ruler 

Jaid from the Center i, through the Marks **, 

55 c. will cut the Line fg in the Points r x 

Ee. then the Poſition of this Dial being to be 
ve with the End a b, to face the South, and the up- 
ber per Part of the Dial to lie parallel to the Equi- 
noctial, (not to the Horizon) the Sun at 12 4 

5 Clock "will ſhine juſt along the Line a m or b 
ear e; and therefore place 12 at m and c, then it s 
, plain, that from 12 to 3, the Shadow of the 4 
the Corner a will paſs along the Line m 1 ; thete- 
0 Pry take 2888 3055 Projection the Diſtance 3 "ol 


[0 * 6 F, * h 
* — — 1 * + - * 1 R 
* * * ; p £ | PEO I * KT " 
= W F > os 24 . . * Kere 5 n * * * n * 1 £ _— YE = A 12 

L J Ty * i 4% A r 8 . — - 

« 45; whe 63 T4 ch bo 3 ef 4 n 2 8 N ** 4 1 =p * 1 A 4 N * 
2 R 2 1 N 7 * . 

r * l . * 5 
i . 5 OS a of, * 


= and place from 12 to 1. 


| equal tom 1; therefore, at 1 place 3, and at 3 
| in the Afternoon the Shadow of the Corner a, will 
go quite off the Side I m, but the Shadow e will 

be come upon the Line f g as high as z ; there- 
fore at z place 3, and at x place 4, and at r place 
3, and then 6 muſt be in the Corner f, becauſe at 
the Sun will ſhine right along the Line e f; place 

C alſo at the Corner c, becauſe the Sun at 6 ſhines 
Tight along the Line c d, and from s till 9 (if it 
be in a Latitude where the Sun continues up ſo 
late) the Shadow of the Corner at d is paſſing a- 


pPaſſes the Diſtance fr, and ſet from 6 to 9. Take 
= ' lſo fx, and ſet from 6 to 8, and the Diſtance f 
e is equal to c b; therefore at the Corner b place 
= 9, becauſe the Shadow of the Corner d goes off 
= the Line bc at 9. Then for the Morning Hours, 
= the Shadow of the Point 1 will enter upon the 
Une a mat the Point a, juſt at 3 in the Morning; 
= therefore draw Lines from 7 and 8 in the Line b 
1 & which let be drawn Saur to a b, or mc, and 
= having-placed 3 at the Corner a, place 4 upon the 
= Fad 68 the Line that comes from 8 and 5, up- 
on the End of the Line that comes from 7, and 
then 6 will be in the Corner m, becauſe at 6 
the Sun ſhines juſt along the Line I m, and from 
'6 till 9 the Shadow of the Point k is paſſing a- 
long the Side i h; therefore having placed 6 inthe 
Dorner i, draw Lines from the Points r x2 paral- 
lel to g h, and at the other End of theſe Lines, 
= 72. upon the Side i h, place the Hours of 7, 5 
= and. 9, and when the 9 of the Point k 
= . comes at 9, the Shadow of the Point b is at the 
OE 4 668 from. 9 30. 25, 1b5 Shadow of * 


kn” >. 6 


n 12 tc Take alſo f X, and 
place from m to 2, and the Diſtance f 2 will be 


long the Line e b; therefore take in your Com- 


4 & — IO e . pk fy op ty ay 


— — wy yy Fey — 


— wes mm, rwrly Spc wes ng” 


4 * 

2 Fan 
N * 
* \ 


* CO $16 "Lt a nn. 9 * wy 
pup aloe the Lins” 4 c, ad at 12, by + . 


and dow ok b is come to c; therefore: take the Th - 3 
l be tances fr, f x, andfz, and ſet from eto 11 and E 


a 3M 10, the Diſtance f z being juſt equal to e d, and 
wil W then is your Dial finiſhed ; the Sun, as jt goes. 9-6 1 
from one Part of it, comes on to another, ſo 4 
ere that the Time of the Day may be always found A 
5 upon ſome Part or other of it, when the Sun 
| ſhines. _ = 
lace WW Tux Reaſon why theſe Dias require Thicks = 
mc neſs, as well as other Dimenſions, is, becauſe be- 
ing placed parallel to the Equinoctial, the Sun 1 
ſhines upon the upper Face all the Summer, and 
>” I at the Longeſt Day is elevated 233 deg. above the 


om” i Plain of the Dial, and conſequently the Shadow- 
ae W of a, will fall at Noon in the Line a * but not 
0 in the Point m, but at an Angle of 234 eg. 


therewith, which muſt be accounted. for. in te 4 2A 


off Thickneſs of the Body of the Dial. > 
RN Note, It is not neceſſary that any of the Ends 9 
Le of the Dial ſhould be. longer than another, only "= 
10 for Ornament; but if you would make one t 1 


thoſe Dials for any Place beyond the Artick or 
Antartick Circles, where the Sun is Inet, 
ſeen all the 24 Hours, it is neceſſary all the Ends 
ſhould be alike, becauſe then the Sun would 
come on to one Part as it goes off from ang 
ther continually, Which now it cannot; for the 


rom Sun coming up in the Morning, the Shadow o 
3 4“ g would have quitted the Line fe at e, 'befofe 
5 the Shadow of 1 would come on to the Line a” 


meat a; but if fg was cut off atz, and f 2 made 1 
equal to a m, or m !, c. the Shadow of » | 2 
would Juſt quit E when the See 11 a enjers 
Won the Line a m at a. bo 


3 [Ps Pe oy * U 

=_ 9 * 4 a 6h - a * * 
rec Drallmn 

_- Ss Sar... —_ 

3 5 = 9 m— 

* . 

$ 8 . 
I pe x + 
$ os 


. Fade Place or ee ma be inſer- 
i Dias as cafily as in any; for if you 
take in your' Compaſſes the Extent'a m, and with 
one Foot in the Point or Corner a, and with the 
Sher fweep an Arch from the Corner, at m down- 
3 - wards, and with that from a Chord: to the ſame 
2 Net" off every 5 or ro Deg. of Declina- 
or the Sun's Declination at his Entrance in- 
t0 each of the Twelve Signs, being ſet off upon 
© Circle, atid Lines drawn throughitheſe Marks 
do tde Corner under m, and from thence parallel 
4 * 3 m, and e d will give the Sun's Entrance into 
== the xz Signs by the Shadow of the upper Point a, 
in the Summer Seaſon, while the Sun ſhines upon 
the upper Surface of the Dial; but in the Win- 
3 . ter, the like Method muſt be uſed with the lower 
YM — Part for: the Southern Sign, the Declination in- 
= crea 8 6 e Op a downwards. 


* 


7 N 


a „ Declinati at bis 2 into the 12 
3 ir as e 


South Meek 
. m. . d. m. 
s Lib o © 

£90 Scorpio 11 30 
12 + Sagittarius 20 12 
30 ww Capricornusz3 30 
> = Aquarius 20 12 
3. 8 25 . 1 30 


8 ** 1 „ 14 
+ * theſe Dis thive is no © Rega to 
xp pra to the, Latitude of the Place; that being to 
I * * confidered i n placing them, which muſt be done 
= 4þ Pat the erer 9 of the JM may be juſ 
ale ODS paralle 


— 4 


— = 5 * 
= 
P 4 
* P < 
_ * 
* Fi I 
— Ty — 
K 
KL 
* - 4 
S © - 
4 6 #4 


&* 


: * 
JG 


"4 | > 1 5 Pp 


*, = 


a ox. 44 


2 


r 7 * 8 
2 * e 9 


9 
* — 
* 2 
- * 
= 1 2 
» 
* a 
N 
6 Y 5 
— #%. © 
x 7 4 ; 
7 * 4 
. 


* — * 
IN pA 
- my * 
, 
K . x 
+ * * 
= 7 
« 1 * 
6 1 # 
#% 


_—_ +4 - 
% 
: "*" 
* 
* * 8 
90 


ö Nl . ” 

r 0 >, 36 
4 1 5 
7" 


oy 


> 


—— 


* 


” 
. 
” 
0 * 4 
OY 
XY 
o 
2 Ara 
2 4 
n 
* 4 4 bl 
N © A 
: bs * 
+ 4 * 
3 * | 
* 
* 
* 
” = 
Ay * * 4 
* ip A 
* OS 
* ? . 8 
ann Ugg 
. 7 
— — * 
; 2 * 
, wr tee Ee — 
os — 
. — 
Sx tous * 2 — o * 
** * %d 


— + 
h | 

ad 
. 


hp 


4 1 1 1 

* * f þ 
ö 8 3 

: ö 1 1 I 

b © Th , 
SHA 
„ 
ES | 


: 
KO 
6 
* 
1 
> 
1 by 
Y & 1 
i . 4 f 
= 1 
7 "£384 
Oo 4 
, <8 } « ? 
3 = 19 5 
: at C 
1 1 l 
n k 
1 Son? 


3 
2 
9 


«=> 


SOM 


— 


5 | 


rn 


* * * 
* Y 2 
; 1 - 
. * wo 29, 
4 ' N 
Lo 5 
12 = 


* T — PLL; PROT 
F 
32 N 
8 ag 


7 
— 
>% 
: * 
KS, . . 
2 
4 
5 
: 
— 
1.5 . J * 
* 
* 
of =. 
. 12 
* Li 
* — 
5 £ 
* 
. 4 
, | 
. 
4 1 4 
7 - F 8 5 
2 i 
5 45 
— a 
4 ; 7 3 l | 
— » 0 9 1 
* "IR : L 
ih o ie, . Li 
T3 . * 8 f * 
4 * : l 
* * 
8 
4 4 5 
"I * « 3 2 
Y - | 
3 ry — 3 
3 - a * 
.* * 
* * 
” . : FE 


8 PS 
NO ac Dok. 


q 
1 1 * 
* 
IJ 
9 
* * * 
TT 
"A 
* 
A 
. 
5 +4 + 
= 
2 
po. 
ib . 
"= } 
” 


* 5 > 
* - 1 * Y * 
4 "x 4 
f 4 - 
- ws + Tag 
# t 17 
* 1 
% 4 5 Y 
«8 
P 
” . x 4 
£ 8 e 
. — 4 $ 
l 7 
„ 
6 of « A * 4 
P 
* + 2 
- ; 2 — 2 
" 5 1 
* . 2 * 1 
Ss 4 * 
Fa _ 
* 8 % 
a - 1 
4 1 5 3 


- 
— * 
* - 
* 
5 þ 99 
1 
: 2 U 1 
a> * 
7 * LY 
2 
* 
a . 
" = 1 Ng * po, 
- 2 x 
* Wr 
- - 
j#- 7% 
* * 
4 * of 
— o . * 
3 N 
* * 
8 > 
2 . 
: &* '& Xx 
s 
1 5 


* 
— & 7 
1 
1 * I * 0 
* * ” 
- * he 
: 


. 
£52.22 % 


* 
* 


x 
* * 


* 5 
. 
" 

„ x , 3 
"4 * 
FE 22 
B — 

+" : 

1 

* oF 
bs. . 4 


4 
* 
2» 
w 
* 
* 
— 
* 
—— 
= 
o 
% 
* 


e 
TIP 
— 


0 


£ - a 
* - - 
4 2 
* - 9 * 
£ 3 , 
** =; 
N : 4 . 
8 " Ja» - * 6 - 1 Feb © 
. 4 3 4 
1 A F 


* v4 2 . * 
4 
. 5 I - 
# * 5 
+ . L G 
i * 
1 — ” ay .” 
/ 
A * 
2 
* - 
b 
EN "I " — , 
4 L . £ . 
;B 
- 
I * 
2 * 
2 . - 
A 
5 
- - 
5 
a” ! 
1 q 
5 * 
& * 
y 7 
8 : [4 
* 
*F. 
2. N 
þ 5 < 
: , 2 
= 4 £ 
44 . 
- * 
: 


2 a 


K 


* 
ye 
2 
=” 


"Mechanick Dialling. 


parallet | to the Equator, the Line a m 8 be 
pointing at the South Part thereof; in Order * 


which, haying found the Meridiat of the Place, - 
ſet the Dial exactly North and South, and lay ” 1 
ſtrait Ruler along the Middle of the Dial, fromm 


g to a b, letting it hang over at the End a b; then 1 
on the under fide, of that Part of the Ruler that on 2 
hangs over, fix a Gunter's Quadrant with one Mc 2 
its ſtrait Sides to the Ruler, and the Center to- * 
wards the End of the Ruler; which done, elevate 4 I 
the End a b of your Dial. by little and little, till 
the Plummet (having free Liberty to play) falls u * 
on the Complement of the Latitude of the Place; 

or, (which is the fame) till the Plain of the Pi 5 
make an Angle with the Horizon equal to the "Pi I 
ſaid Complement of Latitude; then is your Dia! 
fit for Obſervation, there being always ſome Side”: 


5 
"of* 
of it, upon Which. the 1 of * * may 3 E 2 
ſeen if the Sun ſhines. „„ 4 
7 5 : 3 11 8 8 1 bo ; e 9 — — — * 
76 | X VV Py 1 1 
* e . E a BARS ” S454 3 ISIS 5 + EY : bog 
PEST f * OY ö 8 15 7 1 *; 05+ {6% TIKIW 17 * — 25 2 
He - LIES). * OF 4 7 "MA $3.54 5-4 2-4 8 3 2 a+ Ha 


» 


— * F "3 - I 
: 4 Mi ; 2 e * 
. A 5 " * 14 , ba, 
SH. 5 
cl S, Ty B 
x * 4 1 ah! . 5 
4 . 7 3 „ 
. 


a4 * 8 : x * k 1 3 ' ; 
. 2 0 4 * = Ss . 5 7 . 
— * * _ 
__ __— — 1 83 N 3 
5 OE, + x 3 * : s & f 8 8 
1 5 o 5 . - 8 . » 4 
3 BN 94 , - 1 2 I 
E —& * * . - a 
4 : - 1 1 AS x E 5 
4B ; : a . e = | 
8 23 4 . * * 
ha” 4 , 4 4 
ds - 24%... * 0 rm 
* L : : 
Dt Famting o TALS, m 
v +; = + 8 N 
0 3 * : ” P 
=> : * . 5 
3 — * Py 2 p 4 — 3 
; * * 2 


# 
_ 


"3 Se.» Wu? Wa 2 Se 


F 


1 1 4 2 v * 88 Ls 3 w] 


2 : * MLA 2 * Ct _— 
« +. '% * oY 5 * . . 
; - 1 A * I a 4 y x . 
5 . <a a e | 
=:  $TCTITON 1. 
. „ | ES gre 


| x. E 75 prepare your 0 laying on the Coluur © P! 
3 upon Dial. e 


= PAK E one Gallon of Linſted'Oy!, and (et it 
1 upon a Charcoal Fire, and When it is about to 
= boil; put into it two Pound of Red-lead, and let 
itt boil together for about an Hour; but the beſt 
Way to know, when it is boiled enough, is totake 
= - alittle of it out, and let it cool, and then if it 
1 roaps like thin "Tar, it 4s enough. This done, 
put a lighted Paper to it, and et it on Fire, to os 
© _ conſume the greafy Part of it, Which will be done _ x, 
in a Minute or two, or more or Kr, according to 2. 
= the Quantity of *Four O and when it has burnt I coal 
long enough, clap a Geh, or any other thing 3a 
cloſe over it, and extingunſh the Fire; after which bar L. 
let it cool and ſettle, then decant the clear Oy! 4.4 
- from the Dregs, and keep it in a Bladder for uſe. 5. 
Tunis is called drying Oyl, and with this the ſe- ter, a 


3 

E 
> 

4 

4 

Þ 

4 


5 


= Feral Colburs- are to be ground, in order to paint] 6. x 
do as to endure the Weather, (being firſt dry, be. 7 
fore it be expoſed) the ſeveral Colours we ſhall 1 95 


deſcribe hereafter. 


"ey Painting Sun-Dialt | 


. How to make Col Size, with which Zo _ * 
Leaf Gola. PORT 


; Tax yellbm Oker, and grind, it mh Water = 
on a Stone, with a Muller, till it be very fine, | 
and then lay it to dry, and grind it with the afore+ 
mentioned drying Oyl, as you would grind other 
Colours, obſerving to put fo much of each that it 
may be of competent Stiffneſs to work well, and 
of ſuch a Body, that it may ſettle itſelf ſmooth | 
when laid on, but not ſo thin as to run; and take 
Care to grind it very fine, and jt will add the 
aro a bu to you! Gold that is to be 5 pb on 
with 5 a 


—* n % JW | 8 . 


aaa bY 


of Colenrs uſed in painting Sun Deals. - 
TE Colours generally uſed in paint 


Dials, are, 15 | 
1. Fox White, Ceruſe and White-lead. ' _ 
2. Fox Black, Lap} Watck,) Ixory- black, Char- 

coal and Seacoal- black. | 
3. Fok Red, *Red-lead; FAR gs 
bar Lake. | 1 
4. Fox Ereen, Verdigreaſe. EY 
5. F on. Bleu, Indico, blue Bice, : bie verd. 
ter and Smalt. 1 
6. Fon Tellou, Yellow Oker and velon Put 
** Feen ON N Brown. OR wi y 


1/7 
ek 2 


5 SECTION n. 1 


| of a. c Ns you. ney 3 Variety f 0 


ther Colours, ac, 


5 5 a A litle Lamp- black with White, makes an 
| 8 1 

> Bk CINNABAR Lake i is a 4a Crimſon Colour 
bur mixt with Bice, it makes a fine Purple, ac- 
cording to the. Proportion of Mixture ; but mixt 

5 n hite, it makes a fine Carnation. 

: Brew. Bice mixed with yellow Pink, makes 

P — — ; with Lake a Purple; and "with White 

a light Blue. And note, that any Blue and Yel- 

low mixed, make a Green of ſome Sort or other. 
4. InDICo mixed with White, makes a Lead 


= Colour. 


- VERDIGREASE mixt with Yellow Pink, makes 


a lively Graſs-green. 

By this Means may ſeveral other e be 
compounded, and made lighter or darker, at Plea- 
ſure, 7 as a little n will Ry evident. 


Y 


. CD ne 


45 1 


ETI N Ui. 
How zo prepare the Colours for — 2 San-dials. 


BEE ORE you proceed to the painting of 
Sun ⸗dials in their ſeveral Colours, it is firlt 
neceſſary that they be primed ; that is, painted 


two or three Times over with Oy 1 and Colour, 


prepared for that Purpoſe, to fill. up the Cavities, 
which may (after plaining) remain in the Wood, 
and to make it pefeRly plain, and the more cape: 


9 * | . e 
: 5. Rt N ST 8” S * 2 a "Y 4 a : N 
* . „ B q * 1 * 
RT IC» 8 8 . 7 8 8 3 ud : 0 i k 
N % | ; | 3 5 | b T b % ; ; | am ng | 1 __ S 
4 1 2 e U N a - 
_ de ; ; * 
9 bg”; N - b a 
<4 8 7 
_. F , 
4 2 
* 


. * * 0 a q . N * 
” * B rc * r Nr * 12 I 
2 3 — 7 : wy * ev * I EY 3s S 5 * © V FRY \ y 9 7 N 9 * N 2 9 4 1 EY = 15 5 X 
> 8 $ N ND N n 7 
1 72 Wk r 
- | 6 43 . * bo "= 
: : \ : 4 
. | * 15 : : 75 
© ©, : # + 4 — Es * 
5 . Y : y L Faint. 5 l un- bY 1 al k "In 
ö K q 8 " 
: * 


ble to receive end fetüfn ocher Colors; - and of 
all pritning, Spaniſh Brotun is reckoned 10 be the 
chief; for, not to mention its Cheapneſs, it dries * 
kindly, and gives the Oyl ſufficient Time to pe- 
Ml netrate into the Wood, and conſequentiy alſo. 
reſiſts the Weather, and alfo. freely receives allo? 
ly ther Colours which are laid upon it. It is of it- "i 
elf of a Horſe-fleſh-colour, and (beſides its Uſes. * þ 
t fulneſs in priming) it is a natural Shadow for Ver- 4 
milion, and may be made lighter: or darker, ac 
ces cording to the greater ar leſs Quantity of White 
us mixt with it ; but in priming, it A oth (a 1 
el. Mixture, but only the Oyb it ſeltfW17ũ h! 2. 
Ix preparing the Spaniſh ; "£08 for priming, 
cad grind it very well with the afore· mentioned dry- 
ing Oyl, and make it for the firſt priming, ſome- 
kes what thinner than you would do it for painting, 
chat it may more eaſily pe etratè into the Wood ; 
which being dry, do it over again with the rung 
lea Mixture, only mix it a little thicker and letting 
that dry, do it a;third Time; mixing. Mor Cole 
thieker every Time. And take Care in the prime - 
ing not only to rub the Brumm With che Priming 
2 upon the Dial, but alſo bob it againſt it, that the 3 
If Priming may de ure to pierce.into all the Cavities 3 
or Pores of the Wood. This done, and your Di. 
al dry, the third Time it is ready for lay ing on te 
dials. 2olours;-. d., painting the Hour · lines, or "what 
Ornament or 8 g "FOR think fit odere + 
8 of on it. FFT 45S * TATE 3 . SE WEIL 7” {1 40 7 e r : 1 


Re : Be x 27 7 * 2 TY. 2 
9 2 185 v4 * SEE x ' 5 P < N ne <4 ho —— j : 4 4 1 5 ; 8 3 
witles, VVV 1 8. 4 3 a 1 * "> 6 | 
ls 3 | BY | „ 
Vood, | 8 ve gal 30 N 


capa- ))%ͥͤͥͥ HRY To 0123 WO1IH $5 N 
wy Ul 8 ns | 4 by i 
dle e b „ 


e aue dun n. 


2 55 Fen 1 6 1 . Dial, A 
* 2 er, Sori of, Co onrs will be ſafficien..” 


05 1. ». Spaniſh Brown, which prepare; and therewith z 
prime your Dial, as before directed. . 
2. White-lead, well ground in Oyl, with which M - 
after the Priming is thoroughly: dry, go over it 

three or four Times, letting it dry between every 

Pime; which not only lis 4 beautiful white V 
Ground, but fortifies it yer more againſt the Fury fi 
of the Weather. = 
is Leap black, for drawing the Hovr-lines and d. 

1 8 N 5 1 
= 1 Fermillion, for drawing the Pucatlels of De. it, 
* elination, or what other Furniꝛure yon think ft to in 
== put upon it.. 1 nan 
- ore — Browns: Lemp-blark, and Vermil. ve 

an, ate all to be ground in the drying Oy), de- th 

. foribed at the Beginning of this Chapter; and for 1 
7 the White-lead, it is to be ufed in the fame Man- H 
nder, only in making drying Oyl for White-lead; i Su 
3 nficad of Red-tead, uſe Lithacge of Gold, and WY + 

Bor if you would have your Dial more rich, M 
yok mat firſt confider, what Colours you reſolve I Ps 
vo hade your! Lines, Figures, Se. to be; and up- du 
own whww 2 your: determined Colours will ap- 

pear rift benatifut, as, 
1. Gol p appears beſt upon a blue Ground, and 


e ma 


indifferently upon a Red. Le 

2. BLUE and Green appear beſt upon Yellow 2 

and White Ws 
3. Rep ſets off with Yellow, White, Blue, Wl 
or Green. 55 


4. YELLOW ſets off with Black, Blue, and Ji. 


. 


MA 


but not come off; 


dure the Weather. | bh | W os 


Leaf Gold ; 


of Painting Sun-Dials, | FM 
Brepzs the Directions given already W b 


ling and laying on common Colours, it Will de 


k of the laying on, N 1 _ 


neceſſary to 
aloe 18 fight, 


and beautiful 


Hhw 70 lay on Leaf Gold, or 20 nels & any Pk * 
geri, Ke. of Leaf Cell aber your Dil. * 5 


8 your Lines, Figures, or wt | 


What you think fit to have in Gold) with 


fize; (of which before) which let dry 

when you touch it with your Finger, it 1 dick, 
then cut your Leaf Gold, as 
near as you can, into the Form you. would have 
it, whether of Figures, Letters, Lines, Se., (tak- 


ing Care to cut it rather too large, than too little) 


and with a flat Stick lin'd with Cloth, take up 
your Gold (ſo cut). and put it upon the Size, and 
the Gold will leave your lin'd Stick, and 2 
to the Sizo; then preſs it down. with. Conon, 


HFHare's Foor, and take care that you make the 25 I 
gures, Lines or Letters, in the Gold-ſize, and 
that you cut the Gold large enough to cover te 


Figures ſo made in the Size; and when it is tho- 
roughly dry, bruſh off all the looſe Gold, and the _ 4 ? 
Painting will remain der 20080 be e to en- 2 


10 


| How an l e Suan, fo o make a fix Ales. 


Warn you have laid on what you think We 
take White - lead, Mix it pretty Riff 
with drying Oy, and with a Peneil lay that on, 
where you intend your Blue ſhall be, and then put 
your Smalt in a fine Searce, and ſift it on to the 
Dial, and with a Piece of Cotton, dab it demn 
vpon the * before laid on, and when it is 
> : - M &+ | tho- 


"of Painting San-Dials: 


e dry, wipe off all the looſe: Colour 
With a Feather, and blow off the Duſt with a 
pair of Bellows, which will eaſily blow off, 
except what fell upon the White before laid on 
8 retain the Blue, which will be a very beautiful 


_ 
= "Oave as a general Rule, FEY Priming is to 
= - be mixt or temper'd thin, but Colours for Lines 


or Figures to endure the Weather, muſt be tem- 
per'd thicker, the better to reſiſt the F ury of ſtor- 
hf or moiſt Weather. 


* 


* F 
21 4 * 


133 SECTION Iv. 


. | Of the Nie: and Colour of ſome of the 7 
3 . LF, e wed 7 in an 15 dun- Dial . 


„Cd and White-lead, are the _ Co- 
lours to be uſed in painting in Oyl, and de- 
BY "des their Uſefulneſs in painting of Dials, Paint 
„ E made up with them and Oyl, is frequently made 
uſe of in painting Poſts, Paliſadoes, Gates, 
Doors, Windows, Wainteoting, Sc. and an- 
ſwers the End of Painting, both as to Beauty 
8 and Preſervation; for they dry well, and ſtrong - 
Iy reſiſt the Weather. But if you would have 
= them to dry yet more ſpeedily, you may in thc 
TLempering put in alittle Oyl of Turpentine, if 
it be within Doors, but without Doors it is bet- 
ter without, becauſe that en not ſo well reſiſt 

N de Weather. TOTES AF Ta 2 83 
VC 5 Sod SO 2 Lan 


» 12 
* 
— 


* 


? 


— — 2 


1 
. 


21 e | is a "good f Black, 
* burnt, © 


Oyl. 


dinary Uſes; it dries well, but Srear Care m Fe 

be taken that it be well ground: ; Is 
. 8 Sau Brown, the 4 deep bei 

Colour, 19 free from . thy nd bein N 


of Painting, | ' , 


then ground, aud lalliy ae gd” 


3: Charcoal is a Black that wil ſetve "or | 


well ground, is the , beſt for primi g: It. i 
Horſe-fleſh Colour, aud a proper Shadow for Ver: 


milion. | 
5. Red. lead is a great "Dryer and Binder; for 


* 
1 


which Reaſon, it is made uſe of in the Sa 
Oyl; it reſiſts the Weather as well as pay Coton 


| whatldever. 2 | 
6. Vermilion is a rich Colcur, and d. A. 


Body, bur care muſt be taken "that. it be 


work. extraordinary well” 


adulterated with Red-led, - 
perfect Scarlet of 975 ſelf; 


to ſeveral Varig yes 


Tours, 


; muſt be very fine ground. 


Smalt is a very fine 


IY $1 


. _ "W354 2 25 (44 ; 


8 


4 = 
ground, even as ſoft as 0 , and then. it WIfl 
| t is beſt” to buy t in 
the Stone, leſt you meet with ſome that Has ol 
or the like; it s 3 I 
and may be alteted 

„ b wiring with: ou” 19 3 
J. L nm 1 


"9: Cinnabarilake i is a rich Crinifon Colour, and 


7 


| White-lead) yet it will turn black in Lime? 165 
you buy it to work in Oyl, the fineſt is 2 0 


which is'call'd Oyl-Smalt. | 
9. Blue Bice is a pale Colour,” ane works wel 


though alittle ſandy. 


10. Blue Verditer is not ſo good. a Blue , ; 
And gnal, . though it may ſerve in W 5 I 3 


„ 


* 
+ Fo... 


- 


8 4 


| 3 


Blue, aid it is beſt 10 * I \ 
be ſtrewed on, as before taught; for if you Work 
it in Oy), (though you waſh it. and Ts It with - 


2 
1 3 


« FF 
Fj 
af 
.* 


"4 
Y 
4 


"3 * 
*£ 
» po \ 
= 
y * b 
y 
. 


= Sep Calo; it 


F iS «5 "of Pairing $6 $iin-Diats 
I „ Wi they are wanting ; ; it is a little ſandy, and 


pt to fade and turn greeniſh. 

1, Jadico is a very dark Blue, and commonly 
phtned with White, when us'd in Painting, ex- 
3 Ser in Shadowing; i it grinds fine, and is. very pro- 
4H that the lat Colour * Polts, Baliſadoes, Doors 


13. Blue Ball. ut almoſt like Indico, but not 
© good a Colour, nor will it endure ſo long. 

13 Unhber is a Hair Colour, it muſt pe very 

| be. ground, which to effect, requires a great deal 

= FE Labour it dries and binds exceedingly, and is 

therefore aich very proper for painting without 


phe is a natural Shadow. for Gold, and 
. other Colours, 
oe Feng is a. perfe& Willow-green, bat 
Diſccetion,, with Yellows, &. 
ar bein ing very foul, it muſt be mended or clean- 
ich. may be thus done: Grind it fine, and 
22 70 i4 eight Times its Weight, 
* digeſt till ebe Pi _ is ting very green, then 
| 2 . Calbur; caſt away the Feces, and evapo- 
dais the Vinegar in 4 Braſs Leſiaa; ſo have ven 4 
ven N the Bottom, much more fone 
| ,. then before it Was e It dries 


% Jen .Oker the Engh/t;, the Colour of a 
ten Straw; the Tet te is ſomewhat more 
is. much uſed in common Paint- 


ery. fine. 
ings being aan very is a greeniſh Yellow; it gyyods 


3 > alk and is good. bs l wich, tos. Felon, to 


* 5 
* 


Os 


Wh fs : for it reſiſts the Weather, and 


22700 as Doors, Palifadoes, Ec. if calcin'd in a 


Spirit of Vine- | 


% a. ie. ae. oe 3 


* 
rr 


1 


4 » 
8 0 


es 


ore 


nds 


Red Lead, Blue Bice, - Smalt and Hepditer ; which . | 
1s thus performed : 


(after a while) decant the Water. Repeat this 
ing but juſt troubled) put it into another glazed . 


duns be clear, and the Colour remain fine at the * 


| % with a Feather, and keep it for Uſe. 
walking, they are done without) out nex 
is to grind them, which is done thus: 


intend to grind, and put to it a little I. Linſeed-- 2 
Oyl, (but be careful you put in too little rather - 


- Your Stone With a Muller, grind them well, 4 
ding Oyl by Degrees, as you ſee it requires 33 to „ 


it grinds much better when it is thick, than hen 4 


Jou have ances as as you have Orea 


8 of Painting: Sun-Dints: "28 
Or theſe Colours, ſome require wathing, as 


Pur the Colour into 2 glazed Velle!, and b 
thereto plenty of clear Water, waſh it well, aud 


Work ſix or ſeven Times; at laſt (the Water be- 


Veſſel, leaving the Dregs-at the Bottom ; - then + 3 
put ſome more Water into this ſecond Veſſel, 
and waſh uit as before, till the Water after ſer-- 


Bottom. 

Note, Before you take the. Colour ont: of ine 1 
Veſſel, ſpread it about the Sides of the: Veſſel i 
very thin; and when it is dry, it will part of it: 
fall down to the Bottom, which keep by it felf 3; 8 
but that which ſticks to the Sides of the Veſſel is 
the beſt, and is as fine as any Flower, that. ſtrike - * 


"#3 & 2 
1 


. * 3 


25 Colours that require waſhing beine ane: : 1 
I q 


Tak E, a Spoonfal or two of the Colour: _ I 
than too much); mis them together, and 1 199 


make it like an Oyntment, (always obſerving, that 


it is ſo thin as to run about the Stone) every now i 
ahd then ſcrape it up together with a thin, Kei 3 
or Lanthern Horn, to keep it at or near the 1 
dle of the Stone, and fo continue to work; 


6. . w 3, oy L 
. = 

n * Ko 

1 * 1 5 

- — # 


3 n A „ 2 4 Y 
«fa UL A eo WF « g i 
Go: hott | 45 
e 4 

4 7 8 10 7 4s 5 x 0 

* 1 * 2 3 * 1 
5 #72) 4 * 6 2 n N x 

: * b — 5 A 1 : 


for; which done, clean your Stone, by grinding 
Sad and Water upon it, and then waſh and dry 
itt, and the Muller; and when you go to make 
© uſe of it, mix it wi drying Oyl, till it be fo 
E - [thin as to run freely from the Pencil, yet ſo thick, 
that the Ground may not appear through it, or 
to tun when it is laid on, and then it will be 
E the more beautiful Colour, and better. endure the 
I - Weather. „ FS e 1 


© 
[ 


r 


„7 
8 4 EX '8 
oF 6 f * * * 
— 2 „ l 
N 
N + 4 4 } { = 


+5 


are 
mu to make ſome Original Colours, &c. 
I1Ĩ. To male White-Lead. 


Ld 1 
13 


. 1 2 1 
* P 


AK E as many Plates of fine Lead as you 
I pleaſe, and then put them into an earthen Pot, 

or Crucible, fill. the Pot with White: wine Vine- 

© gat, and cover the Top of it cloſe with Clay, bu. 
y it in a Cellar, or ſome moiſt Place, for ſeven 
ct eight Weeks, and there will be White-lead 
= upon the Plates, which wipe off, and keep for 


we 


[> Wy” : 4 
=. 8. 5 „ 
3 - p 
_ = U ' 
Fu 1 * * ws 8 88 . f fa Was. 
3 11 : 3 2 1 oh 1 1394 | ks 33 
"= R . ” 4 5 . * f 
_ y * 5 1 ; 
=_ N e < ; 5» 1 4 1 0 7 ö 
2§85, To make Verdigrea 
3 5 — * — v5 * -. > . © 
we 7 * A & 1 V7. 4 . - * >, * = ”% 5. » 
” - 2 * 4 $4 | 7 


wa : 


\ 


- *, 
6 £8; 
8 

F 


= Hae, Plates of Copper over the Fumes of A- 
qua- fortis, or Spirit of Nitre ; or dip the Plates 
ni the ſame, or in e and the Ruſt or Scurf 
ds by chat Means bred upon the Plates, is 


>» 
7 x8 f 3 
1 #4 « 5% O - 


ou 
Ot, 
le- 
du- 
Tell 
ead 
for 


. Uſe. 
Quart of Water with two Spoonfuls of Honey. 


"is, ae or the Ike. : 


85 (24. ' 45 
85 2. 2 Ultramarine. EG 
5 ? 7 3 . 


Nn Linpi Lazuli, the deepeſt coloured you 9 


can get, having few Veins of Gold in it, cover 
ir cloſe up in a Crucible, and heat it red hot, and 


then quench it with Urine, Vinegar, or Water, 
in an Earthen Pot well leaded; dry it well, tben 


Vith a pair of Piticets pull off the hard; white r. 


, 


grey Parts of it, then grind the reſt very fine 
with Honied Water, and dry it, and Keep it for = 


Note, The Honied Water is made by boiling a 


. How to make the beſt Glue, for glning the Joints wo 
| of Boards for Dials, or # like. "OZ. OR 


** 


Tax Mitk that hath ſtood ſo long, aa! "A | 


seum d 10 often, that no mote Crean i 5 9 


and when · ſcumꝰd very clean, boil it a little in a 5 2 A 
leaden Pot, and if any Cream yet ariſe, be ſure to = 
take it clean off ; then put into the Milk a ſuffi 7 E 
cient Quantity of Glue cut in ſmall Bits, Which 
will ſoon melt : Boil it to a good Body, but not 
too thick nor too thin; then take it from the Fig. 
and keep it for Uſe. . 

Note, Vou muſt take Care, that in boyling . I 
you do not burn it to the Sides of the Pot, for 1 
that takes away much of the Strength of the Glue; 5 
but if it be made with due Care, it binds beyond © 
any other Glhe, and is better able to reſiſt the Wes. 2» 
ther ; and therefore, the fitteſt for plcing Board > 3 


* ; * 1 y 
4 - 
* - y 5 3 
4 \ „ * 7 + 
; \ $ 7 ? TH, 
N * 
* * 
— ** 
e , | : . 
- i dy * 8 * 9 . ry * 
2. * we FA 4 : 4 * > 
Das . Us N x + 7 C A 
F 7 4 


by: WIT * a 


3 = - 5. Hows 46 dngle aa 3 fro 
_— 22 with which to form any Dial. plain upon tle 


= _dher, wot inferior te Shane. 


= - Graphs Lime and Sand, and temper it with bs 
= 2.071 to the Conſiſtency of Mortar, or com- 
mon Plaiſter, and ſpread it upon the Wall to x 


Stone, and laſt mr. Ages; and upon this you 
may deſcribe a Dial, put on the Lines, Fi- 
; N and Furniture, as ae ack directed. 
Note, If you are in the Countr J remote from 
any Opportunity of getting Linſeed- 
- anake u with ſcum'd Milk, which will be very 


. : ap rior. to P laiſter made with Lime, Hair, and 
* Mer. 


= 


to endure. the Weather, it may not be-impro-- 
per to add ſomething of tranſparent Colours for 
- the Colouring of Maps, or any. Draughts upon: 
Vier or Wlan of . in Qrdere 


"I . 
1 # 3 : ; 
2 1 8 * a 5 2 1 1 1 * ” 
1 . 
3 $ - 77 7 
7 4 P n 5 — | 


Berk 1& . makes a very beautiful aon. 
| Secondly, A: Red... | | 


. 0 RES or Plai. 


Side of a Hauſe er Wall, aud to 5 


1 - competent Thickneſs, it will become as hard as a - 


Oyl, you may 


Hava proceeded thus far in Colours for Pain- 


Tus fineſt . you 3 e to uſe, will 
4 18 your Feuch yellow Berries, which ſteep'd in 
I a-Gallipot, af Water, with à very little Allum, 


EI Conde: of Brazil, about four Ounces 
| and boil in a Pint of. Grounds of Ale, adding 2. 
Ge 4 Quarter of a Pint of Vinegar, a ſmall 
1 of Simon Aral, and bout an. 4 


n 


. „ wars, 
0 


of Allum ; ler them boil very well, bans” 
rf Colour through a fine Linnen Cloth. 

I, A Seo Gree. 

; Tax 4 Quantity of Ver about four- 
in: Ounces, boil it in a Pint ds a half of Water, 
m. firſt putting about half an Ounce of Argul to i, "4 
0 2 let it boil till the Colour ſtains pretty . 


$4: * Fo . 


* 


2. 


111 e 3 


. 
** 


UG l 
7 


5 
15 
4 
325 


= for Roads, Barks of b Trees, Ge. is barn. 
5 which you. muſt | 
. Gum-water. 
4 Cu water is only 


* 
* 
® 


N 
4 

” 
+ 
1 

* C 
N 

i 

7 

— 1 

E 


4 
7 
4 
* 
* 
3 
i 
1 
* 


* N eſp, 2 
* þ 1 7 : . x: 
* . * ? oF — — OY * 1 * 5 7 
| F Pq” 2 5 
a 1 
OPS. * g , 
x 7 A FP ” a 3 * © E * + * x 
„ C. S 
Po 3 
3 5 2 | f 
— * * 24 * 5 P & 8 {= . 4 
N f 8 + 2 
. D i ; : 
* * ; 1 * 1 
a f * 89 FA p 5 
7 ” 2 * * , is 22 7 
» » U * * . K e * 
A $4 4 
4 
. ; - ; 
— 4 | | 5 
ö 2 2 > X 
f q x WS 2 
7 7 7 5 PLISS. 
. A i 
* 
2 * 
* * 2 - a hs * pe * 
— F [ir 8 
* - 5 : 
« * « 
. 
* o * . £ * 
* o 
- £ 5 
* 
* 
. D 
4; 
: * 
* - 
; * 
z "I : 
” 
* * » 
7 4 ; 
_ 
* * * — 
» 4 : ? 
o * be & * 2 & 2 
; \ 8 45 q 
l " n 1 n 3 8 


Wore 


_—.  . 


_ 
_ 


\ 
*% * 
» 
On . & 
"hz ; 
0 
= 1 6 
* 1 - 
tg 3. 
* 


hy 


* N * - * 5 ' j 4 
£ bt ins | AER n * Ty. 2 N s , war Lats. 
9 r 12 n r bs rs VE I FER 
2 n SON * F > 4 is he Ac: 4, Sto. cet... = ” a 2 
$4 13 * 3 2 N= E 3. 4 eee a N 
3 BY 5, 2 * 2 f > 1 F . Y 9 1 5 r 
1 ny 2 - SET, OS wa?! * 21 N r 1 5 
* 2 n 7 WES = « IF 0 . TIN * 1 * L 270 
ot 3 8 o 1 ＋ 1 1 3 
4 1 * 1 n 3 "fy 4 x: 2 4 n 
G7 „ 3 i SEV os * f 1 ſg ; : 
: o * 4. . 1 
3 Z%\ 1 n 18 3 WE 5 i 
” 8 | * 4 Ss 127 * %, RAE 
4 * 1. r 8 * * F 7 
: N F f : 4; * L 
x 4 4 MR 
: WY 
\ i . Ls . . X o 
; k & 1 4 
* * 5 : : . oy 
4 1 . * Y 
"IS 8 2 $48 i I 7 8 b 
* * 47 bs 5 
3 | y | F * * — 


4 1 
* » 
> 
9-4 - 
LY 
. — 
a 18 
* 
oy * n — 
7 - 
— P 
* 
4 
= ry 
4 


9 ee Dialing: vo 


* 

E * 0 

1 2 71 
i* -- 5 


104157 


DRE” 9 


9 


A Tarts of the this! e in Dialling, 
for LANG 51 405 301 min. 


2 
2 


P1427 224 


X 
— 


| » 


fung 

1 roms | 
pre 
Jo nonuyr | 


not 


2 


5 


2 


— 


e 


7 


* 


1 
8 


— 


_\© 


—_ 


11 

12 09 2337 30 
13 
14 
15 


1713 05 36 32 


1914 3136 0323*45 


a 0% 5 1335 4824, 57 


F * 1 * 
_» 
EF - 
b „ = : . 
. 3 
-, 
* 
. * - 
44 j 
- 


2 $435 22 08 


03 11138 2305 07 
03. 58 x 20126 23] 


10 o8[37 21j16 26 
10 5437 101] 7 40 
11 38636 58 18 54 
12 22136 43 20 07 
21 20 
13 42 36 18 22 33 


8 - 


1 yes 


At 


- 


— 


aer 


37 


a2 


Tz 35 


77 ne | 
Safrfany | 


1 *uUD1p149 
EE 


5 


16 36 
47-16 


4 
] 


— 
IS 


1 


H 


25 


p 


A. b 
Q. 


5 


rde 
= | Jo 40r2vn Iu] 


| 


A 


il 


18 37, 


19 
20 
21 
21. 


50 
22 
O5 
40 
15 
22 
23 
23 
24 
25 
125 
126 
26 


27 


25 
59 
31 
04 
35 


35 


17 56 


| —— | 


0412 


34 21 


191234 4465 56 


33 42 
33 20 


33 04 


— - 


Nane Dining = "089 


FY 


for Latitude P I deg. 30 min. 


5 
| 


Fog 1,218 | 


3 


FA 
"ſo. u0120u12uT\ _ 


eres 


1 23% 


12011129 


01 
ue 
01701] 


*nv1P1427 


Jo u 


0 8 
. urppiae / 1 a 


P 
urrptie i 23407 
: #q r. gang 


ae rates 


0 
i [ . 


d. nar mid. 


28 2927 5[50 oo] 
8 5526 34 59% 
29 216 07 5157 Os 
29 4625 27 52 55] | 
147 ZO g O 53 53 
48130 3524 380/55 50% 


$24 06055 460 


*r 


5 


18 42/64 18 83, 38 33 4 2084 35 


58 85 38 23003 0 86 o5 fo 2 
2 505 262 2386 % 


A rn, of the three Requilites in 5 Dating = 


06 4981 21} 
06 1282 00 + 2 
| o5 3582 364 
83 34 co 19 16 65 828 04 8883 4334 


. viii. iv. \ 


2717 2590 | 
TIfLE 3. '90 


24 2790 
33127 23,90 


4.49 


226 4: 


. ak 
* 
I 2 
_ 
r % 7 
2 ok 
ay " N * , 
1 5 
—_—_ ” 4 
F == o N 2 
r 5 , . 
_ K 
1 — 
1 1 s 5 a 
— 4 
—_— va ' 
= . 
_ 9 "4 
5 3 - EE 
. 8 3 — * 
5 o 
Z * A 6. 2 D n 15 
1 * 4 
* by 
0 ba 
Z 2 : 
WP 
* 
i 
ma 
4 
* 
i 2 
N 
| 7 


a — — 


* * 


K — WO 


A 


* 


eee. 


2 


rr . N 
8 e * * e _ * a F , \ 
. N < T 2 4 Wo * 0 4 oF 17 "1 L "FS ” ER 4 Ig I , * " bf | 
4 : - N n q 
* - < - IV n 28 A 1 * * = 
43 7 pe. 8 * 1 * * of ee e U * 
— 4 * * * N 1 "RE vp * Q L 6 = 
* : 1 "BY wy 8 * n ie P 
* N 1 £ 5 AP * * 2 
5 
8 Ic p bs 1 - - E 
2 * 
5 
* * 


, 4 


N r. | iii. 


11 vii. v. 


— 


Poſr1 3523 
bibi 45 


211 55 
342 1 


1542 23/25 


55 2 22 25 
5611 2 3225 


Poſe 4053 


[55 - 9172 


38 11 59 21196 cools 


75 0 
55 280 17 90 oof83 


Ds Z T LE of Meridional EDO 1 


AB 


* 
i 
3 
4 * 
4 
9 
þ 
Y . 1 


Elz 4826 5 


155 4575 e = 


\ ns nt EY | a a 5 FRB” =o IP TT OO f Se 9 : _ 
_ Te - ING 82 On" 2 * * i N ' 
Ns n 2 8 o * - ; 
— TE EROS ; / | s 5 PE 
2 \ 412 ; KC N . ; 4 Rae * \ 4 Hat Hg. 
- 23 7 


| FABLE of Meridional Angles. - 


i. ix. 11. 


d. m. d. m. 


viii. iv. vii. v. 


13 
18 


32 
OO 


257 3173 15 


56 175 
56 19 905 
156 34172 
56 4973 


57 17173 7 
57 3073 
57 43173 


3173 
2158 16,7 


58 35174 71190 


2458 44174 16/90 
36.58 52174 20% 
59 20 74 25190 


8'5 


1 
40 
44 
„ 48 


59 15174 34090 


1465 22174 37190 
22159 2 7174 40090 


54% 32 4 44190 


59 40 
59 44 
59 47 
$9 51] 
59 54174 
59 + | 
59 50174 
59 58174 
£9 59.7 


2 38/57 54173 46% « 
508 


58 26174 % 


Si 


to 
O 
— 


A 


LA 


800 1 


my 


* „ nl 


Go A 


"The v 8E fo his” 


TABLES. 


Ts eo wu een Coo 
1 —̃ — 


Tur Delig n HF, the firſt Table, "ray: * 

Table f 54 Three Requiſites in Dialling, for. : 
Latitude 51 Degrees, 30 Minutes) is to fave the 
Trouble of Calculation, according to the Direc- © 
tions given elſewhere in this Book, and is adjuſts -* 
ed to Latitude 51 deg. 30 min. and to all De- £8 
clinations in that Latitude. Its Uſe is, if it is 
required to make a Dial for Latitude 3 deg. © 
30 min. to decline any Number of Degrees from 
the Meridian, ſeek the Declination in the firſt 
Column, entituled, (Declination and againſt it 
in the ſecond Column, you. have the Subſtile's ⁵⁶ 
Diſtance from the Meridian: In. the Third * 
you have the Height of the Stile, or the Angle i 
that the Stile makes with the Plain; and in 


- 8 a 
IRENE! ; of. 4g 

CASE a 1 r 
2 


Py; g p Tas : 
as; 88 ; Me 8 Ra 8 2 
** . N * n 8 83 8 
2 +. I. "FAS "IE 8 r 
8 Ent ALS a iP) ; 
#7 SY . 


ER Joys! 2 
7 2 >. 
n 2 * 
n 


EI OO 
of . ws 
Sy n 


| the fourth Column, you have the Inclination © 2 
| of Meridians, or what is by ſome called nn 
| the Plain's Difference of "HOON: 1 * | 
| culated. - 
4 „ 
| 
1 
4 be 


_— — . HE Reid FB "7 5 * 
A ac 16)" li 5 : , « ; 
oy 2 1 * 7 
* 2 . — we BY 
0 2 „ nes N g 
9 4 * r 8 4 4 
4 3 + Br > lg Hr. Wh! In 4 n "-- 
by _ ay * I I 5 » i 2 
” - I as Let — * F 
* rn 3? . * S — 
» 2 ” 5 W - a 4 
1 RIFT o 
p : 


} L - \ . Y 
- 2 oE n . 8 Wh 
- "Fi 
_ Kb TO ++ r F | * 
\ x! 2 — * — 2 Os . - 
I * n 17 5 * 4 
_ ; Ci as ; Lf. w 
oc | FP 
EW —___ : . 
Av 1 © Z t x . y 2 
8 E 3 Son © 8 4: F 5 
; 5 T.05 RT 3 i * 5 
_- 8 8 4 F 
s * = * : 
L "6 7 * 2 
KC _ 


= Ir is required to make a Dial for Latitude 
eg. 30 min. to decline from the Meridian 
= 36 deg. (it is no Matter in this Caſe, whether 
= the Declination be Eaſt or Weſt, the Requiſites 
= being the ſame in Quantity in both, only upon 
= different Poſitions,) J look in the firſt Column, en- 
= tituled, (Declination) for 36 Degrees the Declina- 
tion propoſed, and 1 find againſt it in the fecond 
= Column 25 deg. 4 min. for the Subſtile's Di- 
=- ſtance from the Meridian, or the Angle, which 
= the Subſtile makes with the Meridian, or perpen- 
= dicular Line of the Plain. In the third Column 
I fnd-30 deg. 14 min. for the Height of the 
Stile, or the Angte that the Stile makes with 
mme Plain of the Dial. In the third againſt 36 
=  vep, you find-42 deg. 52 min. for the Inclina- 
mien of Meridians, or the Plain's Difference of 

= Longitude, which being all found by Inſpec- 
nin in the Table, you may proceed to make 
pour Dial as elſewhere directed in this Book, 
and that without any more Trouble of Calcu- 
Kup by the ſame Rule, if you would make a 
Dial for the aforeſaid Latitude of 51 deg. 30 
min. to decline from the Meridian 86 deg. you 
find in the Table the Subſtile's *Diſtance from the 

Meridian is 38 deg. 26 min. the Stile's Height 
is 2 deg. 28 min. and the Inelination of Meri- 
ALians is 86 deg. 52 min. But in this Caſe, the 
= Heightof the Stile is ſo (mall, that it is beſt to 
5 -mag the Dial without a Center; of which be- 


r 
4 33 
* 


" The Uſe of 


| Taz 6 Table, 8 (A 1 of 1 . 
ridional Angles) contains eight Columns, of which® 
the firſt contains the Latitude propoſed * fore: 
Horizontal Dial ; and the laſt is the Compi, 
thereof, which is alſo the Latitude for direct Sou | 
Dials; - it is of Uſe in both ores, of as 


8 __ 
4 CSV Et " 
N BEE . BY 
. 71 - 55 
g V. 7 
* 4 — 6 
8 * S272 I 2 D 
OE ew 2 
* 
. 
4:4 [ 
. 3X 
\ 


1 ——__ HO A ene Dial for Latitude 
4 Degrees. I look in the firſt Column of he. 2 4 
Table under (an Horizontal Dial Latitude) for 4 1 9 


Degrees, and againſt it in the ſecond Colunin, 1 
find 12 Degrees 13 Minutes, and over the Top p 
of that Caen Xi. i. Which ſhews, that the 
Hour-lines of 11 and 1 make an Angle with the 
Meridian of 12 Degrees, 13 Minutes. In the 

third Column, ,you have 25 Degrees, 2 Minutes, ! 

and over that Column is x. ii, vix. the We 
lines of ro and: z, make an Angle With the Mere I "WM 
dian of 25 Degrees, 2 Minates, and nine 8 
ly, the Hour-lines of 9 aud 3, make Angles with — | 
the Meridian of 38 Degrees 38 Minutes. „ 9 

Hour - lines of 8 und A make Angles of 54 2 9, the 
Hour-liues of 7 and 5, make Angles of 72 ane 
74, the Hour Ane of 6 mY * Tg Ns 1 
oy with"the * 8 i 
| Wn. 1 « 4. 


n 
; 7 3 
M7 2 $ * 2 * - of 
o , <4 M8 
; * W ein alt 3 © 
o_ . : 4+ +. :—_ 
? 9 . 1 
A 6 * A. 
i 
0 


Is you N make a direct 8 Dual, wi i 
Rule is. the ſame, only. you are to find the given 
Latitude on the right Hand, or Column of the "= 3b 
Table, and proceed as before ; ; as ſuppoſe you + 
yould WE a South Dial for Lan 40 SY 


* 


* 


OJ 
„ 


1 


— 


make 
5g 


robe 
« 
t 


eſt 


ihe k 
Dial bei 
fizontal 
e 


Of 
th 


L 


5 Mi- 
rok 
AS in. 


Dial 
er Par 


form 


, 


the la 


- 
. 


8. 

I, 
$4.9 7 ba 
make An 


— 


* 


- 00 
* 


** 
” 
- 
>» 
i; | a 
7 


* 


N Fg 
I Ld dP 
, Ns 


i 


+ 
% 


* 


40, 


Di 
2 
o in 
N 
a U 
n 


in 
Degrees 
d 1 
South 


dian of 11 


dts” of 


N Fable . 


I 


4 
— 


ht 


and 
an 


of 10 
tes; 

rs on a 

to thoſe: 


inf 
of 
80 


agail 
tly 5 au 


* 


* 


urs 


rl 
li 

5 
y. 


* 


ble 


- 


„e 


7 I 2 


4 q 
$M 
WE 


ines < 


In 
cien 


Oh-lines 


Ta 
H 


— 


"fu 


= 


Fable, 


bee 


the 
tlie 
Rue Me 
the H 
ed contra 
en 


: 


* 


9 "a 
a „ % .< 3 
2 a+ 9 
* 
wo * 
2 
— re 


— 


1 


# 
. * 
" — 
1 
> , 5 { 
$7 4 4 
| mn 
. 4 
2 0 
- 


P j * 1 F 
. a 75 4 . 


Ft 8 1 4 1 
445 e 


* 


- 


n 
8 
, 
W 
25 
85 


es to 
. 4 


a Re *Y 


