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Larrrupn and DEPARTURE 


r O0 R i * . 


e r * Ws 
2 GIS i & 


| NavicaroRs, LAND Ne Cc. 


With their Application to of Is, 


PLANE TRIGONOMETRY, 
| And their Uſe in 
PLOTTING AND CALCULATING SURVEYS, 
Which perfects the Hous »-Worx of that Ax r. 


To which is IX 5, g 


An Account of the Diurnal Variation of the Magnetic Needle, the . hens” 


. ariſing and its Correction; the Uſe of a new Surveying Inſtrument, &. 


Being great Improvements of the Fiz. p-Work. | | 
The Whole 2 ENTIRELY New; ; 


Compiled at yg 11 of a G of che 
DUBLIN SOCIETY, | 


7 By JOHN HOOD, AND SURVEYOR. 5 


—— —— 


* d 


1 5 B 1 1 # 
Printed and Sold by WILLIAM SLEATER in Caſile-ftreet, for the AUTHOR; 


** 


' 25 And alſo Sold by EpwWARD SricER and JAuzESs Lyncn, Mathemaitcal _ 
Inſtrument Makers; where may be had the C equered Paper and Compaſs 
_ Theodolite, mentioned i in this Book, and all other nnn for Surveyors, 


- Nena Te: 
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= H E following little Eſſay on Surveying ſuppoſes the Readers who would 
1 become Practitioners of the Method therein diſplayed, to be acquainted 
with Decimal Arithmetic, the Elements of Plane Geometry, Plane Trigono- 
metry, ſome of the beſt Writers on Practical Surveying, as GIBSON and 
Nos LE, and if with Plain Sailing, ſo much the better. | 
Tux End aimed at is to fender e whol detect auer may be, Matter 
of Arithmetical Calculation; and as the” Bi of every civifized> Nation is 
intereſted in Land Surveying, it is preſumed any Attempt towards this will 
be kindly received by the Public. This the Author humbly thinks is here 
accompliſhed. THT 10 | 


_ 


Ta Method of Plotting or Mapping by Calculation is incomparably the 
beſt in all Surveys, but eſpecially in extenſive ones, as the principal Manager 
may have a Number of Surveyors working toward different Quarters from the 
ſame Eine Alerzdtan land- Jar Hel: Any Part of whoſe. Work can be laid down 

at any Time in its proper Place on the great Plan, which cannot be done by 


Lo 


any other Method. 

CALIcuLATING THE AREA, which has been hitherto confined to one 
Lloſe or r here extended to all ſucceeding Cloſes, and with ſtill 
greater Eaſe as their Number ificreafes ; ſo that in large Surveys it is performed 
with one fourth Part of the Labour. And the Reader will find the Subject 
treated in ſuch a Manner as that any Practitioner in the common Methods of 
tolerable Capacity, may acquire a competent Skill in this, in a few Days, per- 
haps in a few Hows: Which it is hoped will tend to bring it into general 
Practice. 1 . | MES OT Fi | | 


NavicaToRs know the Uſe of the Tables too well to need any particular 
Inſtructions; the Sketch of Trigonometry is ſufficient, though they may read 
the manner of preparing for, and laying down Surveys, which is much like 
working their Day's Reckoning. > is | | 


M B. When a Map is laid down on the chequered Paper. 


A OMNH 7 - Perches to an- Inch! Area of the little Squares, | Area of the great Squares. 
10 4 Perce. 5 24 Acres. | 
By aScale of 5 * 5 _ 
(40 © $28 40 


„ AXIOM 


"4 £4.60 4 
N Land 88 the Earth is conſidered as a Plane; the. Meridiane as 
1 Parallels; the Parallels of Latitude croſſing them at Right-Angles: The An 


gles and Diſt ances, taken as on the Plane of the Horizon ; the Area of Ground 
| 2 what it covers of that Plane. : 


Of BEARINGS and AnCGLEs. 


| As the 6 Method here propoſed, requires no other Way of booking 
Angles in the Field for ordinary, than taking the Bearings of Objects and Lines 
from the Meridian; it is ſufficient to have the Circle, whether Theodolite or 
Compaſs, quartered, and accurately divided into four Nineties, whole Degrees 
only ; the Vernier Scale properly accommodated, ſupplying the Want of the 
{ſmalleſt Sub-diviſion of Degrees. 
AND as the Compaſs and the Theodolite have each their Imperfections, 
neither of them ought to be commonly uſed alone. 
Ox of theſe Imperfections or Inconveniencies, is a Phœnomenon of the 
Magnetic Needle, not taken Notice of by Writers on Surveying, which con- 
ne affects the Truth of a Survey made by it; that is, the Diurnal 
ariation. 


Mr. ANDERSON's 3 of this Variation. 


we: . about Eight or nine o Clock in the Morning, the Needle moves re- 
„ gularly Weſtward 'till about Two in the Afternoon, when it becomes ſta- 
* tionary for ſome Time; then the Variation Weſtward gradually decreaſes, 
„and the Needle comes back to its former Situation, or near it by the next 
« Morning. 
' « Turs Variation is s much greater in Summer than i in wy and 1s . 
irregular during an Aurora Borealis. | 


P R O P. I. 


ce The mean Diurnal Variation for every Montb in the Year 1 7.59. | 


&*. 19" 24” 
= 12 19 
11 4 


"8 January . 15660600 0 
% February .. -0 , 3. 58 ml 
„March. „„ DO 1 1 ans 
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Tx Error ariſing from the Diurnal Variation in a Survey of 200.00 Chains 
in Circuit, began at Eight o' Clock in a Summer's Morning, and cloſed at Two 
in the Afternoon, amounts to 0.17. and lies always to the Left-hand, when 
the Face is turned from the firſt Station toward the Center of the Land: So 
that, when the Surround is made with the Sun, it overſhoots 17 Links, and. 
when made the contrary Way, it falls as much ſhort of a Cloſe. 5 

In Figure 1 of four Sides each 50.00 long, the firſt Bearing ſuppoſed to be 
taken right, there will be no Error in the Place of the ſecond © or Station. 
Bur at © ad, the Needle being gone o: 4 to the Left-hand, it will be 
R: Sine o: 4 : : 50.00 : 0.05818= 34; and ſuppoſtng the Variation at © gd 
to be o 8, it will be R: Sine o. 8': : 50.00 : 12 Links, then 4 x 12, 
and e * = 5.8 Links: Let the Variation at © 4th be 00. r2', and by the- 
ſame Reaſoning n 1 = 12 Links, and ꝝ m as much; and if the Figure is right 


_ angled the Root of 1 1 DO +mnO:=17Links= 1 n the Miſcloſe. 


Now, it is eaſy to perceive, ' by tracing the Survey as made the other Way, 
that m will ſtill 'be the cloſing Point; and that this will hold, let the Number 
of Sides be many or few. 


To pre vent the Error otherwiſe arifing from this V. ariation. 


As the Needle is ſtationary about Two in the Afternoon, which is the Mid- 
dle of the Working Hours of the Day, and at its greateſt Diſtance from 
this at Eight or Nine in the Morning; if the Vernier Scale be placed as much 
to the Left of the Needle, as (conſidering the Seaſon of the Year and Time of 
the Day at ſetting out,) the Variation may then be, and working on till Two 
o' Clock, (all other Errors apart) the Needle will have gradually approached the 
Vernier, and then coincide with it, and ſoon after begin to return. | 

On, without the Theodolite; if the Time of Day be noted in the Field 
Book at ſundry ſtations, there may be good Uſe made of the ſame in cor- 
recting the Survey for Plotting or Calculation; or the Allowances may be made 
in the Field, by taking the Bearings a little to the Left-hand of the Needle, 
according to the Diſtance of Time from Two o' Clock. 5 

Bor the greateſt Trouble of all is, the Needle's being drawn aſide by Iron 
in the Ground, or in the Inſtrument ; againſt the effects whereof there is no 
guarding, but by uſing another Inſtrument with it, which works independent of 
the Needle. | 3 

AGainsT the Theodolite uſed alone, there lies this material 6+ grein that 
whereas the Needle gives the Bearing of every Side independent of every other 


Side, the Theodolite makes all the ſucceeding Sides depend in Poſition upon 
the preſent. | 2 | | 

HENce the neceſſity of a compound Inſtrument: And I have contrived one 
of a very- ſimple Conſtruction, in which the Theodolite and Compaſs are united 
in one Circle; whence ſundry Advantages are obtained, beſides what are com- 
mon to all compound Inſtruments, | 


ANY 


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Jo take Bearings with this Inſtrum ent. 


 ArTen levelling, (for which there may be croſs Air Levels in the Bottom 
of the Box,) bring the North End of the Needle to reſt at the Middle Line of 
the Vernier Scale; ſcrew the whole Inſtument to the Ball and Socket; turn 
the Sights, and with the Flower-de-Iuce from you, ſett (or cut. with the Hair) 
the forward Object; look into the Box, if the Vernier point out a whole 
Degree, or ſuch Part of a Degree as the Tables are calculated to; if not, 
turn the Sights a. ſmall Matter till it does; ſcrew faſt the upper Part to the 
lower by the Pin in the Foot of one of the Sights for that Purpoſe :- Then, 
looking thro* the Sights again, obſerve what other Object is. cut by the Hair; 
toward or over this you are to chain: Having booked the Bearing, raiſe the 

Needle off the Center Pin; then may the Inſtrument be ſafely carried by ano- 

ther, while you, with great Care, meaſure the horizontal Diſtance, taking the 
Offsets on Right and Left, and making all the neceſſary Remarks as you go 
on, Amongſt which, if there be Interſections for any Purpoſe, by letting 
down the Needle upon the Pin, the Inftrument may be applied as a Com- 
7. Box, without altering the Poſition of the Vernier, with Reſpect to the 

ircle. | 5 | | 

HavinG arrived at the ſecond O, which let be at even Chains always when 
you can, place the Inſtrument directly over the End. of the Line; and, look- 
ing thro' the Sights:backward and forward, fix the Inſtrument exactly in the 
ſtationary Line; level it, unſcrew. the lower Pin, turn: the whole Inſtrument, 
and, with the: Flower-de-luce:to your Boſom, ſett the Marks-man at the firſt O; 
ſcrew faſt the Inſtrument to the Ball and Socket, let down the Needle on the 
Pin; unſcrew the Pin in the Foot of the Sight; and, with the Flower-de-luce- 
from you, take the forward Obſervation to a whole Degree, or ſuch Part of a. 
Degree. as can be found in the Table as before, &c. | 


E R © B. 1 
To take an Augle. 


BRING the firſt Diameter to the Vernier Scale; and, turning tlie 
whole Inſtrument, plant the Sights parallel to the firſt Side of the Angle; 
ſcrew faſt the Inſtrument to the Ball and Socket; turn the Sights parallel to 
the other Side : The Vernier will point out the Quantity of the Angle if below 
909 ;. but it's Supplement if above 90% _ 8 


(23 

P R O B. III. 
To ſet off a given Angle from a Right Line, 
BRING the Diameter to the Scale, and turn the whole Inſtrument until the 
| Sights are parallel to the Right Line; ſcrew faſt the Inſtrument, and turn the 
Sights until the Scale cuts the given Angle if below go® ; or its Supplement in 
the next Quadrant if above go® ; the Sights ate then in the Direction required. 
| El Lg Pp R O B. IV. 


70 take an Altitude. 


TvRN the Inſtrument vertical; bring the Scale to the Diameter and level 
it; ſcrew faſt the Inſtrument, turn the Sights and ſett the Object: The Scale 


points the Altitude. | : 
Of the TABLES. 


TasLEs of diff. Latitude and Departure, are the natural Sines to different 
Radiuſes, made for the more eaſy and expeditious working of Caſes in Plane 
Trigonometry. | 3 

THESE are from One to an Hundred incluſive, as beſt adapted to the Gunter's 
Chain, (and ſufficient for all the Purpoſes to which they may be applied by Na- 
vigators) and to Quarters of degrees; but as they go to four Places of Decimals, 
will anſwer to every Minute of a Degree, and Diſt. 100.0000. The diff. 
Latitude ſtands under the Courſe, or Bearing; the Departure under its Com- 
plement ; but uſed as Sines ſtand contrary, the Coſine under the Angle, the g 
Sine under its Complement. | | | = | 


To correct a wrong Figure in the Table, or reflore an Obſcure one. 


Add the firſt Number in any Column to any Number therein, which gives 
the next following Number. | : 


Their Uſe exemplified in Plane Trigonometry. 


n 
4 
-» 


+] Lr AB repreſent a Portion of a Meridian. 
"mY CC a Parallel of Latitude. | 
1 THEN will the Angle BAC be the Courſe or Bearing. See Fig. R. 

EE | AC the Diſtance, A B the diff. Latitude. ER . 
EE! | BC the Departure, ACB the Complement of the Courſe. 


Diff. Lat 
| l 


1 


Courſe. 


© | Depart. |: 


„ 4 Diſtance. 
Diff. Lat. 


Required. 
iff. Lat. 
& Depart. 


(9) | 


Plane Right. Angled TRIGONOMET RZ. 


—_— - —Y "2 rn _— . 


xample. 


Quere. 


7.75 


B 47-7015 


r 


7 1 47.7015 in their Columns. 


2 *Forotion. 8 
— Find the Courſe 3 12 

at the Top of the Table, and in that Co- 
lumn right againſt the Diſtance 87. in its 
Column, ſtand the Diff. Lat. 52.7569 and 


ut when the Diſtance cannot be found at 
| once in the Table, divide it into ſuch Parts 


4 a4 i (OA LA 


4 a 4... — 


{lumn ; 
Jef the Diſt. and Depart. in their Columns. 


and look for the Remainder in the ſame Co- 


among the Degrees| | 


againſt which ſtand the Remainders 


AC = 85.521 
AB = 71.69 


is is folved as the laſt Caſe. 


Courſe. 
Diſtance. 


— —_— 


BAC = 345 
BC = 48.84 


Hound a 


Itence to the lower as will make it 


. of the two Departures talen from the greater 
will leave the true Departure; and a like 
Part of the Difference of the 


Seek in the Table till againſt the Diſtance 
nd in ita Column be found the given Diff. 
t. in one of the following Columns, and 
adjoining it ſtands the Departure; the Courſe is 
the Degrees above the Diff. Lat. 
But if the Diff. Lat. cannot be exactly 
found againſt the Diſtance, take the next 
Number below the true Diff. Lat. from the 
next above it, and add ſuch Part of the Diffe- 


equal to 
e Diff. Lat. A like Part of the Difirence 


in Mi- 
nutes added to the leſſer Angle, will give the 
Courſe or very near. 


1 AC: BC : : R: Sine Courſe. 
W 24 
And R Di. 25 


1:87 : :,8415:73.21 


This is ſolved as the laſt Caſe. | 
But'they may both be done by the Table 
uſed as-Sines ; thus: 


; 1: :5402 = the Sine of 323 
Co. 


S. Cou. : Diff. Lt. BC]: = AB. 


_— 


— 


the Courſe above the Diff. Lat. at the Top. 


But this Caſe is better ſolved thus: The 
Root of ABC]+BCO. = AC = 


Seek in the Table till the given Diff. 
Lat. and Depart. are found together in their 
reſpective Columns; then right againſt them 
will be found the Diſtance in its Column, and 


But if the Diff, Lat. and Depart, cannot 
Numbers which rly agree to them, the 
Courſe and Diſtance may be found or nearly. 


| 85.98; 
then AC: BC::R: 8. Courſe. . 
| "85.98: 47 :: 1.: ,5466= the Sine of 333 


= the Rootof Aci 


be exactly found — — dy comparing the | 
nea 


found at the Top of the Table againſt 1. in 
the Diſtance G 


| 


. 83 Courſe C and Diſtance CD are found per Caſe the 6th. 


Diff. Lat. and Departure Columns. 


Jo begin or end a Cloſe at an inacceſſible Point, or to take inacceſſible Diſtances. 


Sides, per Caſe 2d of Right or * Angles, 


(ro) 


Oblique Plane 7 R 700 N 0 ME TR 2. 5 


ra Perpendicular be let fall from one of the Angles of an Oblique Plane 
Triangle to the oppoſite Side, produced if need be,--thence will be formed two 
Right Angled Triangles, by which all the Caſes of no 2 Plane Fan 


try RY be ſolved as 1n the ing Caſes. 


moat. 


r Given. pr ; N | | 1232 ; 
N AC. C acute. I CD: 1 A: Sine D. "TN * <6 
e Sine K. Sine C:: DC: DA. Jor calling A the Courſe, | 
A. AD. land AC the Diſtance ; ; the Diff. Lat. AB and Depart. BC will be 


| I ound by Caſe firſt of Right Angles. 
3. | And making DC the Diſtance and BC the De arture, the Courſe; 
BDC and Diff Lat. BD, will be found per Caſe 5th. 

Then AB — DB = AD, and 1809 — —BDC = == the Angle A ADC. 


ee 7752 AC. ] Sine C: Sine A:: AD; DC, 5 ; 
II. [ A5 CD. fand Sine E: Sine D:: AD: AC, Or e calling A the Courſe, 
3 1 © © ſand AD the Diſtance, AE and ED the Diff. Lat. and Depart. will 


1 22 | {be found by Caſe 1, of Right Angles; and calling C the Courſe, 
IE will be the Depart. whence CD the Diſtance and CE the Diff. 


SY | Lat. will be found per Caſe zd; then AE EC = AC. - . 
A. C. [Calling A the Courſe and AD the Diflance ; the Diff. Lat. AE 
III. AD. D. and er. ED are found per Caſe 1ſt of * JAngles, and 


BY 3 Then the Diff. Lat. EC and Depet. ED bei) g known, the 


AC. | | The longeit Side is to the Sum of the two Thortelt, as the 2 
IV.] AD. The Angles: of the two ſhorteſt is to the Diff. of the Segment of the Baſe. | 
. - And the Diff. of the Segments added to the Baſe, half the Sum 
| 1550 1 {is the greater Segment AE ; then AC — AE = EC. 
£44 | T | Then calling A the Courſe, there will be given the Diſtance AD 
; LE OE Jand Diff. Lat. AE to find A the Courſe. 

| 322 wo | And alſo thc Diſtance, and Diff. Lat. CD and CE to find the 

| 2 — or 22 C per Caſe 4th of Right Ang . e 


18 8 
0 


P R 0 B.: } V. | . | 
7 be Anitude . Slant 3 given, to find the Baſe and Nile 


Tuis is done by Caſe firſt of Right Angles thus: Find the Altitude among 
the Degrees at the Top of the Table, and in that Column right againſt the 
Diſtance in its Column ſtand the horizontal Diſtance and Perpendicular 1 in the 


— 


n 0: B VI 


BRING the firſt Diameter to the Vernier Scale, and take the Bearing 
of the Object; ſcrew faſt the Inſtrument to the Ball and Socket; ſet off 
any convenient Angle, (a right one when practicable) meaſure a ſuffcient 
Diſtance in that Direction; from the meaſured Line at its Extremity, take the 
Angle to the Object: Then are given the Angles and a Side to find the other 


p R OB. 


I 3 0 TS YR , 
2 Sd . Fes , > 2 d 8 er 0 
os IS! — * ws * - > 4s n 1 OY c * 3 * A — 2 
e OO OE r Se 33 Nr TI ROLES. PVC at SE l 
i To Con Ne ER EE Ng, OY» Ie I IAIN = 3 
n En It ahh Tneh ol SN r Foe NG e 4 len n 
2 P 2 r B ERS x SS EE OS: UF Nd ISO e522 E, es I te, Ol 
8 r e 8 SIEGE, - Xx; = 2 GR ONS. 8 OF * 8 PR A 
1 4 * 0 n 5 . — . . . 


oo : * ook r 
N 3 oy 3 
. t Ro 
1 2 FSI 
Wm. 


3 
8 


To take an inacceſſible Height, 


Taxes the Altitude by Prob. 4th, and the Diſtance of the Perpendicular FP | 


the laſt Prob. Then, having the Altitude and 1 the „ ene e gh 
is found * Caſe 2d of Rien Auges | 5 7 


Jt) T2 #2 
abus 41% DIEWO! 
Of P ProvinG a 2 Survey by the Tals. ond ors a vin 

A X 1 O N II. 1 oat: 


1 chaining 3 a F ield, the Sum of the Nontings a to be * to 


che Sum of the Southings; 3 and the Sum of the E Eaſtings en to the Sum of | 


the Weſtings. „ Uh 

Lux the following Field Book he pot gr in which are - fon Columns next 
after the Offsets, for Northing, Southing, Eaſting and Weſting. 

' Draw a Daſh acroſs the contrary Columns to each Courſe, and cloſe angles 
it, draw another acroſs all the four Columns. Theſe two Lines are to be op- 
polite to the laſt and e Man in the Diſtance Cob belonging to 
that Station. | 55 

Tx firſt Bearing in oh Field Book is N. W. Therefore, in anhe 8. and E. 
Columns, and oppoſite to to 5, the laſt Number in the Diſtance Column of 
that ©, draw the Daſh, and cloſe-below-it the croſs Bar. 

Tux ſecond Courſe being N. E. draw the Daſh in the S. and W. Columns, 
and cloſe under it the (croſs Bar; and thus with all the Courſes. "ron; 

Tux next Thing in order is to fill the Blanks with their/peculiar Dif. Lat; 
and Depart. taken from the Table by Caſe firſt of Ri ight Angles. Thus 

Tur firſt Bearing is 14. which find among the Degrees at the Top of the 
Table; and in that Column Tight againſt the Diſtance 535, ſtand the Diff. Lat. 
4.889 and Depart. 1.21, for the N. ane W. Columns being Blank. Aud ſo 
fer every Courſe and Diſtance. JT. oi 

Wren: the Diſtance conſiſts of no more chas! two > CamiGennt 1 as 

97.00. or 9.70. or „97, the Diff. Lat. and Depart. are found at one Inſpec- 


tion; Care being taken to placs the decimal Point right. But if the Diſtance 


conſiſt of three or more ſignificant Figures, as 1 12.00 1 1. 20 1,12; then the 
Nurs may be taken out at twice, and added on waſte Paper. 

Bor a little Practice will enable one to carry and add the Numbers together 
in his Mind without ſetting them on waſte Paper... 

Havins taken out the Diff. Lat. and Departure for every Courſe and Diſ- 
tance of the Cloſe and put them into their proper Columns, add the Numbers 
in each Column together ſeverally; if the Northings be equal to the Southings 
or nearly equal, and the Eaſtings equal or yearly equal to the Weſtings, the 
. Work is allowed to be right. 

Bur if not, there is an Error or Errors committed ids in the Houſe or in 
the Field, which muſt be found out and amended before you can proceed. 
AND when, there is but one- Error, the ingenious Practitioner will (by conſi- 
3 the Excels in Nortung,, as Eaſting or Weſting, BAG that Bearing 


cr 


— 


(1) 


or Diſtance, the altering whereof would account for it,) gueſs well where to 
look for the ſame ; But when there art two or more Errors it is impoſſible. 


Of Prorrins. | 
A XI oO M III. 


I x North Latitude chaining toward the North, and in South Latitude ——_ 
toward the South, the Latitude increaſes; add the Diff. Lat. to the Lat. left 
gives the Lat. come t6;: | | | | 

Bur in North Lat. chaining toward the South, and in South Lat. chaining 
toward the North, the Lat. decreifes; Subtratt. gives the Lat. | 

Tux ſame is true of Longitude and Departure, (or Diff. Long.) and when 
the Longitude and Departure are of different Names, that is, the one Eaſt, 
the other Weſt, their Difference is the Longitude of the ſame Name with the 
greater. The ſame is true of Lat. and Diff. Lat. e 16-i 

Tat Work being proved to be right, the next Thing to be done is to 
correct the Diff. Lat. and Depart. that is, to bring the Northings and Southings 
to a perfect Equality, and the Eaſtings and Weſtings alſo, which they ſeldom 
of never are, even in pood Cloſes. | 8 „% 2D; 

I the firſt Ctoſe of the Field Book, tlie Notthings exceed the Southings by 
2 Links; the Eaſtings are leſs than the Weſtings by 6 Links, which is noted 
in the Field Bock, thus: | 2 | [EL SES 
| * 1 + 8. 6.02. 


+ E. . O. 06. ES. 5 
and fignifies that the two Links are to be taken from the Nerthings 6f added to 
the Southings, or partly both; and the fix Links added to the Eaſtitizs or 
weer from the Weftings, or partly both, to make them Teſpettively 
equal. n FFF f 
Tuo' the diſpoſing of this Exceſs or Defect be a Matter ef Judgment, 
the general Rule when there is no Reaſon to the Contrary is, to 
Divioe the Exceſs among the comparatively ſhort Legs or leſſer Numbers in 
the Columns of Diff. Lat. and Depart. in Proportion to the Diſtances on 
Bearings nearly equal; placing always the greateſt Streſs on Bearings moſt 
remote from 4.59. | | + £2 | : 
Ap put tlioſe little Dividends or parts above their Diff. Lat. or Depart. 
with their Sign + or —. = | | 
Tus goes on the Preſumption that the Diſtances are better taken than the 
Bearings; which Experience ſhews to have been uſually the Caſe. (See 
Noble's Surveying, in which the Correction of a Survey is ingeniouſly and 
{argely handled.) 1 | | 5 | 
Bur if What is ſuid above of taking Bearings and of the diurnal Variati- 
on be attended to in Practice, the Corrections will be found very inconſide- 
rable, and require to be made by ſhortening Diſtances as much as by alter- 
ing Bearings; that is, by leſſening both Legs proportionably, and ſometimes the. 
longer Leg only. | | 5 
Havi diſpoſed of the Exceſs in little Parts, proceed to find the Lat. 
and Long. of every Station according to Axiom gd. Thus: Aſſign the Lat. and * 
Long. of the firſt O, ſuppoſe it o, oo for it is Matter of choice. 2 8 
0 1 


3 


N 
9 
N. . 95 8 


W 5 
AL Sh 
RW rake 
N Ee 
e 5 
n 


TS. 7 . 4 I”, 24 

KCl OY Metz 
8 8 . 

8 + KY p bb r 

N gone N 8 
8 * 89 2 . Er 44200 
5 1 7 * n 7 8 


1 


- 2 : nen 
Te Rents omar 
1 * * . 
= ND 1 
$ n 


1 . 

To the Latitude of the firſt Station add the Diff. Lat. of the firſt Statio- 
nary Diſtance, and put the Sum 4.85 under the firſt croſs Bar for the Lat. of 
the ſecond Station, againſt which it now ſtands. „„ k 
To the Latitude of the 2d ©. 4.85 add the Diff. Lat. 5.24 of the ad ſtati- 
onary Diſtance, placing their Sum , under the ſecond croſs Bar for the 

' Lat. of the 3d ©. Sc. ſtill adding the Diff: Lat. to the Lat. foregoing when 
they are of the ſame Name, and taking in the little Parts of the Exceſs by their 
Sign + or — as they occur. | Fs Re 2 TOE 
Bur when the Latitude and Diff. Lat. are of different Names, ſubtract the 
leſſer from the greater, and put the Remainder under the croſs Bar in the ſame 
Column with the greater for the Lat. of the next ſucceeding © -according to 
the Axiom. | | 2s 

So at © 5th the Diff. Lat. 2.16 being South, is taken from the Latitude 
20.02 being North, and the Remainder 17.86 put under the croſs Bar in the 
N. Column for the Lat. of the 6th ©. + 3s | 

Taz ſame is done for the ſame Reaſon at all the ſucceeding Stations of the 
Cloſe, and the laſt © having its Lat. and Diff. Lat. equa}, but of contrary 
Names, there is no Remainder, which proves the Additions and Subtractions 
to be rig... 3 mw 5 

In by ſame Manner begin with the Departures; bring down the firſt which 
is Weſting r.19 below the croſs Bar for the Longitude of the 2d O; and be- 
cauſe the Depart. 9.42 next following is contrary and greater, from it take 
the Long. 1.19, and put the Remainder 2.23 under the croſs Bar in the Eaſt 
Col. for the Long. of the zd ©, to which add the next Departure becauſe of 
the ſame Name, and put the Sum 5.755 under the croſs Bar for the Long. of 
the 4th ©, and ſo proceed in all Reſpects as with the Diff. Lat. and at the 
laſt © the Long. and Depart. will be found equal and- contrary. | | 

AnD this will always happen in ſipgle or firſt Cloſes when the firſt Meridian 
and firſt Parallel are made to paſs tie the firſt O. "OE 5 

THERE now ſtands the Latitude and Longitude of every © under the croſs 
Bar oppoſite to itſelf, or in the ſame Line. By this Set of Nambers the Survey 
is plotted; Thus: | | 5 

On. large good Paper, chequered into Squares of two Inches im the Side with 
ſtrong Lines, and into Squares of two Tenths of an Inch in the Side with very 
fine Lines, aſſign the proper Point for the firſt ©, which, in this Cafe where 
the firſt Meridian and firſt Parallel are made to paſs thro' the firſt ©, muſt be 
the Interſection of two ſtrong Lines. | ELD, 
Ax the Ends of theſe two Lines write No. o, and from thence number the 
other ſtrong Lines 10, 20, 30, Sc. then is the Sheet prepared for laying down 

by a Scale of 5 Gunter Chains or 20 Perches to an Inch; one Set of theſe 
2 repreſenting Meridians, the other, Parallels of Latitude, as in a Plane 
art. | 

Bur if the Map is to be laid down by a Scale of 40 Perches to an Inch, the 
Capital Numbers o, 10, 20, 30, Sc. muſt be wrote on every 5th Line. 

II is plain that every Point in the Sheet has now its peculiar Latitude and 
Longitude, and that this would hold if the Sheet were ever fo large; and ſince 
the Lat. and Long. of every Station of the Cloſe is known, it will be eaſy to 
align their Place on the Papzr or Chart. | ES 


:. ; | | T3 


( 14 ) 
Tobexin from the firſt ©. (Ste the Specimen Map.) 


Tax the Latitude of the 2d © 4.85 in the Dividers, and, with one Foot 
in the Longitude thereof 1.19 on the firſt Parallel, ſweep Northward. Take the 
N 1. 19 in the Dividers, and, with one Foot on the firſt Meridian in 
the Lat. 4.85, ſweep Weſt to cut the firſt Arch in the 2d ©. 


Fon Trial take the Diſtance 5-in the Dividers; if it juſt reach from the firſt 
to the 2d ©, all is right. | | 
Joix the firſt and ſecond ©'s with a fine penciled Line, and proceed to ſet 
off the Lat. and Long. of the 3d O; but as its Lat. is more than 10.00, take 
only the Overplus 2.09 in the Dividers, and ſet it off in the Long. of the 

2d © 2.23 E. from the Capital Parallel numbered to the Northward 10. 
Takx the Long. of the 3d © in the Dividers and ſet it off from the firſt 
Meridian Eaſt to cut the laſt Arch in the 2d O; join the 2d and 3d ©'s, and 
thus proceed round to the firſt ©. | 
N. B. Ir the fine Meridians and Parallels are truly drawn, it will be ſufficient 
to take only the odd Links in the Dividers ; and, as Paper is apt to ſhrink or 
ſtretch as it is dry or damp, this will be often the trueſt Way ; but when the 

Paper and Scale exactly agree, the firſt is the eaſieſt Way. 


To prepare Second or Succeeding Cloſes for PLOTTING. 


Havinc taken out the Diff. Lat. and Depart. for every Courſe and Diſ- 
tance, and inſerted them in their proper Columns as before directed, add the 
Northing and Southing Columns ſeverally ; take the leſſer from the greater, 
noting their Difference : Do the ſame with the Eaſtings and Weſtings, noting 
their Difference. | | | 

IT is plain the firſt of theſe Remainders is the Diff. Lat. the laft, the Depart. 
or Diff. Long. by Account, between the Beginning and End of the Cloſe. 
Call theſe the falſe Diff. Lat. and Diff. Long. 

AGAIN, look into the Field Book for the Latitudes. of the Station at the 
Beginning, and ſtation at the End of the ſaid Cloſe : If they are of one 
Name, ſubtract ; but if of contrary Names, add: Their Sum or Difference is 
the Diff. Lat. of the Beginning and End of the Cloſe. 

Do the ſame with the Longitudes of the Station at the Beginning, and © at 
the End of the Cloſe ; the Sum or Difference will be the Diff. Long. of thoſe 
Stations, Call theſe the true Diff. Eat. and Diff. Long. | 

Ir the true and falſe Diff. Lat. are equal or nearly equal, and the true and 
falſe Diff. Long. nearly equal, the Work is eſteemed right: Then proceed 
to make the Corrections as directed in the firſt Cloſe. | 


E X A M- 


(5) 
E X A M * E. In the ſecond Cloſe. „ 


Bro An 4109 fliſt of firſt Cloſe, Let. - - .c0N, Long. o 
ENDED at © 7th of ditto, - - Lat. - 6. 19 N. and Long. 19.12 Eaſt, 


True Diff. Lat. - - 6.19 N. and Diff. Long. 19.12 E 
Falſe Diff. Lat. - 6.20 N. and Diff. Long. 19.08 E. 


Error too much - - ©.01 N. Error too little 0.04 E. 

Wulck Error is noted in the Field Book as before, and is diſperſed in the 
Columns of Diff. Lat. and Depart. as directed, in order to make a perfect 
Cloſe. re | | 
THe proceed to find the Lat, and Long. of every Station by Addition 
and Subtraction in all Reſpects as in the firſt Cloſe; and as this Cloſe ends at 
.- th of the firft; the laft Lat. and Long. will be the Lat. and Long. of 

at ©. | | 

Tus in all Reſpects are all ſucceeding Cloſes prepared. 

THz Method of Plotting preſcribed in the firſt Cloſe, is univerſal. 

Tavs the Survey of an Eſtate or of a Country, may be carried on with the 
greateſt Regularity, and a little Practice will make it very delightful, and 
_ ſufficiently ſpeed G. | 

When a Map is laid down by this Method, it is vaſtly eafier caſt up by 
numbering the little Squares, and generally truer than in any other Way, ex- 
cept Calculation, for it is rather laid down by Number than Dimenſions ; 
therefore, the ſtretching or ſhrinking of the Paper has no effect on the Co 
tent found by counting. | | | 


Of CALCULATION. 
L E M M A. 


Every Four-ſided Figure having two of its Sides parallel and a third 
perpendicular to them, is equal to half the Rectangle made of the Sum of 
the parallel Sides drawn into the perpendicular Side. 


FIG. 2. | 

PRODUCE the parallel Sides AB and DC, and make BE equal to DC, and. 
CF equal to AB; draw EF, which (becauſe AE and DF are equal and parallel) 
will be equal and parallel to AD, and the Side BC being common, the two Fi- 
gures AC and FB are ſimilar and equal. | 

Bur the whole Parallelogram AF, when it is rectangular; is made of the 
Sum of the parallel Sides AB + DC (BE) drawn into the Perpendicular AD; 
the Figure er is therefore its Half. 


7 e ki. | 


HEeNcz the Area of a Field may be found by Offsets, taken from a right 


Line paſſing either beſide or thro' the ſame, to the Angles thereof. F 
| OR, 


. r OE —_ * 
Nr * * 
. : 4 Ar . 1 a. 
4 . 


C4 0 


* 2 _—__ LOS 
„ 
9 


3 
2 8 
* th ent * 
ͤUG—ſQANAQ—7—I—U —— 0s ARIA TY — — ũ TY = os A A neg — —ß — —— — 
2 WP * 


616) 


W F u Hg. z. ZN Fw. 
** | che Rectang le A4 ＋ Bb X AB S the the! AabBA.-- : 

2 lalf the Redkangle BE + Cc x BC the Fig. Bbc CB. 
* 15 Half the Rectangle Ce + Dd X CD= the Figure CedDC. 
5 Half the Rectangle Dd +'A7 x DA = the Figure DdaRD. 
4 ur two firſt Fi Bures or Areas, taken from the two laſt, 3 the Area 
"the Field abeda. 
To” 70 Half of A4 E Bb x AB = the Area AabBA. 
| Falk of Ce + Dd x * S the Area CcdDC. 

= $4; 21 Half of Ce & C = the-TnangleCxc. + re 
7 Half of DIXDz = the Triangle Ddr. 5 
From theſe four Areas take the two Triangles Aza and ** there remains 


the Area of the Field abeda. 1 EET 
©) 0: R. * hs | 1 


| 4 : >Hencs the darin of the Method of calculating the Dn of Me 


lined Figures Trigonometrically. 
Fon if the Line N. S. be a firſt Meridian, the Offsets will be the Longi- 


tudes of the Angles or Stations of the Field; the 1 of the Meridian, 
the Diff. Lat. of the ſtationary Diſtances reſpeCtivel and are all found . by 
Caſe firſt of Right Angled Trigonometry, as is OE” ſhewn at large. 
AY C as E I. When the firſt Meridian paſſes bf de the Map. 
„„ „e R, E; 
| Hs Halt the ReQangles made by multiplying Big unn i, the LAI of 
every two adjacent Stations into their Diff. Latitudes be taken; the Difference 
between the Sum of the North, and the Sum of the 5 Sourh Areas, will be ther 5 
Area of the Map. : 
1. 3. | „ 
LET abcda be the Map! whoſe Area is required; a "ha firſt O, h the ſe- 
cond ©, Sc. ahd N. S. the firſt Meridian paſſing on the Weſt Side of 
the Map: Then are the Perpendiculars drawn from the ſeveral Stations 
to this Line the Longitudes, and the Segments of the Line the Diff. Lat. of 
the Stations; of which AB and BC are Northings; CD and DA Southings. 
HaLF the Rectangle of the Northing AB into the Longitudes "Aa and 
Bb = the Area AabBA; and Half the Rectangle of the Northing BC into 
the Longitudes Bb and Cc = the Area BCB. The Sum of -theſe . Arens is 


the whole North Area A abc CA. | 
N, Half the Rectangle of the Southing CD into the Longitudes Ce and 


8 \rea CcdDC. 


Da = t 

2 A Ja e Rectangle of the Southing DA into the Longitudes Da and 
Aa = the hex iaAD. The Sum of theſe Areas is the Whole South Area 
Ceda c. op. 


Tur North Area Aat#CA taken from the South Area cad. leaves the 
Area of the Map abcda..Q_E. P. 31 
The Theorem demonſtrated in a more complicated Figure. 
„ 

HAL the. Rectangles of the ſeveral Southings into the Longitude, make 4 


the Figure + pricing off * Ddc CD + E/eEF. en, A F 
| - ; xD 


1 


—— 


————ͤ d q — PPP Pr Sup * r " Rr 


x x 1 N —2 28 Nn LY Pq 4 . 2 * ; by 2 bl 
us - FD EI IG, 8 5 og: ar 3 8 Sh MS ot Eg” 5 2 * 5 . * 0 1 
AE XL Gs ** os SIKTAS ER S D Os < ne mn 0” i agate it N FS» Chant race * „ 5 C52 3 Ne T - 5 
2 ³oÜö³A ͤ ⁰ or lohan hg: mY! . /// EDD NS $24 EFF Ted 7 I Cs a EEC 200 n 
8 8 CEE 185 . + » Feb TORS fn. 8 A MWg N r — 2 . * He ch n n 5 : ELIT 232 gt 
ts; re NI; - >; 2 "ENT bo wt 2-0 1 "oe 2 23 5 3 n SEO Sr, Ae Rh. Th 9-3. 5 > ve : 8 7 4 
7 EP Cha er BT Dn TR PIE EEG c SL oo ee ood 5 i. en RO Eg SE At 
. wet 1 2 0 1 N * 7 — 4 * K 8 * , _ 
%& — 7 r * P NINE" ** — we 8 c 


85 SE LA 
; ET LNG 
F 2 a 
e 7 EM rd 
E "IF * + 1 
% 


—. 
eee * 
* — 5 
PT 
rt 5 25 
— * 3 A 3 8 Di 
PERS. 7 * - LY 
+ tad ”" 


n 
n 


gf: 


ay will lie without; and the contrary: Their Difference: therefore is the 


| gle Gr of the WBS Longitude Gk into the SouTaiNG GB. 


7 "_ Ss 
_— 3-72 SH 3 
„ 
- _ 


* r _— 
4 —— _ 
: T - 2 by 5 == + "RG 25 
; Z 
- , 10 1 
W by Ro Pa Ey . 
* * , * 2. 


Ap Half the Rectangles of the ſeveral Northings into. the 


make the Figure AabBA + DA) + EEE: The firſt leſs; the last 
Or, the Figures 1 rv 2 _— AabBA take 

BbrdefaAB, leaves abcdefa the Area of the Map. Q. E. DP). 
W L E MIM A. (kg;6)  :.- 


E 
* * 
# > e | 
- 3 
= = 
2 . 
by & * 


Ik a ſtationary Line croſs: the Meridian, Half the Rectangle made by mul 
tiplying the Difference between the Eaſt and Weſt Longitudes into the Diff. I 
will be the Cgantity by which the Survey is inereaſed or diminiſſiet. 
Ler ag be the ſtationary Line, Aa and gz the Longitudes ; make ax .equal-to. "Wl 
Then is Ax the Diff. of the Longitudes, and Ax the Diff. Lat. Com- EY 


pleat the Parallelogram s..... perl te © 5 
Ir is plain, that when the Triangle gay lies within the Figure, the Triangle | 


Quantity by which the Area is increaſed or diminiſnhed. SE. 
Bur by ſimilar Triangles zu or uA, is the Difference of thoſe Triangles a 
But zu and zA, are Halves of the Rectangle made of the Diff. Lat. Ax into. 


the Diff. of the Longitudes Ax. Q. E. DDP). 
| Ci: OR. 27) 


} 


Ir the greater Longitude lies within the Figure, the Semirectangle is to be 

added to; if without, ſubtracted from, the Area. 
Cask II. When the firſt Meridian paſſes thro' the Map. 

| T HRE OR EM II. -: 2 

EasT Longitude multiplied into SouTHINGs, and, WEsT Longitude raultiplied 
into Nox THINGS ; from the Sum of their Semirectangles, take the contraries; 
that is, the Semirectangles of EAs r Longitude: into NoxTHiNGs, and WEST 
Longitude into SOUTHINGS : The RRE MAIN DER is the Area of the Map. 

Tur Semirectangle of the SouTHING BA into the EA sr. Longitude Ba and 
Aa- the Area B da AB, + Ne "A 

Tas Semirettangle of the Nox THIN zG into the WesT Longitudes Ge and 
zb=the Area GcbzG. 7 Ws | | 

From the Sum of theſe Areas (by Cor. to the Lemma) take the Semixectangle 
Au of the Easr Longitude Ax into the Nog THinG Ax; and the Semirectan- 


— 


The REMAIN DER is the Area of the Survey adcha. Q. E. D. 

x . R E M A R K. : 
Tu two Theorems ſuppoſe the Field kept on the Right - hand in the Survey; 
but ſuppeſing the Contrary, the Theorems reverſed will be true. 
Fon, becauſe the Diff. Lat. changes its Name, the Products, which were before 
North Areas, will now become South, and the South Areas, North. Gs 
1 et PR Q-Þ:L M, i; rind 5 
From the Field Notes prepared for Plotting, to find the Area of Ground by Calculation: 

On the Right-Hand of the Columns of Diff. Lat. and Depart. in the Field 
Book, are four large Columns; the firſt marked D. Long. for the Sum of every 
two adjacent Longitudes; the ſecond marked N. Area for the North or Nega- 
tive Areas; the third marked S. Area for the South Areas or Products; the 
fourth for Offsets. Bos ko, 9s wa | | 

ThE Numbers in the D. Long. Column, are formed from the Longitudes 
of the Stations, exactly in the ſame Manner in which the Langitudes themſelves 
were formed from the Departures, and the Latitudes from the Diff. Lat. 

| N | er 


* * 


8 * of "> 
: WS 


% 
* 


(8) 


227 is, -by adding or fubtraQing eveiy | two adjacent Longitudes as they 
are like or unlike; and putting their Sum or Difference juſt at the End of the 
croſs Bar above the lowermoſt of the two. And fince the Work is the ſame in 
er the Lat. Long. and Dou. Long. this ſhort Rule may be uſeful in all. 

| RuLe. When like, add. When unlike, ſubtract. 
E X AMP L E. 

11. the Girl Cloſe of the Field Book, the Long of the firſt Station is 0.00 to 
which add the Longitude of the 2d Station, 1. 19 and put the Sum 1.19 at the 
End of the crofs Bar in a Line with the 2d Station with the Letter W. 
to the Right of it, becauſe it is Weſt- Longitude. 

AGArx, the Lon "g of the 3d Station being unlike and greater, from it ſubtract 
the Long. of the 2d Station, placing the Diff. 1.04 at the End of the croſs Bar 
in a Line with the 3d Station with its initial Letter E. becauſe it is Eaſt Longitude, 


App the Longitudes of the zd and 4th Stations together, becauſe like or 


of the ſame Name, or in the ſame Column. And fo to the End of the Cloſe. 
ON waſte Paper take out theſe Numbers ſeverally as they ſtand, and multiply 
each into the Diff. Lat. in the fame Line with itſelf, and place the Product in 
the ſame Line with them in the N. Area or S. Area Column, by the following 
| Rule, deduced from the Theorems and Remark. 
The Survey taken. _ 1 1 on the Right-band. 
L 


Warex the Longitude is EAs r, put the Products in their proper Columns; 


but when WrsT, in their comrary Columns. 
Trar is E. x N. in the N. Area Column. * 
AnD - E. X S. in the S. Area Column. 
| Bur W. X N. in the S. Area Column. 
AnpD-'- W. Xx S. in the N. Area Column. 
Tus Difference of theſe Columns is double the Area of the Map or Cloſe. 
Tbe Field kept on the Lefi-bund. 
g&U L E- 
Wren the Longitude i is Easr, put the Products in Weir curry Columns; ; 
but when Wesr, , their proper Columns. Or ſhorter: | 
AST Es contr 
Right 6 But Left West — 
Ix the firſt Cloſe of the Field Bock, the firſt "Ay is of Weſt Longitude 


into Northing, and is by the Rule put in its ootiary Column, to wy The 


South Area Column. 


Azz the reſt being of Faſt Longitude into , Northings, or Laſt Longitade into 


Southings, are put in their proper Columas. 
THe Area Columns added feverally, their Diff. is donble the Area of the Cloſe. 
To Half of which add the Offsets as their Sign + or — directs: The Sum i is 


the Area of the Survey. 
NB. Tur Offsets of ſtationary Diſtances, which are common to two 


Cloſes, muſt be totalled by themſelves; and the Sum wich its FO FO — put 


into the Offset Column oppoſite to them. 
Of ſecond or ſucceeding Cloſes. 


Tux four large Columns of D. Long. N. Area, S. as and Offeers, are 


filled in all Reſpets as in the firſt Cloſe _ when hae are thus filled, it 
N . 1s 


— 


RIS" ARS: (> OY EO —_ 
— CEE IA I LINN z 

* „ CE >" * 4 
nme ẽZꝛp he 5 8 


25 . 
py Poe 21 9 \ 7 } _ N 1 PRs 1 
F * ? no; RT "\ . 1 ne 2 n — 

. N Web een, hn diane em Ent, J F N ene eee 
ARS, — * E * 2 e W Dr, re to. a 8 8 3 X CA Mach wi. pee 3 r 
rern % : . OR * mY . Derne nde "I * 9 * r — = x PS - 

K > \ x Ma” od AST Pn *. K. EN Nr ICE l " # "3d — des A ES * — 
:) te ET NE —˙* Sn, ano erin FFC 
* vs A * * oy, 1 Ca” I” N 4 8 Ge 8 * 2 
1 r a . . 1 * 3 2 Ya © DONOR LAG 
23 Le De wh, 
* 


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« CO ATI HAIR 9 2. * 
r 3 „„„„FFFFERE ; 


* 


y- 8 55 : 4 

* tt 
* "$4 

. 4 F 


%\A 


wa COT 


ne 3 * 
e OG AS 


= OS GR 
- 8 N 22 2 AE] Cx = . 1 25 

C7 e 2 e CESS DI 
J 5 ed reronig Og he on SG hed 
8 1 * A RS 


N 
v 60 . 
e PICs 
* N 1 3 ö 


n «<< 
* 

2 My 8 

yd oy _ 5 n 
2 7 EE 

* ms 46+, om” N52 
I 4 i, AS. 8 

* r ke SE 


7 RR WL 
Re 
ER GL geo 


NL 1 3 * ; 
V 3 K = — « * N 2 
© "RF n v5 N . ann PE ET. 
* S's TB 8 8 N 
2 . n r N K X * 9 n 2 oth o 
: - 5 * Nas 1 * þ 8 2 * F A N P ou dion er waa Repos 1 
5 p 2 > * 2 3 
RAS 


OO DU Er Pee ——— eg 
* wi, Claret Se e ESI SE 


th 5 | the greateſt Eaſe and Expedition. 


Li 4” 5 


3 1 
F * AC | a LA 


b 


Cloſe, as before. | NV IE 7 
Tus Offsets of the two ftationary Lines which lay in the firſt Cloſe, are 
alſo brought over and put in the Offset Column, but with contrary Signs 9 
what they had in that Cloſe, and added with the other Offsets of the Cloſe, 
which put to the Area of the Cloſe as their Sign or — directs, the total is 
the Area of the Survey. „„ | | 
In the third Cloſe, began at Station 5th of laſt, and ended at Station 6th of 
firſt Cloſe, Part being taken on the Right-hand; and Part on the Left in the 
Field; the Areas are collected and put in their proper or contrary Columns, as the 
Ruk i / / . 0% | | 
Bur Note, That Areas as well as Offsets, brought from other Cloſes, may be 
put into the contrary Column to that in which they ſtood in their firſt Cloſe, 
without conſidering the Rule: Becauſe two Cloſes cannot but lie on contrary 
Sides of a common Line. „ | mw 
N. B. It makes no Odds in the Plotting or in the Calculation how the Sur- 


LF vey is taken, whether in large Cloſes firſt, and then in leſſer ones, or in the 


ſmalleſt, that are neceſſary from the Beginning : For every meaſured Line is to 
be plotted or caſt up once, and only once. | : : 
In ſurveying Pemeſne Lands, Town Parks; Or various Diſtinctions of Ara- 


bie Paſture, Bag, Cc. in the ſame Farm, it is needleſs to chain every internal 


or ſubdividing Line; they are often as well taken by Bearings, Offsats, or 


other Remarks, as is uſuaſ in Practice. 


Bur theſe Sub- diviſions or Particulars cannot then be caſt up always by Cal- 


culation ſingularly. 


| Yer, when a Cloſe, the Area whereof is determined by Calculation, con- 
| fiſts of a Number of Sub- diviſions: If theſe are accurately caſt up by counting 


the little Squares or otherwiſe ; and the Difference between their Total and the 
W Area by Calculation, divided among th 


4 . 


Content, thay are in effect done by Calqulation. TY 3o 85 = 
Te prove the lun of a -Ubſt.- let be 
App or ſubtract every two adjacent Latitudes in the ſame Manner that the 


e Patticulars in Proportion to their 


38 Longitudes are here, and draw them into their intercepted Departure: They 
will produce the ſame Area. | | 


Anp the Latitudes might be univerſally nfed inſtead of the Longitudes; but 


: 7 have preferred the Longitudes, becauſe they ſtand next the outer Side an the 


Columns, which makes them eaſier added together. f | 
Tubus may the Calculation of an Eſtate or of a Country be carried on with 


J III 8 


tc 


NoveMBER 


: 
7 


\ 


11 


; F % 
NoveMBER 
— 4 0 4 — 2 
: LS | - 1 


(ir ) 
71h, 1768. ASURV E 4 2. Moyle Moſs, in the 222570 


Cz 


1 
1 * * Ly * 1 1 
4 f » 3 C 
: « H 2 = 
| . 


No. Stat. Bearings. Leſi-hand Oflsets, &e. 
Ne 
444 1 1 5 * i 1 854 
13 1 


12 5 | es Tx 
of waſte Paper be- 


in n the 5 ield Work. 


2 


Proceed from Stat.] firſt of laſt Cloſe . 05 o. 00 John Thomfon's. | o. oo 
1 JS. E. 46. along the Road. oz} 140.60]  _ ROE 
2 g SE. 147 | isl 212 1,00 5 
- 1 05 4 
0 5.00 


tween every two Cloſes | 


.o6 Avenue, 


—T 


:nto middle Park. 
30 : 


54 | | 


— N. ＋ S. 0,22 
+ B If IE W. 0.06 FS - 


Diſt, Right-hand Offeets, Ws N- S. 

. «000 05 Black Park. 0.00] ooo 
 $-08[0.90 4 
5.00 01551 [25 4.88 — 
Q: 510 N . 4.85 # 

1.50 . go to o Cabin, | 
2.601. 10. 
8.00 12 - 7a $4 | onom_—_ 


— 
[ 4 


N. E. 70 


— 
——— 1.21 
— — 

; 1.19 ö 
+1 


* E. ml. 


| 


SG 5» 


—_—_— 


* 9 


a 
LE (tc! tet es 


Taughboyn and County of 
| Double Long- N. Area. | 8. Area. Offsets. OPER 
3 e : 4 « 5 HA 
— | | | b 
| . a q 8 
| | | q 255 . Key 
2. 19 W. 5.7715 ſ—1.850⁰ If the Field Book be lar 
5 | | © Quarto, it will admit of Waſte 
; | i enough in this Place, for calling 
| up the Areas of the Cloſe. 
1.04 E. 7.5296 —9.7080 . | N 5 
5 . The Offsets will be done 
N detter on looſe Paper. 
7.98 E. 2.994100 0. 7060 
25.56 195.0228 | 
41.70 | 90.0720 —1.0800 
41.01 | 478.4867 + 5.5200 | - 
28.64 | t 3 
, 51 2656 — 3.9040 N ; 
; | 1 | 1 
9.52 41.8880 —8.9080 
| 2049464 667.3838 | —20,6360 The double Offsets. 
8 —— 5 "= 2 | 
| Areaof the Cl. 23.1 3187 | Sometimes it is convenient to 
Offsets - - = | — 1,03180 drop the Field Work of a Cloſe }þ 
EZ Hs 3 to take a Bog, a Park, or other 
Area of Survey] 22. 10002 Thing, and to return immedi- 
- — — agately again; ſuch, by Work. 
— | | may be circumſcribed as Paren- 
7-19 E. 49-9705 » ab and, if it be intended to 
— | be laid down by the Tables, 
| let the Parentheſis take in the 
1 Columns of diff. Lat. and De- 
1 6 parture, otherwiſe not. 
15.04 75-6976 : - In large Surveys, let the ' 
5 Latitude and Longitude of the 
T 4 firſt Station be alf ed ſo as to | 
| caſt the prime Meridian and 
| prime Parallel about the Centre 
| of the Lands. | 


Donegal, E art of the Eftate Hens — Haie. 5 


— —— ̃ QrCT— n+ — 


2 


1 | 1 EE 
* Diſt. Right dne. N. 5 S. ; E. | 
| 3-00 0. "Brook Call. — e | 
4+ 7 ö 
Ho 
1 6.20 | © + 1 7 
| Middle Park, 7.60 | .54 | $70 looks ent Ii 
ä r e 
f 5.00 Avenue, 15 4 
| 1 ö \ 4.76 555 by 
— * 5 — Seas | Cy | es ͤ — | i 
— 5 N. . 9 A : | x 4 +32 17.44 — 5 
| * | ; 4 6 2 
Cloſe at | Stat. 7th | of laſt Cloſe. 110.64 | .40 10.51 1.66 
So I 6.19. | 19.12] | 
+ N.—S, O.O1 | 1 
= +E. — W.o.04 
Return to| Stat. 5th [of laſt Cloſe. o. oo | | | 4 32 17. * 
213 18S E. . | 2.00 93 | 
| de Sluice Park. -| 437] 0 5 ? 28 4.26 * 
2 [S. W. 44 1% i Ge 30 21.70] 
| b 70 ' 
. r | 
3 E. — 1 '$ 4 1.00 | 590 | 5 J.89 8. 21 alt 1 
| | 3.00 | · . 1 | 
4 | ene 210.25 
4 N. FE. 4x | E | i 8.91 | 31-70 ; 
0 O. Oo - 1 
a Bullock Park N. W.. 70 3.70 SEA. | 5 
15 | 762 to Avenue. f 5.76 0 ö 2 N 
4. Horſe Ile Park o 9 . ob 2 f 
N. W. 78. 43 12.99 | to Avenue. | 29.5 5 1 
re — men enero wa Lud 8 Ede | „ 99 — 
MACE 5 3-44 3267] 
| 50 Oo i 25 
2 50 „20 72 
— — — — a 7-00 ea , * 6.71 - 
6 [N.W.487| 2 6 e _— | 
; | : 1 LY F k 0 40 f — N. ＋ — 0.02 . : 
1 - | g 80 1.40 + E. W. o. oa ; g 1 
| | 8 90 2.70 c e 5 ; 
«00 3.50 ty 7.86 21.89 "14 
| | 4-65 | 1.6g | 
Avenue, 6.44 
| of : 7.15 1.40 | 
7.60 | 0, | 
Stat. Ech of firſt Cloſe.] 11.69 | | | | 1 
3 


36.56 


+ 12.8120 


Brought from 


Area of the 


125. 6681 
1 99. 1536 


608. 8831 
218. 8217 


218.8217 


990-001 4 
19-5580 


409. 65794 


2.48597 


* 


Double Area. 
Daubie Offsets, | 


39-14 E. 
43-14 


53-14 
Brought from 


64-37 


63.38 


52.59 


EY.” 


|| 
794-9695 
425-2798 


— EDEN \ 
— — 
* — cn 
— 
- 


| firſt Cloſe, wo 


- + 8.4300. | 


24.2500 


Double Olkets 


*» 


1056.52 1 
1.3460 


„ 
» 


1 2 a 3 25 ; — — a — : * — - : — * 4 „ I} 70 — 
Double Long.| N. Area! "| 8. Area, | Offs, |- _ g . 
is , The Book, role, cet 
N and Station where yon begin, 
and where you end a Cloſe, is 
j punctually to be quoted; or 
. ESE ; 7 at leaſt thoſe Stations ſo well de- 
| e | ſcribedas to be readily f 4 
24.33 1 66.0343 | 7 | 05 —_— ) 
| ” * f 
5 . 5 
33-32 ' 158.6032 N 1 
＋ 2.4900 0093117: 
c | ＋ 4.2360 g 
f 384.2456 


Brought from the firſt Clofe. 
. Q £ 1» = 2 : 


Double Offiets; 


: 
> 
2 
KY 
* : 
[ 
= 
7 3 
* 3 
: 4 
; 
= 


t From the ad Cloſe 


A ' i b 
25-5200 [ Brought from the laſt Cloſe. 
; ; 7 1 , PO he . 1. x 
| þ 1 
+ 
1:4 
1 22 
1 2 | 7 1 
1 WE 7a 1 * | 
f Fr ICS 
: t x07 
* i [ 


1057.4081 | 


= Ara of ns x | c 
Pune} £300.73} HOOR: 
: 4 75 Tp 
; _— : 1 
4 4 * 1 £1 


| I..0000 90044 | 1. 000 1 59999 „0321 * >a 
2.0000 ,0087 ||: 1.9999 0175 || 1.9998] ,0262Þ | 
2.0000 „0131 2-9999 ,0262 || 2.9997 | 0293 1 | 
4. 000 ,0175]| 3-9998] 0249 || 3-9997| 30524f | 
5.0000 | 20218 4.9993 0436 4.9996 . „0684 
59999 5252 5.9998 „024 5.9995 785 
6.9999] »2305|| 6.9997 „611 6.9994] „o 
7.9999] „349 7.9997| 0698 || 7.9993] »104) 
8.9999] »2393|| 8.999 0785} 8.9992 „11780 
9.9999] 0436 9.9996 28878 9.99914 1309 | 
10.9999] 0480||10.9996| 2960 10. 9991 _— 
11.9999] +0524 [11-9995 41047 [11.9990] „1571 
12.9999] „0867 12.9996 »1134 12.9989 1702} 
1413.9999] „06110 13.9995] 1222 [113.9988] 1833 
1 14.9999] 0654 14.9994 21329 [| 14.9987 BUS a: Ho 
16115.9998] 5598 5.9994] 51390 [| 15.9986} 22094 
17] 16,9998] „0%42 16.9994 14846 9985] 2225| 
| 18/17.9998] ,0785||17-9993] 51571 [[17 9985] 2356 
| 19|18.9998] ,0829|[18-9993 ,1658 [118.9984| +2487 
| 20119.9998] ,0873[|19-9992|_+1745|| 19.9983] 2618]. 
| 27 [20.9998] „5916 20.999] 21533 [120.9982] 2499 
22 [21.9998] „09 21.999 1920 [121.9981]. ,2880| 
| 23[22.9998] ,r004[|22.9991] 22997 1122.9980] 3011 
| 24[23.9998] 10471|23-999! »2094-[|23-9979] 3142 
| 25|24.9998]__*10911[24- 9990|_22182 24.9979|__ 3272 | 
| 2625-9998] 1134 2.999 25.9978] | ,3403 
226.999) „17780 26.9990 2356 26.9977 3534 
26027. 999% 1222 27.9989] 52443 [[27-9976] 3665 24 
290 28.999) +1265||28-9989| 253 28.9975] 379% 5 "8 
2 20129.9997] 1309[[29.9989|__226151|29:9974|_ +3927] | . 
130.9997 5135311 30-9988] 22795 [[30.9973] „4% 
| 32121-9997 | ,1 39611 31-9988 22792 [31.9973] 41890 


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23132-9997] „1440, 32-9987] 22550 1132.9972] 40% 6 
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47 40.999 „ 178940.9984 73575 40.9965 5367 „ 1 

42 41.9996 „1833441. 9984 3665 41. 99644 5498 | 


| 42[42-9996] 418761[42.9984| „3752 4299630 520 
44.43.9996 - 319201143-9983] . 3849 [143-9962] 55% 
| 45144-9996]__»1963 44-9983] +3927 1144-9961} +5599 
| 46145-9996] 2007 45,9982 „4014439961 +6021 
i} 47 46-9995] 92052 146.9982 | „4101 ||46-9960| „6152 
4847.99 s 20944): 9982 4189 4.9959 6283 


149 48.9995] „2138 $66... off 4.276 [143.5958 
| £0149.99951 _,21821149.99811 +4363 1149-9957} | 


+1 90 HL $2 
9 52.9931] 444511; 59. 995. 
51.9995] „22690[ 61.958] 4535[| 51-995: 
72.9995 »23131|52-9989] 462552 9955 
53.9995] »23561153-9979] © +47 1211 53-9954 
4.0995] _+24921154-9979] _ 248221 154-9953] _27 199 
;5 9995| 2443/5997 +48371| 55-9952 
56.9995 »24871|56 9973] +49741[55-9951| 
57.999 f] »2531][57-9975] +526111 57-9950 
-3.9994| »2574||58-9978] 51498 9949 
-9.9994|__+26181| 59-9977] _52361| 59:9949| _ 2 
55.9994] »26621162-9977] »5323]| 00.9945 
51.9994 »27051[61.9976] „54100519947 
32.9394] »2749|162-9976] 5498 62.9946 
53.9934] 27930639976] „558563.9945 
54 9994| _+2836[164-9975| 88224945 
55.9994 »2880[|65-9975] »57551105-9943 
56.9994 +2923||66-9974] 5847 65.9943 
57.9994] „29676799744 5934/79942 
58.9993] 73011 68.9974 „602 1J][68.9941 
| 39.9993|__+3954|\69:9973] _»610c 29249 
19.9993] »3099| 79-9973] ,619t1179-9939 
11.9992] »3142|;71-9973] ,628: [171-9939 
72.9992] »31851\72-9972] »637c1}72-9937 
73.9993] »32291| 73-9972 »645<117 3-9937 
[74-9993] 327 \74-9971] +<654<1174-9926 
15.9993] »3316[175 9971] ,663:1|75-9935 
16.9993] „33607699710 ,671c[170 9934 
17.9993] »34931[77-997v] 6807 [779933 
78.9992 +3447 [78.99% ,6394[78-9932 
79 9992] +3491|[79:997C] ,699 11179-9921] 
30.9992] 35345969 ,706t [150.9931 
31.9992] 3578 [61.9969] ,7156]|51 993 
32.9992] ,3622 [82.9968 ,724: [32-9929 
33 9992] 3665 83.9968 ,733c[53-9925 
34.9992] +3709 . 1741811 94-9927 
35.9992] 3752 85.9967 „750 8.9926 
36 9992] ,37961[36-9967] ,75921[36-9925] 
b| 37.9092 „3840 87.9966] ,767c1| 37-9925 
$8.9992] „2883 88.9966 57767 88.9924 
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90.9991] , 39719. 9905 ,7941 [199-9922 
31.9991] 44014 91.9963] .802t [191.9921 
32.9991] „4058 [92.9962] ,81161][92-9920 
33-9991] „4102 [93.9964] ,820: 1193-9919 
954.999 1 4145 [24.2984] _,829c [194-9919] 
95.9991] 418995. 9902] „8377 1195-9916 
96.9991] ,43321196-996:} 846 1196-9917 
97-9991] 4427: [197-9965] 4855: 1197-9916 
98.9991] ,4320|198.9962} ,863c [195.9915 
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RR 
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% 


No 1 89 || 1; | 88: . 
1] »999t| „5175 .999 „02160 „999 02621] 49995 
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61.2784 
62.2668 
63.2331 
64.243 


67. 2086 
68.1969 


69.1853 


51-3250} 


65.2319 
66.2202 


10.0401 
10. 1923 
10.3444 
10.4965 
10.6486 


170.2201 


173-1872 
174-1762 


86.0444 


71.2091 


72.1982 


75.1652 
76.1542 
17-1432] 
78.1322] 


80.1103 


81.0993 
82.0883 


33.0773 
84. 84.0663 


85.0554 
87.0334 


88.0224 
89.0114 


79.1213 


10.4945 
10.64.23 
10.7901 
10.9379 
11.0857 
11.2335 
11.3873 
11.5291 
11.6769 
11.8248 
11.9726 
12.1204 
12.2682 
12.4160 
12.8638 
12.7116 
12.8594 
13.0072 
13.1550 
12.2028 


— 


70.1737 


71.1620 


72. 1504 
73.1388 
74.1271 
75-1155 
76.1038 


77.0922 
78.0806 


| 79.0689! 


80.0573 
81.0456 


82.0340 
83.0224 
84.0107 


85.9875 
86.9758 
87.9642 
88.9525 


84.9991 


10. 8008 
10.9529 
11.1050 
11.2571 
11.4093 
11.5614 
11.7125 
11.8656 
12.0177 
12. 1699 
12.3220 
12.4741 
12.6262 
12.7784 
12.9305] 
13.0826 
13-2347 
13.3869 
13-5390 
12.6911 


90.1144 
91.1047 


J 92.0949 


93.9852 


2194-27 55 


95.0657 
96.0560 
97.0463 
93.0365 


99.0268 


12,9431 


13.2214 


12.6648 
12.8039 


13.0823 


13.3606 


I 2.4998 | 


13.6390 
13.7781 


90.058 3 
91.0479 
920376 
93-0272 


94.0169 
95.0065 
95.9962 
96.9858 
97-9755 


12-9173 


98.9951 


13.0578 
13.2013 
13.3448 
13.4883 
13.6318 
13.7753 
13.9188 
14.0623 
4.2058 


14-3493 


— 


96.9235 


99.0004. 
90.9895 
91.9785 
92.9675 
93-9505 
94.9455 
95.9345 


97.9126 


13.450) 
13.5985 
13.7463 
13.8941 
14.0419 
14.1897 
14.3375 
14.4853 
14.6331 


89. 9409 
90.9293 
91.9176 
92.9260 
93-5943 


13.84 32 
I 3-9954 
14.1475 
14.2996 
14.4517 


94.8827 
95.8711 
96.8594 
97.8478 


98.8362 


14.6038 
14.7560 
14.9081 
15.0602 
13.2123 | 


98.9016 
E 


14.7 809 


N 3 * 
— — RAUL i See ſo — - — n 
Rare” 


e 


2 
8 


9 


94 


9 


802 


3.9508 
4.9384 


29877] + 
1.9754 
2.96311 


79870 


1.9740 
2.9610 


3.9480 


4.9350 


OO 


10.8646 


5.9261 
7.9015 


6.9138] 
8.8892] 1. 


9.8769 


11.8523 
12.8399 
13.8276 
14.8153 


5.9220 
6. 9090 
7. 8960 


8.8830 
9.8700 1. 
10.8570 1. 


11.8440 
12.8310 
13.8179 
14. 8049 


10.8491 


15.8030]. 


16.7907 
17-7754 
18.7661 
19.7538 


20.7415 
21.7291 
22 7168 
23. 2045 
24.6922 3. 


25.6799 
26.6676 
27.0553 
28.64.30 
29.6306 


42.4706 


30.6183 
31.6060 
32-5937 
33-5814 


34.5691 - 


35.5568 
36.5445 
37-5322 


38.5198| 
29.5075 


40.4952 
11.4829 


43-4583 


44.4460 


43.4337 7. 


46.4214 
47.4000 
48.3967 


49 3344 


15.7919 
16.7789 
17.7659 
18.7529 


22229 2842 


20.7120 


20.7269 
21.7139 
22.7009 
23.6879 
24.6749 
25.6619 


26.6489 4. 


27.6359 
28.6229 
29.6099 
30.5969 
31,5839 
32.5709 
33-5579 


34-5449 


35-5319 
36.5189 


37.5059 


38.4929 


224222 
40.4669 


41.4538 
42.4408 
43.4278 
44.4148 
[145.4018] 
46.2888 
47.3758 
48.3628 


49. 24.98 


* 


329.5886 
130.5749 


22334/442829 


59863 
1.9726 
2.9589 
3-94 51 
4.9314] 
5.9177] 
6.9040 
7-8903 


9.8629 


11.8354 
12.8217 


13. 8080 


15.7806 
16.7669 
17.7531 
18.7394 
19.7257 


21.698 3 
22.6846 
23. 6709 
24.0571 
25.6434 
26.6297 
27.6160 
28.6023 


31.5611 


33-5337 
34.5200 


8.8766 


14.2943 


32.5474 


23301 
24951 
„6602 


58252 


59903 
1.1553 
1.2204. 
I-48 54. 

1.6505 
1.8155 
1.9806 
2.1456 
2.3107 

2.4751 
2.64.08 
2.8058 
2.9709 
3-1359 


3.4660 
3.6310 
3.7961 
3.9611 


4.2912 
4.4563 
4.6213 
4.7864 


g. 1165 


5.2815 
5.4466 


5.7767 


51650 


gt 
+9856 
1.9711 
2.956) 
3.9422 
4.9278 


3321 


4.1262 


4.9214 


5.6116 
344945 


35.5063 
26.4926 


38.4651 
39.4514 
40.4377 
41.4240 
42.4103 
43.3966 


37.4789 


5.9417 
6. 1068 
6.2718 
6.4369 
6.6019 
6.7670 
6.9320 
7.0970 
7.2621 
7.4271 


5.9133 
6.8989 
7.8844 
8.8700 
2.8556. 
10.8411 
11.8267 
12.8122 
13.7978 
14.7833 
15.7689 
16.7545 
17.7400 
18.7256 
29-7001 
20.6967 
21.6822 
22.6678 
23.6533 


24. 659 4 


25.6245 
26.6100 


27-5956 
28.5811] 


30.5522 
31-5378 
32.5234| 
33-5089 


25.4800 
36.4656 
37.4511 
38.4.267 
22.4222 
40.4078 
41.3924 
42.3789 
43.3645 
44-3500 


45.2691 
46.3554 
4.7-3417| 
48.3280 


7.5922 
7.7572 


79223 
8.0873 


49-3143] 


8.2524 


48.2922 


45.3350 
46.3211 


47.3067 


49.2778| 


29. 5667 [_5:0905 


* | 


8 


50.3721 
51.3598 
52.3475 
33.3352 
54.3229 


8.1246 
8.2910 
8.4475 
8.6030 


[55-3105 


56.2982 
57-2859 
58.2736 


59.2613 
60.2490 
61.2367 
62.2244 
63.2121 

64.1997 
65.1874 
66.1751 

67.1628 
68.1505 
69.1382| 
10.1259 

71.1136 
72.1012 


73.0889 
74.0766 


75.064 
76.0520 
77-9397 
78.0274 
79.0151 


80.0028 
80.9904. 
81.9781 
82.9658 
83.9535 


8.700; 
8.9168 
9.07 32 
9.2296 
9.3861 
9.5425 
9.6989 
9.8554 
10.0118 
10.1682 


10.3247 | 


10.4811 
10.6375 
10.7940 
10.9504 
11.1068 
11.2633 
11.4197 
11.5762 
11.7326 
11.8890 
12.0455 
12.2019 
12.3582 
12.5148 
12.0712 
12.8276 
12.9841 
13.1405 
13.2959 


88.8919 


84.9412 
85.9289 
86.9166 
87.9043 


2593.8 304 


89.8796 
90.8673 
91.8550 
92.8427 


94.8181 
95.8058 
96.7935 
97.7811 


13.4534 
13.6098 
137662 
13.9227 
14.0791 
14.2355 
14-3920 
14.5484 
14.7048 
14.8613 
15.0177 
15.1741 
15.3306 
15.4870 


7.9702 


98.7688 


15.6425) 


50.3368 
51.32.38 
52.3108 
53.2978 
34.2848 
55.2718 
56.2388 
57.24.58 
58.2228 
59.2199 
69.2068 
61.1938 
62. 1808 
63.1678 
04.1548 
65.1418 
66.1288 
67.1158 
68. 1028 
69.0897 


TEE! 


8.1979 
8.3586 
8.5194 
8.6801 
8. 8408 


9.0016 
9.1623 


9.3231 


92 


Fo.” 


9+ | 89% 


50. 3006 
51.2869 
52.2731 
53-2594 
5424.57 


8.4174 
8.5825 
8.7475. 
8.9126 


9.4838 
9.6446: 
9.8053 
9.9660, 
10.1268 
10.2875 
10.4483 
10.6090 
10.7698 
10.9305 
11.0912 
1t.2520 


65.0948 


36.2183 
37.2046 
58.1909 
59.1771 


35.2320 


9.242) 
9.4077 
9.5728 
9.7378 
9.9929 


00.1634 
61.1497 
02.1360 
63. 1223 
64.1086 


10.0679 
10.2330 
10.2930 
10.5630 
10.7281 


66.0811 
67.0674 


68.0537 
69.0400 


10.8921 
IT.OG82 
I1.22 32 
11.3883 


11.8833 


70.0767 
71.0637 
72.0507 
73-0377 


74-0247 


75.0117 
75.9987 
76.9857 
77-9727 


78.9597 


79-9467 
80.9337 
81.9207 
82.9077 
83.5947 
84.8817 
85.8687 
86.8557 
87.8427 
88.8297 


11.4127 
11.5735 
11.7342 
11.8950 


12.0557] 


12.2164 


12.3772 


12.5379 
12.6987 


13.0202 
13. 1809 
13-3416 
I 3.5024 
13.6631 
13.8239 
13.9846 
14.1453. 
14.3061 
14.4668 


12.8594 


89.8167 
90.8037 
917907 
92.7777 
93-7047 
94.7517 
95.7387 
96.7256 
97.7126 


98.6996 


14:0276 
14.7883 
14.9491 
15.1098 
[15-2705 


15.5920 


15.7528 | 


15.9135 


15.4313] 


70.0263 
71.0126 
71.9988 
72.9851 
13:97 14 


11.7184 
11.88 34 
12.048 
12.2135 
12.3786 


9.0776 


3 — 


59.2024 
51.2489 
52:2345 
53.2200 


95-1911 
56.1767 
57.1623 
58.1478 
59-1334 
60.1189 
61.1045 
62.0990 
63.0756 


| 04.0611 


65.0467 
66.0323 
67.0178 
68.0024. 


168.9889 


69.9745 
70. 9600 
71.9456 
72.9312 
73-9167 


54.2056 


9.3142 


9.0529 
9.8223 
9.9916 
10. 1610 


10.4997 
10.6690 


10.8384 
11.0077 


11.1771 
11.3464 
11.5158 
11.6851 


12.0238 
12.1932 
12.3625 
12.5319 
12.7012 


11.845 


8.63685 
8.8062 


8.9735 
9.14499 


10.3303 


74.9577 
75.9440 
76.9303 
77.9166 
78.9028 
79.8891 


80.87 54 
81.861 


82.8480 
83.8343 


12.54.36 
12.7087 


12.8737 
13.0388 
13.2038 
13.3689 
13.339 


7113-6990 


1 3.8640 
14.0290 


34.8206 
85.8068 
86.7931 
87.7794 
88.2582 
89.7520 
90.7353 
91.7246 
92.7108 
93.6971 


14.1941 
14.3591 
14.5242 
14.6892 
14.8842 
15.0193 
15.1844 
15.3494 
15.5145 


15-0795 


946834 
95.6697 
96.6560 
97.6423 


15.8446 
16.0096 
16.1747 

6.3397 


14-9023 
75.8878 


12.8706 
3.0399 
1. 2093 ; 
13.3786 
13.5480 


81.8012 


82.7867 
(182.7723 


84.7578 
85.7434 
86.7289 
87.7145 
88.7000 


14.2254 


14-3947] 


14.5641 


15.0721 


13-7173] 
13.8867 
14.0560 


14.7334 
14.9028 


15.2418 


89.6856 
90.6712 
91.6567 
92.6423 
92.6278 


15.4108 


15.9189 
6.0882 


15.5802 | 
15.7495} 


94.6134 
95-5989 
96.5845 
97.5701 


16.2576 


16.4269 
16.5962 
16.7656 


q 


N 


16.0742 


1 
98.6286116.5048 


98.5556 


16.9250 


—— * 
5 « FP 
1*„ — 


———— 
—— 


„ 
” 


I WORN. —„—- BI. HP LI Ai Brag — 3 
Rr Lv Dy 


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9 


Z | 
8 1 


12 


< |= | | 
[OO ex calm + ww 0d = 


9848 
1.9696 
2.9544 
3.9392 


| 4.9240 


5.9088 
6.8937 
7.87855 
8.8633 


10.8329 
11.8177 
12. 8025 


13.7873 
14.7721 
15.7569] 


16.7417 


17.7265 


18.7113 
19.6962 
20.6810 
21.6658 
22.6506 
23.6354 


25.6050 
26.5898 


9.8481 


1736 


23473 
55209. 


56946 


„58682 
1.0419 


1.2155 


1.8628 
1.236 
1.9101 
2.08 38 
2.2574 
2.4311 
2.6047 


3.6466 


3.8203 
39939 


4.1676 


24.6202 4.3412 


4.3149 
4.6885 


27.5746 4. 8621 


28.5594 
29.5442 


30.5290 
31.5138 
32.4987 
33.4835 


35.4531 
36.4379 
37.4227 


39-3923 


38.4075| 


5.0358 


5.2094 | 
30.5053 


5.3831 
5.5567 
5.7304 
5. 9040 


34.4683Þ_0.0777 


6.2513 3 
6.4250 
6.5986 
6.7723 
6.9459 


n 


1.3892 


10 | 80 | 102 79 | 


9840 
1.96811 


2.9521 
3.9362 


4.9202 | 


5.9042 


6.8883 1 


7.8723 
8.8564, 
. 9.8404 
10.8244 
11.8085 
12.7925 
13.7766 


14.7606 
2.7784 
2.9520 
31257 
3-2993 | 
_3:4730 []19-9005 


15.7447 


16.7287 


17.7127 
18.6968 
19.6808 


20. 20.6649 


21.6489 


22.6329 
23.6170 


24.6010 
125.5851 


26.5691 
275531 


28.5372 


29.5212 


31.4893 


32.4733 
33.4574 


34-4414 
35-4255 
36.4095 


37-3935| 


38.3776 


39.3616 


51779 

73359 

75338 
5711 


1.4235 


1.9574 
2.1353 
2.3133 


2.4912 | 
14.2488 
15.7321 


2.6692 


2.8471 
3.0250 


3.2030 
3. 3589 


22859 


3.7368 

3.9148 
4.0927 
4.2706 
44486 


4.6265 
4.8045 
4.9824 
5.1614 
5.3303 
5.5102 
5.6942 


5.8721 


6.0501 
6.2280 
6.4060 
6.58.29 
6.7619 
6.9298 
LIIII 


40.377 


41.3619 


42.2467 
43-3315 
44-3163 
45.2012 
46.2860 
47. 2708 
48.2556 


49.2404 


7.1196 
7 29232 
7.4669 
76405 


7.8142 


7.9878 
8.1615 
8.3351 
8.5088 


40.3457 
41.3297 
42.3138 
43.2978 


44.2818 


45.2659 
46. 2499 
47.2340 
48.2180 
49.2020 


7.2957 


7:47.36 
7.6516 


7-9295 
_ 8.0075 


8.1854 
8.3033 


8.5413 


8.7192 


3 


12 


102 


98330 
1.9665 
2.9498 


| 3.9330 


1 1.7991 
13.7656 
16.7153 


17.6986 
18.68 18 


28897 [21532212 
1.0677 || 


2456 


3.8998 
6.8828 
7.8660 1. 
1.6015 


1.7194 


8.849 
9.8325] 
10.8158] 


12.7823 


20.6484 
21.6316 
22.6149 


123-5981] 


} 


37.3637 


27.5311 
28.5144 

29.4970 
20.4809 
31.4642 


33.4307 


36.3804 
38.3469 


40.3135 
41.2967 


43.2632 


45-2297 
46.2130 


47.1962 


2.99 


32.4474 


42.2 800 


144-2405 


48.1795]. 8. 


| 10% 


24.8814 59 
25.5646 5646 
26.5479] 


34.4139. 
35.3972 


32.3302 | 


49.1627} 


126.5262 
27.5086 
28.4911 
—22.4233(—. 
30.4560 7 


18.6666 
19.6490 


33.4033 


39.2980 


43.2278 
44-2103 


47.1576 


9825 
2.9474 


| 3.9299 ; 
| 4.9123] 

5.8947 
6.8772 
28590 


8.8421 


10. 8070 
11.7894 
12.7719 
13.7543 
14.7268 _2-7979 
115.7192 


16.7017 
17.6841 


20.6315 
21.6139 


22.5964| 4- 
23.5788 


24.5612 


. — * 


25.5437 


31.4384 
32. 4209 


* 
35.3682 


36.3507 6. 
37.3331 


38.3156 
40.2805 


41.2629 
42.2454 


45.1927 
46-1752 


48.1401 


1.9649] 


I 
+> 
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— 


4 


8.6824 


8.8222 


49.1225 


the th 


* 
as 


8 


* 


1 18 


50.2292 
51.2 100 
52.1948 
53-1796 
54-1044 


55.1492 
56.1340 
57.1188 
58.1037 
59.0885 


60.07 33 
61.0581 


62.0429 


63.0277 
64.0125 


| 66164-9973 
7165 9821 


66.9669 
67.9517 
68.9365 


| 80 
8.8561 
9.0297 


9.2034 
9.3770 


9.7243 
9.8979 
10.0716 
10.2452 
10.4189 
10.5925 
10.7662 
10.9398 
11.1135 
11.2871 
11.4608 


11.6344 
11.8081 
11.9817 
12.1554 


2:5597| 


69.9213 
70.9062 
71.8910 
72-8758 
7 3. 8606 


12.3290 
12.5027 
12.6763 
12.8500 
I 32.02.26 


74.8454 
75.8302 
76.8150 
17-7998 
78.7846 


13-1973 
13.3709 
13.5446 
13.7182 
13.8919 


79-7094 
80.7542 
81.7390 
82.7238 
83.7087 


14.0655 
14.2392 
14.4128 
14.5864. 
14.7601 


10+ 


[| 10+ 


797 


50.1861“ 


51.1701 
52.1542 


53.1382 
eg 


54.1222 
55.1063 
56.0903 
57-0744 
58.0584 
159-0424 


61.0105 


62.9786 
63.9626 


64.9467 11.7443 


65.9307 
66.9148 
67.8988 
68.8828 


60.0265 


61.9946 


11.9222 
12.1002 
I2.2781 
12.4560 


50.1460 
51.1293 
52.1125 
53-0958 


55.0623 


56.0455 
57.0288 


58.0120 


60.9618 
61.9451 
62.9283 
63.9116 


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[No] 30 | 6o [ 30s | 594 | 30+ | 59+ || 30+ | 

1 ,8660] ,5000|| ,8638þ „5038 ,8616] ,5075|| 8594] „5113 
2| 1.7321] 1. 0000 1.7277] 1.0075] 1.7233] 1.0151 1.7188] 1.0226 
3] 2-598] 1.5 , || 2.5915 1.51131} 2.5849] 1.5226 2.5782] 1.5329 
4| 3-4641] 2. | 3-4553| 2.0151 || 3.4465] 2.0302 3.4376 2.0452 
5. 4.33010 2-5 J 4.3192 2.8189 4.3081] 2.8327“ 4.2970 .2-5565 
6 5.1952 3.0000 [ F. 1830 3.0226 5.1698] 3.0452 5.1564] 3.0678 
5 6.0622] 3.5 6.0468| 3.5264 || 6.0314] 3.5528 6.0158 3-5791 
8| 6.9282| 4. 6.9107|. 4.0302] 6.8930] 4.0603]] 6.8753] 4.0903 
gf 7-7942] 45 || 77745] 4.5340 7.547 4.5678 7.7347 4.6016 
100 8.5503 5. 8.5384 5.0377 || 8.6163] 5.0754|| 8.5941] 5-1129| 
11] 9.5263] 5.5000 ||. 9.5022] 5.5415] 9.4779] 5,5829 9.4535 5-6242 
12 10.3923 6. 10.3660] 6.0453 [10.3396 6.905 [}10. 3129 6.1355 
13 11.2583 65 11.2299 6.5491 |j11.2012| 6.5980||11.1723] 6.6468 
1412-1244] 59, 12.0937] 75.0528 ||12.0628| 75.1055||12.0317| 7.1581 
15|12.9904] 7.5 12.9575 7.5566 ||12.9244| 7-6131||12.8911| 7.6694 
16|13.8564|. 8.0000 13.8214] 8.0604 [f13.7861| 8.1206|| 13.7508 8.1807 
-17|14.7224| 8.5 14.6852] 8.5642 14.6477] 8.628 214.6099 8.6920 
18 15.5885 9. 15.5499] 9.0679 15.5093 9.1357 15.4693 92033 
19 16.4545 9.5 16.4129] 9.5717 [16.3710 9.6432 16.3287] 9.7146 
| :20]17. 3205] 10. [17.2767]10.0755|[17.2326[10.1508|| 17.1881] 10.2259 
| 2118. 1664 10. 500018. 1405 10.5792 18.0942[10.6583}| 18.0475 10.7372 
| | 22 [19.0526|17. 19.0044 [11.0820 j[18.9558[11.1658|| 18.9069] 11.2484 
| '23|19:9186j21.5 19.8682 11.8868 [19.8175 11.6734 19.7663| 11.7597 
| 2420.784612. 20.732112. 0906 20.6791 12. 1809 20.6258 12.2710 
| 25 21.6506|12-5 21.5959 12.5944 21.5400 12.6885 21.4852] 12.7823 
| 2622.516713. 000 [224597 13.098 1 22.402413. 1960 22.2446] 13-2926 
27 23.382713.5 23.3236 73.6019 23.264013. 703523. 2040 13.8049 
2824.248714. 24.187414. 1037 [24.1256 14.2111 24.0634 14.3162 
2925.114714. 25.05 12 14.6094 (24.987214. 186 24.9228 14.8275 
3025.980815. 25.9151[15.1132 [25.8489 1.2262 2.78221. 3388 
3126.846815. 5000 [26.7789 15.6170 [26.7 1051.733726. 64 160 15.8 501 
| 3227.712816. 27.6427 16.1208 ||-27.5721]16.2412||27.5010| 16.3614 
; '33]28-5788[16.5 1[28.5066[16.6245 [|28.4338|16.7488|| 28.3604 | 16.8727 
3429.444917. 29.370417. 1283 [29.2954 17.2563 29.219817. 3840 
| _35]39:3109]17:5 _ [[30.2343[17.632r [[30-1579[17.7628|| 30.0792[17-8953 
| 3631.176918. 0000 [31.098 1018. 1359 [[31.0187[18.2714 || 30. 9386 18.4066 
| 1 27132-0429] 18.5 31.9619 18.6396 || 31.8803|[18.7789|[31.7980| 18.9178 
3832.909019. 32.825719. 1434 [32.7419 19.2865 32.6574 (19.4291 
3933.775019. 5 33.6896 19.6472 33.6035 19.7940 33.5168 19.9404 

40 34.641020. 34.553420. 1310 [34.4652 20. 2015 34.3763 20.4317 ; 


41 | 25.5070] 20.5090 [35-4173 20. .6547 [35.2268 20.8091 (35.2357 20. 96 30 
4236.373121. 36.281121. 1385 [ 36.188421. 3166 26.0951|21.4742 
43372391 21.5 37 1449 21. 6623 [370501218242 36.9545 21.9856 
4438.105122. 38.0088 22.1661 [37.9117 22.331737. 3139 22.4969 
 45138.9711|22.5 38.8226 22.6698 [| 38.7733] 22.8292 38.6733 6733 22.0082 
4639.837223. 000 35 7364 23. 23-1736 ||29 6349 23.3468 39. 5327 23 5195 
4740. 7032 23.3 [40.6003 23.6774 [40.4966 23.854 31] 40.3921 24.0308 
4841.559224. 41.4641 24.1812 [41.3582 24.361841. 2515 24.5421 
49 42.4252 24.5 42.3279 24.6849 42.2198 24.869442. 1109 25.0534 
5014.351325. [143.1918 25.1887 [[43.0815{25.3769142. 9703! 25 8647 


| 


3 


No] 30 | 60 || 30 | 594 || 30+ [597 || 394 | 59 
51044. 167325. 500044. 0556 25.6925 [43.9431 23.8845 [43.8297 26.0759 
52045033326. 44.919426. 1962 [44.804 26.3920 44.689 126.5872 
 53145-8993126-5 45.783326. 0004.666326. 5995 45.5485127-2985 
5446.765427. 46.64) 12). 2038 46.528827. 40% 146.4092. 8 
55047 6314\27.5 __ 5 47-5110[27.70761[47.3896|27.9146 [47-2674 28.1211 
_ 56148.4974. 28.0000 48.3748|28.2113|148.2512|28.4222[148.1268 28.0324}. 
57149. 363428. 5 49.2386 28.7131 [[49. 1129 28.9297 [48.9862 29.1437 
5850.229529. 50.102529. 2189 49.9745 29.4372 [49.8456 29.6550 
5951.095529. 5 50.9663 29.7227 [50.8361 29.944850. 705030. 1663 
60051. 9615130. 51.8301[30-2204 |[|51.6978| 30.4.523[| 51.5044}. 30.6776 
6102.827530. 500052. 6940 30.7 302 [|52.5594| 30.9598 52.423831. 1889 
6253.693631. 53.557831. 2340 [53.42 100 31.4674[53.2832 31. 7002 
630/54. 4596031. 5 54.42 16031. 737 854.2826031. 9749 54.1426032.2115 
645.4256 32. 55.2855 32.2415 [55.1443 32.48 25 (55.002032. 7228 
6586.291732. [86.1493 32.2483 (5.0089 32.9900 [ 55-8614 [33:2341 | 
66157-15771 33-0000[|57-2131] 33-2491 [156.8675] 33.4975 [56.7208 033.7453 
67158.02371j 32.5 57.8770133.75291157-7292| 34.005 17.580234. 2566 
6858.889734. 58.740834. 2566 58.5908 34.5126 58.439634.7679 
69159-7558; 34-5 59.6046 34.7604 [|59-4.524} 35-0201 || 59.2990| 35-2792 
70460. 6218 35. 60.4685125-2042 [160.3140|35.5277|| 60.1584|35-7995 
71161 4878 35.5000 61.3323 35.7680 61.1757 36.0352||61.0179| 36.3018 
7262.353836. 62. 1962 36.2717 [62.0373 36.5428 61.8773 36.8131 
73 63-2199|30.5 063. 05⁰⁰ 36.7755 62.898937. 0503 62.7367 37.3244 
74.64.0859 37. 63 733557 2793 [63.760637.857863.596137·8357 
75164-95191 37-5 64.7877 37-7831 [64.6222 38.064 64.4585 88.3470 
76165 8179 38.0000 65.65 15 38.2868 | 65.4838 38.5729 65.3149 38.8583 
. 77166.6840|38-5 |[66-5153138.7906 [| 66.3454] 39-0805|[66.1743] 39-3696 
78167.5509] 39- 67.3792 39-2944 || 67.2071 | 39-5880|[67.0337 | 39-3809 
79168.4160| 39.5 68.24.30| 39.7981 || 68. 0687 40.0955 67.893 140.3922 
8069.282040. 69.1068 40.3019 68. 68.9303 [42.6031 |168.75251[40-9034 
81070. 148 1040. 500069. 970% 40. 8057 [[69.7920!41-11061|69.6119|41.4147 
8271.014141. 70. 834541. 3095 [7o.653641.618 1070.471341. 9260 
8371.880141. 5 71.6983141.8132||71.5152142-1257||71.3307 [42-4373 
84172.7461[42. 72.562242. 3 170 ||72.3769142.6332|| 72.1901 [42-9486 
85.22.6122 42.3 |173:4260[42.8208 [| 73.2385143-14981[73.0495143-4599| 
86174-4782[43.0000[[74-2899[45:3246 [[74-1001[43-64831[73-9090[43-97 12 
$7175-3442[43-5 |[75:1537[43-8283 [[74-961744-1558[{ 74-7684 [44-4825 
8876.210244. 76.0175 44.3321 75.8234 44-6634 |} 75-0278 44.9938 
89]77.0763[44.5 76.8814 44-8359 76.6850 45.1709 76.487245. 5051 
99177-9423[45. _[177:7452145:3397 ||77:5466[45:07851|77-3466[46:21 64 
9178.808345. 5000/8. 6090 45.8434 [78.408 346. 186078. 2060 46.5277 
9279.674346. 79.472946. 3472 79.2699 46.6935 79.065447. 0390 
93,80. 5404. 46.5 80.3367 46.85 1080.13 154.2011 79.924847. 550g 
9408 1.406447). 81.200547. 3548 [80.9931 4). 708680. 7842 48.0616 
282.2724422. 82.0644 [47.8585 81.8848 48.2161 81.643648. 5728 
96083. 1384/48. 000082. 9282 48.362382.) 16448.) 237 82.50 3049,81 
9784.004548. 5 83.792048. 866 [8 3.57 80 49.2312 [83.3624 49.5954 
9884.870549. 84.655949. 3699 84.439749. 7388 84.221850. 1067 
9985.7 36549. 5 85.5197 49.873685. 301350. 46385. 08 12050. 6180 
100 86.60251 50.0000[[ 86.38 361 50.2774. || 86.1629! f0. 73885. 9406 51 1292 


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»8572] 355150] „8549 ons | »8526} „5223 ;8504| „5262 
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4.28580 2.8782 4.2745 2.8239 42632 2.612511 4 2517] 2.6311 
5.1430] 3.0902 5.1295 3-1126|| 8,1158 3.1380 5.10210 3.13733 
6.0002| 3.6053 3.9834 3.63 14% 5.9653 9:6575 3.9525 3.68355 
6.8572] 4.1203] 6.8393 4.1302 6.8211] 4.1800 6.8028] 4. 2097 
7.7145 4.6253 7.6942 4.6690 5.6438} 4025 7-6532] 47339 
100 8.3517] 5.1504 8.5491 8.1877 8.3264 3.220]. S. S038 45.2621 
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13111432] 6.69551. 1139] 6.744164 30 6.925 11.0546] 6.8408 
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174.3718] 8.755614. 5435 8.8191 [114.4949] 8.8825 14-4560] 8.9456 
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22 18.857 11. 3308.16.80 111.413018.758 1011495 18.7077 5767 
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2622 2863 13.3910 22.2277 13.488 1022. 168613. 5850 | 22.1092 13.6816 
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3028.218015. 411 25.5424 1.563228. 92 18.5780 25:5106| 15.7864] 
3126.572215. 9662 26.5024 5023] 16.08201126.4318116.1975|| 26.9609 16.3126 


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37131. 7752 19.0564 31 6317 19.1946 31-5457119.3314|| 31-4630 19.4699 
| 28132-5724 19.57 140/3286619.) 13411 32-4993119-35491] 32:31 34119-9961] 

390334295 25.5865 33.341520. 23220 93.2530120.3774 || 23-1637 20.5223 
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4236.001021 6316035. 9063 21. 2 35.8 10921.9449 ] 35.714822. 1010 
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14639.429723.6918 39. 3259 23.96 3611 39. 221472 4.0349 39-1162 24.205 
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1 8290] „5592 [ „8266 55628 282416 „5664 ] 582166 „5700 
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3 2-48 2.4798 1.6884 2.4724] 1.6992 2.4649] 1.7100 
4] 3.31620 2.2368 3.3064 2.25121} 3.2965 2.2656] 3.2866 2.2800 
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. 7.4613 5.0327 7.4393] 5.0652 75.4171] 5.095% 7.3948 81800 
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q 13]10.7775] 7-2695 |[10.7457] 7.316510. 7136 5.3633 10.68 14 7.4100 
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2] 2.4575 I. 7207 il 2.4499] 17314 2.44.23],1 7421 2.4347 1.7827 
4 3.2566 2.2943 3.2666 2.3086 3.2565 2.3228 3.24630 2.3370 
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32.1796 


33-6423|31-3719 
34-37 36: 32-0539] 
35-1050; 32.7359] 
25.8303 [33-41 79 


24.5519 
25.2339 
25.9159 
26.5979 

27-2799 
27.9619 
28.6439 
29.3259 
39.0079 
32. 9109 20.6899 


26.113524. 7 808 
26.8389 25.4691 
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28.2896 


22.3933 


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29.0150127.5342 


29.7404|28.2225 
30.465) 28.9109 
31.191 129.4992 
31.916530. 2876 
32.6418 30.9760 


31.7840 


33.367203 7.6643 
34.092632.3527 
34.8180 23.0410 
35-5433] 33-7294 


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124-5004 23.5114 | 
25.2827 24. 2030 


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26.0051 24-8945 
26 7275 25.5860 
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35.3958 


26.1182 


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402 
——— 


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28.3520 


No 43 | 47 l 4 43: | 40; [| 43+ 
 51137-2990[ 34 7819{[ 37. FE 34- I 35. 9940 35-1061 36. 1859 35.2672 
1 52 36.030436 46391137-8753|35. 6529537719535. 7944 37.562935 9587 
| 53[38-7017130-14591138.6037| 36.3147[38-4448| 36.4828 || 38 2653 36 6502 
_ 5439-4931 [36-8279] 29.3320] 36.9999\| 39.1702 37-1711 |} 39.0977 [37.3417 
5540. 2245 37.5999 40.0604. 37:6851 32-5956[37.8595 39.7300 35.0332 
56/40. 9558 38.191940. 888 38.3702 40.2 10038. 547940. 4524387247 
5746872038.873941.5171039.554 (41.3463 39.2362 41.174) [39.4162 
| 55142-4185139-55591[42-2455| 39.7406 +2-0717139-92461[ 41.8971 [40.1078 
 59/43-1499140-23791142.9739[40.4258 72-797 1040.6129 42.619540. 7993 

4.999043. 223 41.1110 43.3225 41:39121[43-3418[41-4908 
| 61]44.6126[41.6019 44-4306 41.79611144-2478[41.9896 44.0042[42.182 2 
62145-3439[42-2839\145.1590[42.481 3 +4-27 32142-0750|1 44.1866 142.87 38 
63146-0753142-96591145-8874[4.3-16651145.6986 43-3603 || 45.5089[4.3.5653 
64146.8066[43-6479|[46.6157 43. 851746. 42 40,44. 547 || 46.2 31344. 2508 
_65147-5380[44-3299|[47-3441 44-53991147-1493[ 44-7430 45.9537[44-9484 
66148.2693[45.0119|[45.0725|45.2221 47-8747[45. 4314 47.6760[45.6399|] 
67149-0007 [45.6939|[48.8009[ 45.907 311 48.6001 46.1198|[ 48.2984[46.3314. 
65149-7321[40-37591[49-5292[46.59241|49.3255146.808: 49.1208[47.0229 
69150.4634[47-0579]] 50.2576 47.2776 59.0508[47.4965 49.8431[47.7144 
79/51-1948147-7399|[50.9860{47.9628 22:7702148-1848 |} 50.5655|48-4059 
71151.926r[48-4219][51.7143 48.648051. 5016048.87 32 51.2878 [49.0974 
7252.657549, 1039 52.4427 49.3332 92-2270[49.5615]| 52.0102 49.7889 
73[53-3888[49.7859][53.1711| 50.0184 52.952350. 2499 52.7 32650. 4805 
74154-1202150-4079[[53.8994 50.7035 53.6777 50.9382 53.4549 51.1720 
75154-$515151.1499]| 54.6278 51-3887 [154-4031] 51.6266 54-1773151.8535 
76[55-5829[51.8319 55-3502 152.09 39|[55-1285| 52.3149 54-8997 [52-5550 
77569314252. 139 56.0846 52.7591 [55.8538 53.0933 || 55.6220 53-2405 
78157-9456[53-1959|[ 56.8129 53-44431150-5792[ 53.6917 || 56.2444 53-9380 
19157-7709{53-8779]| 97.5413 54-12951157-3940[54,3800|| 57.0668 54.6293 

0158. 58.5082[54.5599 58:2697 54.8146 58.0300} 55.0684 57-7891[55.3210| 
81159. 2396|55.2419 58.998055. 499858. 755355.7567 [58.5115 56.0126 
5259.971055. 9229 59.7264 56.1850 [59.4807 56.4451 59.233866. 7041 
8360.702456. 605 60.4548 56. 8702 [60.2061 57.1334 39.956257. 3956 
84614237 57.2879/]67.1832 57.5554 ([60. 9314 57.8218 60.6786 58.0871 
85.62.1651 57-9699]|61.9115 59.2406[[61.6568 58.5101|| 61.4009 58.7786] 
86162.8964 58.6519 [62.6399 58.9257 [62.3822 59.1985 62.1233[59.4701f 
8763.627859. 3339[[03-3683[59 6109 03. 1076|59.8868|| 62. 845760. 1616 
88104-3591160.01 59 04.0966[60.2961 03.8329] 60. 5752 63.568060. 8 5 32 
8965. 0905 60. 697964. 825060 9813 64.558 3061. 2636 64.2904 |61 5447 
920068.8218 61.3700||65. 65.5534|61. 6665 65. 05.2837]61 01-9519]] 65.0128[62. 2262 
91 66.5532 62.06191[66.2818. 02.2517 66.0091 009162.6402 6403 65.735162. 9277 
9267. 2845 62. 7439 2. 0101 [62.0268 [| 66. 7244(63.3286]| 66.4575 63.6192 
93108.0159[63.4259 07.7385 63 7220| 675 459864. 0170 67.179964. 3107 
9468.74) 264. 100 668. 466964. 4072 68.185264. 705367. 902265. 022 
95109-4786164.78981[69. 9-1952165.0924| 68.9106 05-3937 || 68.6246 68.6937 
9670. 2100 65.4718 69. 9236 65.777669. 6359 66.0820 69. 3469 66.28 2852] 
97179-9413[66.1538 70.0520[66.4628 70.36 1466. 7704 70.0693[67.0968| 
9871.672766. 8358|[71. 3803[67. 1479 71.0867] 67. 4587 70.791767. 76833 
9972.404067. 5178072. 1087 67.8331071.8121 68.1471 71.5140 68. 45 
100073. * 19981172.8271168. — 22.224068. — 22-2364 169-1512 


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11 7193] „6947 7163 „7133 57102 
2 1.4387] 1.3893 1432 611 1.4265 1.4204] 1. 
3] 2.1580] 2.0840 || 2.1489 2.1398 2.1306 
4 2.8774] 2.7786 || 2.8652 1] 2.8530] 2. 2.8407 
— 51.3 59071_3:4733 ||_3-5815 3:5663|_ . 2.28090 
6] 4.3160 4.1680 || 4.2978 4.2795 42671 
715.0354 4.8626 5.0141 4.9928 4 49713 
8] 5.7547] 5.5573 5.7304 {1 5.5060 5.6815 
9 6.4741 6.2519 || 6.4467 6.4193 J 6.391] 6. 
2934.946162 ©.9779|| 7.1325]_7-009t || 21019401 
IIf 7.9127] 7.6412 7.8793 7.8458 7.8120 
8.6321] 8.3359 8.8956 8.5590 8.8222 
9.3514] 9.0306 |] 9.3119, 9.2723 9:2324 
10.0708] 9.7252 [0.0282 | 9.9855 9.9426 9.4 
10.7901 10.4199 10.7445 10 9 10.6988 | 10.6528 10.5602 
11.509411. 1145 [11.4608 46 [111.4120 [11.3630[11.2642 
12.2288|11.8092 . 12.1771 | 12.1253 112.0732011. 9682 
12.948 112.5039 [12.8934 12.838512. 12.7833 12.6723 
9013.667513. 1985 ff. 609) [13.5518 I3.4935| 13-3703 
[14.3868[13-8932 [[14.3260 14.2650] ([14-2037| 14-0803 
{15.1061]14.5878 15.0423 14.978314. 14.9139 14.7843 
15.8255 15.2825 [15.7586 15.6915 ([15.6241[15.4883 
16.5448[15.9771 [116.4749 16.4048 | 16.3343 16.1923 
17.2642116.6718 [7.1972 17. 1180 17.044416. 8964 
17-9838117-3665 17.9075 2.4448 |{17-8313[17:5227|[17.7546[ 17-6004 
618.7028 18.0611 [|18.62 38 18.5445| 18.464818. 3044 
19.4222[18.7558 [19.3402 19.2578 19.1750] 19.0084. 
20.1415[19-4504. || 20.0565 19.9710 19.8852]19.7124| 
20. 860920. 1451 [|20.7728 20.6843 20. 5954 20.4164 
21. 5802 20.8398 [21.4891 21.3925 21.305621. 1204 
22. 29952 1.5344 [22.2054 2 = 22.0157|21.8245 
123-0189[22.2291 [|22.9217 22.8240[22.42911122.7259|22.5285 
23-7 382122.9237 [23.6380 23.5373|23-1300j[23.4301]23.2325 
[24.4576|23-6184 ||24.354.3 24-2505|23.8309|[24.1463]23-9365 
_251]25-1769[24-3130 25-0706 24.4227 24.9038 24. 24.5318 [24-8565] 24.6405 
125-8962[25.0077 28.7869 (125-6770[25-2327|[25.5667 25.3445 
26. 6156]25.7024. 20.5022 1126. 3903 25.9336 [26.2769 26.0485 
27.3349 26.3970 [27.2195 27. 1035 26.634626. 9870 26.7526 
28.0543 27.0917 || 27.9958 [27. 27-8168[27.3355|(|27.6972[27.4.566 
28.77 36]27.780623 || 28. 28.6821 28.5 300 28.0364 28.407428. 1606 
29.4929 28.48 10 [ 29. 29.3584 28 6094 29.2433|28.7373 29.1176 28.8646 
30.2123 29.1757 30. 0847, 29.3072 || 29.9565|29.4382 29.8278 29.5686 
30.9316 29.8702 || 20. 8010 ' 30.0050 || 20. 6698 30.1291 30.5380] 20.2726 
31.6510] 30.5650 [31.5173 30.7028 || 21.3830, 30.8400|[21.2482| 30.9766 
32.3703 31.2590 32.2330 2330 31.4006 4006 || 32. 0963] 3 31.9583 31. 6807 
33.0896 31.9543 32.9499 32.0984 || 32.8095 32.2478 32.6685 32.3847 
33. 8090 32.6489 33.6662 32.7962 33.522832. 9427 [33.3787 33.0887 
34.528333.3436 [34-3525 33-4939 [| 34-2360; 53. 34-0889] 33.7927 
35-2477 34-9383 [| 35-0988 34-9493] 34-344 01134-7991] 34-4907 
35.9970 24.3291 25.8151 34-8895 125.6625! 34 11 35-5093" 35-2007 


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42.4410 40.9848 
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No | 
Il O71 || 511 36.06 | . er Fore; 
J 14742 82(36.566 [Or DIVIDING LANDS. 
: 2.8264 2 324330 TF* any two oppoſite Stations of a Cloſe, already caſt 
5| 2.5255|| 55|38.8909 up or prepared for caſting up by the Tables, be ſup- 
* a "Gin ola poſed to be joined by a right Line, theſe may be eſteem- 
7545 [39-59 Iſſed adjacent Stations, whoſe Longitudes, being put to- 
4 3 22149-3051 gether, and drawn into their Difference of Latitude, 
| 2 = 940122 and the Product, together with thoſe of the Cloſe on 
42 24 f 7193 the one Side, or on the other, diſpoſed into their proper 
19 Lei 42.4264 Columns, Sc. will give the Area of that Side as a new 
110 2.7782 61043. 1335 Cloſe. And thus may any Cloſe, or any Survey, tho 
12] 8.485362 43.8406 conſiſling of many Cloſes, be divided even into its 
131 9.1924 63144-5477 Conſtituent Triangles. 1 
14 9-8995 || 64/45. 2548 The Invention and Importance of the Calculation of 
15 10.6066 65 45.9619 50 Secondary Clyſes. EE SE 
16|11.3137 || 66]46.6690]] Since by the Corollaries to the Lemma, the Area 
17 12.0208 67147. 2762 of a Field is found by taking the Area which lies he- 
18|12.7279]| 68]48.0833 twixt the Prime Meridian and its NEAR Side, from 
19[13.4350 || 69{[48.7904 the Area which lies betwixt the fame Meridian and its 
2014. 142 · 49.49% [FAR Side; by retaining the ſame Prime Meridian, 
21 74.8492 50.2046 an adjacent Field will be eaſier calculated; as the Areas 
221.5563 50.9119 of the Common Sides are already taken from that Meri- 
23.16.2635 51.6188 [dian: Only Affirmative Areas in the firſt, will be Ne- 
24|16.9706 52.3259 gative Areas in the laſt, and the contrary ; becauſe the 
25|19.6977 53.0320 far Side of the One Field, with reſpect to the Meridian, 
518.2849 is the near Side of the other. And a third Field, ad- 
6 [RM 93-7491 joining both, will be ſtill eaſier caſt up, more of its 
x 422 5444/2 [Sides being done to Hand. | 
25147990. 55.1543 And thus, in any Succeſſion of contiguous Cloſes 
29/29.5061 55.8614 (as in the Field Work and in the Plotting) whatever 
30[21:2132 8.8685 is done need not be repeated, by which =_ one half 
| 31121.9203 f| 8I[57.2757[of the Labour of Calculating an Eſtate will be ſaved. 
| 32[22-6274 || 82157.9828]] And taking this Method of Calculation, as it ſtands 
3323.334583 58.6899 connected with the Method of Plotting not invented, 
3424.04 16 849. 3970 ff but now firſt Publiſhed by the Author, three fourths of 
35.24.2487 8560. 1041 [the Labour will be ſaved. And the Tabular Method 
25.4558 || 8660. 8 112 freed ſrom every thing troubleſome, and compleatly 
26.1620 || 87 [61.5183 |[[accommodated to the daily Work of the Practical 
28[26.8701 || 88]62.2254||-Surveyor. 
127.5772 || 89]62.9325|| __ | — 
28.2842 [ 90162 6396 . i ; 
28.9914 (97 64.346) The Rules for Plotting and Calculating comratted. 
29.6985 || 92]65.0538 Fer Plotiing. ] Lat's, or Lon's. like, Add; unlike, Subtract. 
6 29.4056 [ 9365.69 For Calculiting.] Field on the Right; Eaſt Products, 
; 31.1127 || 94j06.4680{[[put in their Proper Columns; — Welt, in Contrary. 
31.8198 9567. 1751 Field on the Left; Eaſt Products, put in their Con- 
32.5269 96[67.882 3 || trary Columns.—Well, in Proper. 
33.2240 [| 9768. 5894 Carried Products, put in Coatrary Columns. 
33-9411 || 9869. 296 8 5 
34-6482 || 99%. 00% FF bp fot > 1: | 
eee nel ene mt 


