1000000030

-¡oo

1\'1

fet on' f,om Ihe fe.\:e of cqmi pans

line cordpone!–

jng lOIhe Illeali,rcd di Iancr 01' Ihe IIdl ioos,

~nd

Ihis will

{ielermil1e Ihe poinl

Thel1 relllove Iheinflrument 10

l he flalion G,

~"d

applying Ihe index 10 Ihe IIOe repre–

f;nling Ihe dllbnee 01' Ihe

Il.ui"

"s, pldce Ihe inllrument

fo tilo!! Ihe firn

fI~lion

mal' be feenIhrnugh the fi ghl'.

:rhenIheinllrumcnl rem,iningimnlOve,ble, lecthe index

~pl,lieJ ~I

che puim rcprcf,·nting Ihe feeonel flalion G,

and be fueeelliv.!y dire,qed by

me~ns

of ies

fi~hes,

~II

l he angles of che lidd, d,.\\,lng (as before)

lI~fCure

li;'cs:

~nd

Ihe interfe,qion of che tll

obrcure lines Ihal were

eraIVn 10 che

f~me

angte from Ihe IWO nalions IVill al–

\vays reprerenl Ihal angle on Ihe plan. Care mufl be la–

ItenIhae thofe lines be noemill,kcntúrone anolher. Lines

joining!hofe interfeélions will lorm a figure on che paper

Jike to Ihe

field.

SCHOLIUJIf.

1t lI'ill not be ditlicult 10dothe fame

the

gr~phometer,

if you keep a diflinéf aecollnt of your obfervalloos of the

<.ngles Olade bythe line jQining Ihe (hlions,

~nd

the lines

dra",n from Ihe nalions IDIhe refpeélive angles of Ihe

lield. And Ihis is the

moa

eommon manner of laying

down whole countries. The 10pS of tIVOmouneains are

raken for two flations, aod their diflanee is eilher mea–

Cured by fome of the meehods mentioned abo"e, or is

ta–

I:eo aécording to common repute. The fights are fue–

(enively direéfed towards eieies, ehurehes, villages, fom,

Jakes, tumings of rivers, woods, &e.

Note, The di(lance of the Ilations ought to be great

enough, with refpeéf to Ihe field Ihal is tO be meafured;

fu eh ought 10 be ehofen as are not in a line with any

2ngle-()f the field. And eare ought 10 be laken like–

~vife

that !he angles, for example, FAG, FDG, &e.

be neilher very aeute, nor veryoblufe. Sueh angles are

be avoided as mueh a; ponible; and Ihis admonition is

fouod I'ery ufdul in praéfiee.

O S

T ION

XXVI.

FIG.

10.

lay j ,,",n o.y

fdd,

hlJ1u,v,r ¡rn–

gulor

¡II

ftgu n

lU.1y

1It•

ht, hy

Ih,

h,lp

I~'

gra–

ph.m'/tr.-Let AHCEDHG be fueh a field. Lel its

angles (in going round it) be obferved wieh a graphome–

ter (by Ihe

12.

of Ihis) and nOled down; let ils

~des

meafured wi(h a chain; and (by what was f,id on the

:21 .

of this) lel a figure like 10 Ihe givenfieldhe protraél–

<d on

p~per.

If any mouneain is in Ihe cireumference,

Ihe horizontal line hid under ie is to be taken for a fide,

lvhieh mal' be found bytIVO or Ihree obfervalions aeellrd–

ing to fome of Ihe Olethods deferibedabove ; and

il~

IJaee

on the map is to be dillinguilhed by a lhade, Ihat

may

be known a

mount~in

is there.

not only the eireumferenee of the field is to be.Iaid

(¡own on Ihe plan, but alfoils eonlenlS, as I,i!lages, gar–

.dens, ehurehes, publie roads, we mull proeeed in Ihis

enanner.

Let there be (for examp!e) a ehureh

r ,

to be laid

<lown in the pilA. Let the angles ABF BAF be obfer–

" ~d

and protra.:tcd on p' per in their proper .plae:s, Ihe

interfeAinn of the IWO fides

and AF wdl gll'e Ihe

pl.ee

of Ihe,

ehu~eh

.on the paper:

O~,

exalll~,

r!\e lines

HF Ar

helnl' meafured, let melts be defen–

LId hoOl the

"Oll tS

Il anti A, wieh parlS froOl the

fca le

eorrefl'0n"in~

lO Ihe dia.lOres BF anJ

.tr,

and che

pl,ee of th. chli leh \ViII be al tileir inlcd'célion.

Note t. Whik che ,ngles obfeTl'ed hythe

gr~phomeler

are taken clown, )'ou ,"utl be eardul 10 dif¡'ngoilh Ihe ex–

ternal angles, 's E and

thaeIhey OIay be righdy pro–

traéled afeerwards onpapero

NOle

Our obferv, tions of the angles mal' be exa–

min,d hy eompllling if

,11

che ineernal .ngle, m,ke ewiee

a' Olany righl angles, four cxc, pttd, as ehere are fides

I~C ~gure:

(for this is

demonnrat~d

32.

Eud.)

Bllt

pllee of any exeernal angle DEC, its eomplement

cirele is 10 he I, ken.

PRO P O S 1 T ION XXVII.

Ft G.

I I.

r . I.y dlYU'.

a pla;n

fdd wilh."1

¡nJlr,,-

1/Im/I .-If

a [¡lldl field is 10 be meafured, and a OIap of

bemade, and yoo are not pro,'ided wilh 'iollrumenu '

I~t

it be .(uppofed to be

~ivided

into Iriangles, by right:

IIOes, as

Ihe figure; and after meafu ring the three

fides of any of Ihe triangles, for ex,mple of ABC, lel

ies fides be I,id d?",n from a eonvenient feale 00 paper,

(by che

22.

of thes )

Ag.in,

let

Ih~

other two

~des

CD of che triangle CSD be meafu red and protraéled on

the paper by the fdme feale as before. In the fame man–

oer proeeed with the retl of Ihe triangles of whieh Ihe

fie/d is compofed. and the map of the field will be per–

feéled; for the Ihree fides of a triangle determine Ihe

triangle;

when~

eaeh

tri~ngle

on the paper is fimilar tO

its correfpoodeot.(riangle iD the field, and is fimilarly fj–

tuated; eonfequendy the whole figure is Jike 10 Ihe

whole field.

()

L 1 U

Jlf.

the field be fmall, and all its angles may be feen

from one Ilalion, it mal' be very well laid dowo by Ihe

plain-Iable, (by Ihe

24.

of this). If the

~eld

be larger,

and have the requitile eonditions, and great exaéloefs is

not expeéled, it Jikewife mal' be plotted by means of the

plain-table, or byrhe graphometer, (according to the

25.

of this; but in fields tbat are irregular and mouotainou"

when an exaéf Olap is required, we are to make ufe of

the graphometer, (as iD the·26. of chis,) but rarely of

the plain.table.

HaYing protraéfed the bounding lioes, the particular

parts eontainedIVilhi nthemmal' be I.iddownby the proper

operations for Ihis purpofe, (delivered io the 261h pro–

pofitlon; and Ihe method deferibed in Ihe 21th propofl–

tion may be fometimes of ferviee; ) for we mal' truf!

more to Ihe meafuring of fides, Ihan tO the obferving of

angles. We are not to compute fOllr-fided and many

fided figures lill they

refolved ioto triaogles: for the

fide! do not determine thofe figures.

In Ihe laying down of cieies, or the like, we mal'

m.ke

ufe of any of Ihemethods deferibcd aboye that may

b! moU eonvenient.

Thc map being fioilhed, it is transferred on clean pa–

per, bypuuing the firU

Ikmh

aboye it, ,nd marking Ihe

ang!es by Ihe point of a fru,1I needle. Thefc roines be,

ina joined by right lines, and Ihe whole illuminaled by

col,lllrS

propcr

eaeh part, and the ligure of the mari·

ners eOOlpals hcing add.d tOdillinguilh Ihe norlh and

fou.h, wit" a

fc~le

on the margi

Ihe Olap or plan

wiU

finilh.d auu nl'dl.

\Ve