1000000031

't¡le

cb:u t,

its

J.ltilUd~,

anu

the diíTcrence

of longitude

uet",cen it and fo me kno,,"n place uFon Ihe eharl being

g:ven.

EXAMPLE. Let Ihe known place be ,he L izard Iy.

ing on the paralld of

50° 00'

t1orth, and Ihe place

k;d down St Katharines on ,he can

co~fi

o( America,

ddlúiog in longi\llde from the Lizard.4'0

36',

I)'ing fo

much to

lhe

we:tlward of

it.

Lel L reprefenl Ih. L izard on ,hecharl. (fee No.

12 .)

Iy .

¡ns on rhe para!lel of 50° 00 '

nort~.

its

mt:rtdian. St:t

off

f rom

upon the equa<t'r

E~,po

36',

low"ds

whieh

"iU reaeh from E to F . Throuhh

dr:.w lhe m"idi.n F G,

and this·will be the meridian of St Katharin-:s;

Ihen

fe t

off

from

~to

upon Ihe g' aduated meridian

Q!!.

degrec:sj and Ihrough H draw the p..

ralld

of Jalitudc!

HM,

whieh wiU meet Ihe former merid,an in K, Ihe place

upon lhe

chan

required.

PROBo

11.

Given tWO place, upon Ihe ehart,

find

their d.frerenee of laliluoe and di/ferenee of longilude.

Through.the two pl.ces{)raw paraUels of latilude ; Ihen

1he di(lance between thefe paraUels oumhered in degree,

and minutes upon the graduatcd meridian wiU he the dif·

ferenee of latitude required, and Ihrough the twO plae..

drawiog meridians, the ddlance between thefe, counted in

degrees and

roinult's

on the equator or

any gr2d1l 2ted

parallel, wiU be the differeDee of longitude required .

P ROB o

1II.

T o 50d the hearing of ooe place from aoo'

ther upon ,he ehart .

EXAMPLE'. Required ,he hearingof St Kalbarioe. a,

K ,

(fee No.

12.)

fro:n ",e L izard at ·L .

Draw tbe meridiao of ,he L izard

AE,

and join K.aod

\Vi,h ,he rigbt liDe KL; theo by the line of ehord,

meafuriog ,he angl,\

KLE,

aod with that eor.ering tbe

'ahle" we fh.all have ihe ,hing required.

Thi, ruay alfo be con'e, hy having eompalfe. drawn 'on

the ehart (fuppofe at ' \VO of its eornen;) theo lay the

-edge of. ruler over ,he IWO plaees, and let ,.U a perpeo–

dicular, or t2ke the nearcll dinance (rom (he centre o(

~he

eompaf. Dext the 6,(l place. 'o tbe ·,ule,'s edge: ,hen

with lhlS di(lance in your eomp.lfes, Cide Ihem along by

the ruler', edge, keepiDg one rOOt of them c10fe to the

ruler,

aod

the orher 25 near

-Y0U

can }udge perpeodi.

cular to

¡t,

which will defcl il>e lhe rhomb required .

P'OB. IV. To fi nd ,he diRanee betlVeen 'wo giveo

pl.ce.

upon the ehar,.

Thís problem admiu or (our cafes. according

lhe

litualion or lhe

twO

placcs Wilh re{pea

to one

another.

CA"

WheD the Siven plaees Jie bOlh upon Ihe e·

<¡uator.

In thi. eafe thei r di(lance i. found hy eonverting ,he

degr.., of differcnee of longi,ude iOlerceplcd hetweeo

them into minutes.

ll.

When the tlVO place, lie ho,h on the fame

meridiano

D ..

w the p.rallel, of ihofe plaees; .nd ,he

drg,e~~

tlpOO

the graduatcd meridian. inlcrcepted bct\':een thofe

paralle)s, reduced

minutes, give the difiance required .

CA SE

lIl.

Wheri ,he tIVO place, lie on Ihe fóme p.ral.

leI.

EJltAMPLt

Requirc:d to find lhe dinance uetween Ihe

poiols K and N, (fee No.

12.)

boll, Iying on the parallel

VOL.lI1. No. 85.

28° 00

north. T ake from your fcole tLe coord of

60·

or .:tdius in your comparres, and with lh",t extcnt on

lJafe make lhe ¡fofeeles lriangle

KPN;

lh(n take

from lhe ·Iine o( fin es lht: co·fine of

the

Jalituc!e, or

fin'!

of 72° .nd fet thu off from

to S .nd T. J oio

'Dd T

wilh the right line ST, and that .pplied

the gradualer!

(qu:Jtor

will

give lhe degrees and minutes upon

equ~

tOthe difiance

which, coovertcd ioto miúutes, wilJ be

the difl.nce required .

T ite reafon of .hi. is evident from the fe{lion of

Para/–

/tI

Sailing:

for it has heen ,here demonflrated, ,.ltat radiUI

the eo-fi oe of any parallcl. as Ihe leoglh of any areh

on the equ:uor, to the length or the fame areh

0 0

thar

paraUe!. Now in thi, ehart KN is the di(laodt of the

meridians or the two plaees

and

opon lhe cqlt2tor..;

.• nd Gnee, in the triangle PNK. ST is the paraJld to KN,

therefare PN:PT: :NK:TS. Ccnfequently TS wiU

the di(Jance of tbe tWO place, K and N upon ü;e paralld

28°.

Ihe paraUeI ,he two places lie

he no, fa, from

the equalor. and they not (ar afonder ; tben Iheir di·

(lance may he found thu.. Take ,he

~(lance

hetIVe,,,

,bem in you, eompalfcs, and appl'y Ih.t 'o ,he graduated

mcridian, fo as the one (oot may be as many minutes

a–

bove, as the olh.,. i, helo\V ,he giveo .paraUd; aod the

de.crees and

minutes

intercepted, reduced to minutt',

~'i1l

give the diílance..

Or it may alfo he found Ihu..

T.ke

the length of.

degree on che meridian at the given paraJleJ, and

turo

lhzt

cver

the parallel (rom ché on: place tO lhe olher,

oft as

you

can; then

oft as that extent is contained be–

t\Veeo the place!, fo' many times

miles \ViII be con–

tained

the dinance between them.

CAS

IV . Wheo the places dilfer hoth iDlongilude aDd

Ia,i.ude.

E XA

E .

Suppofe i, were required 'o 6nd ,he di–

nance between tbe tWOplaces "

and

tupan tbe chan:.

P ROB o

11.

Find the difference of latilude he',,·..

them;

aod take tha, in your eompalfes frcm ,h.

gr~d"a,ed

<qua·

lor, which fel off

lhe meridia nof ". from

to "

then

,hrough

draw

paraJlel tO

¿, ;

. nd taking

in your

eompalfcs, apply it to the graduated 'qua,or, aod it will

Ihew the

de~ rtes

and minutes conuilld:d io the dil1ance

required, whieh multiplied hy

\~iU

give the mil"

dillance.

The reafon o( Ihis i, evid,nt from

Arl.

of .hisS, n.

for

is phin

lhe eo)arged difTerence.-or Jatilude,

anJ

the proper ; eonf<quenrly

the enlarged d,(lanee, and

the proper.

PROS. V. To lay down a place upon the ehart. '"

lati tude

aod bearrng from fome koown

rl ..

ce upon the

eh.,t being knowo. or ("'hieh is Ihe fame) having ,he

cuurfe and dlfFt!rence or Iatltude th;:O( a

n\ip

has

mad~,

hy down the ruooing of the lItip, and find her place upon

the

charlo

EXA., PL E.

lItip from tite L izard in ,h: la,itude

50°

oo'

nOrlh, fails SS\V till. lite ha, di·trered

h" I..

i–

tude 36°

40"

Required her place upon the chart

Con nt rrom the Liz.ard at L . onthe graou:ltcd rncridiar.

dowcwards (beeaufe Ihe eourfe is foulkerly)

36.

40'

tbrouJ:h