1000000031

m oridian 'It the Ia,itude of

degrcr" or the diflanee

b« we<n the paralltl of 75" 00' and lhe paralld cf HO

01' ,

will be: I:qual

(heJe Itoes , and

-lu

(!jof

ane

them. By

mak.ng

the fame proportion, il will be found,

dUI the length of a minute on the meridian of this chárt

.t the parallel of 60°, or the di(lance bctween the paral.

Id of 60° 00' and ,hatof 60° o ,', is cqu. 1 'o 'wo of ,heCe

lloes. A fter the

rame

manncr, the lengll. of a minute on

,he enl"ged meridian may be fouod a< ¡oy Ia,i,ude ;

and eonrcquently begioniog

(he

equato r,

aod campu ·

ting the leng,th of every in:ermediatc: minute betwc:en that

1lnd aoy par.llel, ,he (um of al! ,he(e Olall be the lenglh

of a meridióln intc:rcepted betwc:en (he

eqllawr ami

that

parallt l; ..mI ,he dillaoee of eaeh degree aod minute o( la·

titudc:

from

the equatar

"'POD

the meridian of Ihis charr,

computed in minutes of lh: equawr, forms

what

ís coro·

monly ealled a uble of meridiooal pam .

,he areh BO (No.

11.)

rcprefeo, Ihe lalilude of any

POiOl B, theo (CO b.ing radius) CE ",ill be lhe (eeao'

that Luitude :

bUl

has beco

fhown aboye, chat radius

to the reeant of any

latitud~,

as lhe lt:nglh of a

minute upon lhe eq113tOr is to lhe lengl h of a minute

on che meridian of this chart al that

latitud~;

lhercfore

CE,

as the lenglh of a minutc on lhe equalor

is to rbe length of a minute upon thc mcridiao, at the

I. ti,ude

.he poin' B . Con(equeody, if the radius CO

be ..ken equal tO , he leoglh

a minute upoo lhe equa·

tor, CE , or ,he (ecaot of lhe I.,ilude, will be equal to

lhe length of a mintlte upon the meridian al that

lati–

lude.

Thtreror~1

in general,

lhe length of a minute

upon the equator

b~ mítd~

radius, lhe length of a minute

upon lhe enlorged meridiao will be e..ry ",h. re equal lO

the reeanl of the arch eontained belween

and ,he (;'lu31or.

Co • . • . H eoee il (ollow" fioce the leoglh

.very

intermediate minute betweeo lhe equHor and any p;¡ralld,

is eq'1al

the (eeaol of the latitude (lhe radiu, b.iog

qual lO a mioule upon lhe equltor) the fum of all lhefe

I, ngths, or , he dinance of lha< paralld on ,he enlarged

mer;di.n fr om lhe equOlor, will be cqu al 'o ,he (um of

all lhe fecanu, to evcry minute eontaincd betwetn it aod

,h. equator.

COR o2.

Coofe~

u.nd

ylhc .!in. oee b..,W«O any tWO paral

leI, 00 Ihe (.me (ide

lhetquatOr i, equal tOthe difl'<renee

of the fums or

,,11

the (eeant eonrained betwcen the cQua·

tor and eaeh pa ralld , and lhe diOance between

fl.ny

"tWO

pa " lIels 00 eontrary fides of Ihe equalO[ is equal tOthe

fum of the

fU~lS

of all ,he feean.. eoolained belwcen lhe

<quator and eaeh paralle/.

5. By lhe ..bl.s of meridional parlS, whieh may be

feen in Paton, and other writers on this fu bjeét, may be

eonflruéled lhe nauti..1 ehar', commooly ..lIed Merea–

tor'! chart . Thus, for

ex ample~

let il be reqnired ro

make a chan that

(hall

commence at ,he equator. and

«>eh ' o the

~arallel

of 60 degre.s, aod (hall e nain 80

de~rees

of loogitude.

Draw lhe line EQ¿el're(entiog the equa,or, (ree No.

.2 ,)

tben takt". from

any~eonvcnient

line or I!qu¡¡1 pu u,

~8oo

(the number of minutes contained in 80 de,!rces.)

whieh (e, 011' (rum E 'o Q.:.. and thi, will delermine ,he

br.ádth of lh. ehart.

Dil'ide ,be line EQ.inlo . iglll <qual

pan.,

in lhe POiOl'

"377

'ro ,

20,

~o,

.&c..

each eontaining

des,rec!, and c3ch

of , h.(e dlVldcd IOlo 10 equ.1 pans will give the fingle

degrees upon lhe equolo,r

lhen rhrough ,he points

E.I

JO. 20,

&c.

draYllOg IInes perpendicular to

thefe

(h.1I be meridians .

. from Ihe

feale ~f

equal pans take 4P7 .4 (Ihe meri.

dlOoal pa", anfwerIOg to 60 degrees,) and

(ct

that ofl'from

E t o A ar.d from Q..to

~nd

join AH; thCA this line

wllI repre(cot ,he parallel of 60, aod will de,ermiDe ,he

I.ngth of Ihe ehan.

Agaio, from the (cale of equal.,parts take 6°3. 1 (the

meridional parts anfwering to

degTees.) and

(ce

thu off

from E

1000 lhe IlOe EA; aod throufh the poiot

draw ro , 10, p"allel ' o EQ ; aod ,his will be the parallel

of 10

d.gr.

... The (ame w' Y. fetliog off from E 00 lbe

lioe EA, the m.ridiooal palls an(weriog lO eaeh

degr~e.

&c.

of latilUde, aod lhrough the feveral poiolS

draw~ng.

lioes parallel to EQ.:.. we (h,1I h..'e ,he f. veral parallels

oí

lati,ude.

. If the ehar' does ooleommenee (rom the equator, but

only to feTve fo r a een ain difhmce on the: meridiau

hetweeo two giveo parallels on lhe (ame fide of ,he equa.

tor

then the meridians are to be drawn as in the lan

eX4

ample : aDd for lhe parallels of lalitude you are to pro.

ceed

lh.us

!Iiz ..

from .lhe meridioncV paru anfwe ring

lO.

each pOlOt of ht1r ude

your ehart, fubtraél the mería–

dioal pdrts aofwering lo the I••fllatitude, .od fet off the

difl'acnees feverally, from the paraflel of le. U Iatilude.

upon (he t\Vo extrem'e meridians

and lhe lines joiniD&

lhefe poinlS of , he meridiaos (hall repre(eot the fever¡l

par. llds upon your ehart.

Thus let il be required tO draw a ehart lhat (hall (erJe

from lhe lati,ude of '20 degre.. oonh 10 60 degr<e'

oonh, aod lhat (hall eoo,ain 80 degrees of loogitude .

Having drawo the lioe O C to reprefent lhe par.lld <\f

degrees (fee No.

12 , )

and tbe meridians to ir, as in

the forcgoing eKample; (" off 1>63-.3 (lhe differeDcc be·

nl/een the meridional par(S anfwering ro

degrces, and

thofe of 20 degrees) from O tO 30', aod from C 'o

30; ,hen joio Ih. poiolS 30 and 30 w!th a right liD"

aod thal (hall be ,he paralldof30. AI(o (et 0fi" 397.6

(rhe diflo!rence betwct:n lhe meridional pJru anfwc:riog

40 degrees, 30d ,hofe of 20 d.gre..) froOl O 10 40, ar.d

from C to 40, and joi niog lhe POiDU 40 and 40 ",i,h .a

righ t lioe, thal (hall be lhe para!lel of 40. And pro·

cceding arter lhe Came wa)', we may draw as m;lDY

orthc

iOl errnedi:Hc p3rallds as we have occaflon for o

Rut if lhe t\Vo parallelo of lati,ude ,hal bOUDd lhe

ehan, ·are on the contrary fides of the cquator

then

draw a line repreCenting the equatOr and meridians to ir,

as in the firfl example; and rrom the equator

(tt

off on

eaeh

C.de

of il the fevera l paraflel, eon"ioed belw«n i,

.• nd lhe giv.n par. lle1s as .bove, aDd your eh" i,

fi·

ni(hed.

M erealor', ehart , eonO ruélcd as .hove, h"h its e–

quator extended on eaeh C.d. of lhe POiOl E 180 degrecs,

and ihhe feveral plae.. on the

furf.ee

of the ea"h be

there laid dowñ aeeordiog to their lati,udes aod loogitudes.

we (hall have whal :is eommooly e.lled Merca<or', map

of the eanh . This map is 00' to b. confider.d as a fimiJ.r

aod juCl reEre(eolalion of the e3lth's furfaee; (or in il lhe

figure:;