1000000031

378

jigaresof conotries are di(lOl'lrd, efpeeially near Ihe poies:

but fince: (he

d~gree5

Jalitude are every where

~ncred.·

fed in (he

fame

proponian as (hoCe

Jon~itude

are, the

bearings between lhe

prace5

will be (h e

(ame

in (his ehart

as on lhe

globe

and (he

proponíans

between

the

lati ·

ludes,

longitudes,

and

nautical d¡lhnces,

will

al(o

be the

{,me on ,h.. ehart, " on ,he globe i,felf; by which

meaD! (he reveral cafes of navigatian are folved arter a

moO e<lfy

manDer,

and adapted to (he meaneH capacities .

N . B. Befe you muH take notice, thar in all eharts,

1he upper pan ís (he

north

fide,

and

(he lower pan or

boltom is ,he fouth fide ; alfo th.1 part of il towards Ihe

r ight hand

the ..n, and that towards {he left hand ,he

'W.cllide of the ehart.

6. Since, according

this projeélion, the meridians

"re parallel right lines ; it is plain, that the rhombs which

form alway. <qual angles wi,h the meridians, wiJl be

-(Ireig"t lines; \Vhieh property renders this projetlion of

the eanh·, [urface much more eafy aod proper for u[e

Ihao any -other.

7. This method of projetling the earth 's furface upon

plane, was fidl inveoted by Mr Edward Wrighe, but

Jirn publilhed by Mercator; and hence tbe failing by,he

chut, was

called

Mercator's failing.

In No..

13 .

let A and

reprefeot two plaees upon

Mercator', ehan, AC the meridian of A, and CE the

p.rallcl ofla,itudc patliog through E; draw AE, and fet

off upon AC the leng,h AB equal

,he oumber of mi ·

nutes contained in the difference of b\tiwde between the

two places, and taken from the fame fcale of equal pares

the ch:ut was made

by,

or from the

equator, Or

Rny

graduated paralld of ,he e11art, and through B dra\V

BD parallel to CE meetiog AE in D .' Theo AC will

be the enlarged differenee of Iatitude, AB the proper

:lifFerenee of latitude, CE me difFerenee oflongitude, SO

the departure, AE the enlarged di(lance, and AO the

proper dillanee, betwccn the two plaees A and E; alfo

tbe angle BAO will be ,he cour[e, and AE tbe rhomb

iine between them .

Now finee in ,he triangle ACE, BD is pualJcI to

one of ies fides CE; it is plain ehe triangles ACE, ABO,

\ViII

be fimilar, and confequently the fides proportiona!.

Henee arife ,he folutions

the [everal cafes io tbis (ailing,

-whieh are as foll ow.

CASE

The latitud.s of two pllces given, to find

·the meridiooal or enlarged differenee of latitude

btt\Ve~o

Ihem

Of this carethere are three varieties,

viz.

tither one

of the places Jies on ,he equator, or both on the fame fide

of it ; or la(lly, on differtnt fides .

1 .

If one of the propofed places lies on the equator,

then the meridional diíFercnce of latitudt"

is the fame

with the la,itude of the o,her place, taken from the

"able of meridional

pans .

EXA

MPL E .

R~~ uired

Ihe ",eridional difference of la·

tilUde betwefn 51 Thomas, Jying

the cquator, and

AntonIO in the latitude of 17°

20'

nonh .

look io

the tables for ,he meridional

pans

anfwering to 17°

20',

and fi nd i,

1056.2,

the enl. rged difference of lati–

lude r<quirrd .

;¡.

the tWO proFored places be on the fame fide of

the

e~uator,

,hen the meridional diff<rence of la,ieude

is (ou nd

(ubtraéling the meridional parts anfwering

le)

the lean latilude from tbofe

tlofwering

to lhe .greatefi,

Oind

lhe dlfferenc.e is lhat required .

EXAMnE . Required ,he meridional diflúence of

latitude between

lhe

Lizard in

lhe

latllude o( 50""

00'

nonh, and Antigua in

lhe

~ritUde

30' nonh.

From the meridional patlS of -

50·, 00' - 3474. )

[ubtratl tbe meridional partsof

17~,

30' - 1066. 1

Ihere remain.

24°7 .8

lhe meridional di.fFc:rence of I:ttitude required.

3. I f tLo places lie on diffúen, fides of the equator, the.

the meridional difference of Iatitude i. found by adding

together lhe

meridional

part! an(wering to eaeh

latitude.

and lhe fum ,ís that required .

A M

PL E. Required the meridional difFerenee

lati,ude between Antigua in Ihe latitude of

17° 30'

nonh , aod L ima in P eru in the latitude of

12°

30'

South.

To tbe merid . parts anfwering to

17~,

1066.7

add chefe anfwering to

12°, 30' -

756. [

the fum i.

the meridional difFerence of la,itude required_

CASE

The latitudes and longi,udes of two placel

given, to 6nd the dire(t eourfe and d,nanee between [bem.

EXAMPLE. R equired tO 6nd Ihe direél eourfe and

diflanee between the L,zard io Ihe lalitude of

50°

00'

north , and Port· Royal in Jdmaiea in [he Ia,itude of

17"

40';

differing in longitude

70' 46',

Port·RoJaj Iyiog

far to tbe wellward of the Lizard.

PREPARATI.QW

From the lati[.de of the Lizard

[ubrratl the latitude of Pon-Royal

and

lbere

rernaios

3'1 ,

2 0

equal

tO 1940

minutes,

lhe

proper

ddfercnce

of latitude:,

Then from the meridional parts of

50°, 00' 3474.5

fubtratl mofe of

,40 1077.2

Qnd th<re Temains

2397.3

Ihe meridional or eolarged difFerenee of longitud•.

G EO METR, e ALLV . Draw Ihe line AC (No

14. )

reprefenting the merldian of the L izarc\ at A, and fet off

from A , upon that line, AE equdl tO

1940

(from any

fcale of e'lual

parlS)

the proper d,fferenee of lati,ude, al[o

AC equal [O

2397 3

(from the fame [cale) ,he meridional

or enlarged difference of latitude. Upoo ,he point C

raife CB perpendicular to AC, and make CB equ. 1 to

4246

the mioutes of dtEfereoee of longitude.

J ojn AB, and ,hrough E draw ED parallcl to BC: fo

Ihe

e.fe

is eonflruéled ; and AD applied

,he fame f" le

eq ual pares the

olher

legs were t;¡ ktn frrm

wilJ

give

,he diretl di(lance, and the angle O AE meaf.red by tbe

lioe of chords wiJl give ,he rourfe.

CAl.CULATIOll.

For the angle of the courfe EAO, it will be, (by Rea–

. ngular Trigonorretry,)

AC : CB : : R : T, BAC,

, .

As the meridional ditr. of lato 23 973

3·37970