1000000031

;80

R: AC : : T , A: CK .

i • .

As radi as

¡o .00000

is tO Ibe merid. dift. of lat. -

233 .6

2.36847

fo is tbe ..

of tbe courfe -

34"',51' -

9 .8430 7

to mino of d;ff. of longitude -

1628 -

2.211

equal tO 2°

48 " , tbe difference of loogitade eAtt·

.rly.

CASE

VI.

One latilude, courfe, and difference of

longitude, ,

i.eo;

to 6nd tb: olber latitude, and diHance

failed .

EX.MPLE . Suppofe a Ihip from the

I..

ítude of 48°

50' north, fails fouth 34° 40' IV

dI,

till her diff<rence of

longitudc: is

44' ; rcquired (he

hlitudc

come to, and

lbe dillaDce fáiled .

GEOMETRICALLV.

Dra... AE ( No. 18) to repre ·

fcot (he mcridian

(he

fhip

in the

lira

latilUde . and make

t be angle EAC equ. 1tO 34°40', Ihe angle ofthe courfe;

t hen draIV FC pa..lleI 10 AE, at the diUance

164 the

minutes of dif1'erence of longilude, wbich will meet AC

in the point C . From C let fall upon AE Ihe perpeo·

dicular CE ; tbeo AE w,)1 be the eolarged diflereoce of

Iatitude. To fiod ·which

6.1 Calcula/r.",

it will be, (by

reélangular trigonometry,)

T, A : R::

CE: AE,

i .

r .

As tbe taog. of the coude 34", 40' - 9.83984

Í1

the radius

10.00000

fo is mio. of dif1'. longitude -- 164

2.2 1484

to the enlarged diff. of latilude - 237. 2 - 2.37500

20d becaufe the fuip i. fai ling from a north latitude fouth ·

erly, thereCore,

Frortl Ihe merid . pans oq

the latilude failed from5 -

48°,

so'

take tbe merid. differeDce of Ialitude

237.2

2Dd there

r~mains

3129.7

the meridional parts of (he Jatitude come

lO,

viz.

46°

° 9'·

H ence for the proper difi'crence of latitude,

From the lali lude C ..led from

48°,

so'N

take the latilude come tO

46 , 09 N

and (here remains

2 ,

•qual

161, the minute. of difi'erence of latilude,

2. Set off upon AE the length AD equal to t61 the

proper diff<rence of latitude, and througb D draw DB

parallel rO CE : then AB will be the diretl dillance. T o

/iod which by

Calcula/ion,

it will be, by reéhngular tri·

gODOOletry,

R : AD : : Seco A : AB .

i .

t .

As radius

10.00000

is tO thc proper diff. ofl"itude

16¡

2.20683

fo is the (ecaot of tbe cour(e

40' 10 08488

Ihe dird l diHancc

19S·8

2. 29 '7'

CA SE

VII . Ooe latitude, courCe, and

depanure,

¡¡iven; rO fiod the o,her latitude, dillance failed, and dif·

ference of loogitude.

Ex.

PL ' . Suppofe a fu ip Cails from the lat itude of

54° 36' north, Couth 42° 33' eall, until Ihe has made

of departure ,,6 miles, R ' quired the latitude O,e is in,

her diretl dillance failed, aDd how much !he has ahered

her loncitude.

GEO M ETRICALLV.

Havinn dra-wn the meridian

AB , (No. 19') make the aDr.I·e llAD cqu.1

42° 33'.

DraIV FD p>rallel to

Ihe ddlance o( ,,6, wbicn

\ViII m«tAD in D . L et f. 1I uponAS the perpendicu·

lar DR. Then AB will be the proper difference of la.

titude, and AD Ihe direél dillaocc : To fina \Vhich

calcul..ioo, 6r1t, for the

ditt~nce

AO it will be (by reél·

angular trigonometry )

S , A : BD : : R : AD.

i. '.

r~e

fine of the courfe

~ 2°,

33' 9.81010

°is to ,he deparrure

2.06446

fo is radius

10.00000

to the diretl dillance

-- 17" 5

2.23436

Then for Ihe proper dinereoce of lalilude, it will be,

by retlangular trigooometry.

T, A :

BD : :

R :

AB.

i .

••

As the taog. o(the cour(e

~20 ,

33'

9.96281

i, tO the departure

116

2.06446

fo is radius

10.0 0000

to Iheproper difference of larilude 1264

2. 10165

equal 'o 2°

6':

cooCequendy Ihe fuip has come to the la·

tirude of p 0 30' north, and (o the meridional differeDce

of lalitude will be 21 2.' .

2 . P roduce AB to E, tiJI AE be

eq.al

to 212.2; aod

through E draw EC parallel to BD, meeting AD ; rodu.

ced in C; tbeo EC will be Ihe diff<reoce of longitude ; tD

find which by calculatioD, il \ViII be, (by retlangular

tri·

gonometry)

R :AE: : T, A: EC.

i .

t .

As radius

10 COOOO

is to the merid . diff. of latitude

212 .2

2.32675

fo i, the tangoofthe courfe

42. ,

33'

9 , 9628 ,

to the mino of diff. of lo.gitude

194.8

2.2895 6

rqqal

3°

'4'

48", the difl'erenceof longitude eallerly.

This might have been found ol berwiCe, thu.: b<cauCe

thetriangles ACE, A[)B, are fimil ar; rherefore it willbe,

AB :

BO : :

AE :

EC .

As th. proper diff. of latilude 126.4 2.1016,

i, to the departure

116

2. 06446

fo is the enlarged diff. of l" ilude

2'2 .2 2.32675

to min diff. of longitud e

'94 'S

: .28956

CASE

VIII.

Both lalitudes and deparlure g,veo, to

find courCe, diaance, and dilference oflongitude.

EXAMPLE . SuppoC. a fuip (rom the latinide of

~6·

20' N . Cails betweeo (outh aod well, till fue has

m.de

of departure ¡ 26 '4 miles; aod io ,he. fouod by ob–

(ervatioo

be 'in th e Iatilude of 43°

3S'

north . Re·

quired the courCe and ditbnce (ailed, aod difference of

longitude.

GEO".T~ I CALLY .

DrawAK (No. 20.) torepreCent

the meridian of ,he fui p in her firll latitude; Ce, off uJ'On

it AC, equal to

165,

the proper differeoce of latitude.

Draw BC perpendicular 'o AC, equal to 126' 4 ,he de·

parture, aod joio AB . Set off from A, AK equal to

233.3, ¡he enlar,ed difference of latitude; aDd through

K dr.w KD par. llel to BC, meering AB prodaced iD D;

(o the caCe is conllrutled, aod DK will be the difference

of longitude, AB the dillaoce, aod tbe angle A tbe

courft:: ; to find

\\>1

¡eh

CALCULATION:

Fidl, For DC the dill'erencc of 10Dgitud., il will be,

AC: