1000000031

the differcnce of long. - 4246.0

3.62798

fo is radius

0 .00000

to the tango of the direa courfe 60° 33' -

10.34828

which, becaufeJ'ort Roy,1 is fouthwud of the L izard,

aod the difference of longitude werterly, will be fouth

60° 33' \Vdl, or

SWhW

well nearly.

Th. n for the dillance AD, it \ViII be, (by reaangular

trigonometry)

R : AE : : Seco

A :

AD,

As the radius

10.00000

is tO .he proper diff. of 1>1.

1940 -

3.28780

fo is the fecaot of the courfe

60° 33' - 10.30833

tO the dillance

394 5.6 -

3· 596t3

confequenlly the

~ireél

courfe and di!l,nce between the

Lizard aod Port. Royal in J amaica, is rODth 60° 33',

3945.6 miles .

CASE

Ill.

Courfe

a"d

dirtance (ailed given, to 6oddif.

ference of latitude and difference of longitude.

EXAMPLE. Suppofe a !hip from .he L izard iDthe lati·

tude of ¡0° 00' north , fails fouth

35°

40' well 156 miles.

Required the latitude come-to,

~nd

how much !he has .J.

tered her longitude.

GEOMETRI CALLY .

Drawthe lioe BK (No . 15 .)

reprefenúng the meridian of the Lizard at B ; flom

draw·.(he line BM, making with

an angle equal to

40" aod upoo this lioe fet off BM <qual to t 56 the

¡iven dillance, and from M let faJl the perpendicular MK

"pon BK.

Theo for BK the proper difference of latitude, it

will

be, (by reaangular trigonometry,)

R : MB : : S, BMK : BK,

As radiu$

10.00000

iltolhedillance

156

2. 19312

fo is the eo·fine of the courfe 35' 40'

9.9°978

to the proper difference of la!. 127 -- 2. 1029°

c:qual tO 2° 07'; and fince the fhip is failing from a north

latirude: towards the fouth , therefort: the

latitude

come to

will be 47° 53' north . Hence the meridion.J difference

of latitude will be 19304-

2. ProduceBK to D, tifl BD be equal to 193 .4;

through

draw DL parallel to MK, meeting DM pro·

.duced in L; then DL will be the difference of longitude:

to find which by e.Jculation, it will be, (by reélao,ular

uigooometry,)

R : BD : : T, LBD: DL,

i .

As radios

JO.Ooooo

to the meridional diff. of lat . 193'4

2.28646

fo is tbe tangent of the courfe 35°, 40'

9.85594

to minute. 01 diff. of long. -

138.8 --

~ .14240

equ,1 102'

di'

48" the difference

longi.ode the lbip

has made wellerly.

CASE

IV.

G.ven courfe and both latitudes,

viz .

the

latitud. f.iled from . and the latitude come to; to 60d the

dlll.nee f.iled and the d.fferencc of longitude.

FXAMPLE. Suppofe a lbip in the latitude of 54° 20'

oonh, lalis fouth n° 45' eall, until by obfervallon !he i.

fou .

be in rhe hititude

o 45

nonh;

rcquired

the

~ifi.nce

failed, and Ihe diflúence of longitude.

GEOMET.,CALLY . Draw Al:! (No. 16) tO repre·

fent the mendi,n of the !hip in lb" firll latitude, and fet

off from A 10

155 the minutes of the proper differeoce of

Val.. 111.

N° 84'

~79

Iatitude. alfo AG equaJ to 257.9 the minutes ofthe enlarged

difference of latitude. Through B and G, draw the hne.

BC and GK perpendicular to AG; alfo draw AJe mak–

iog with AG an angle of

33°

45',

which will meet the two

fo rmer lines in lile poinu

and K; fa the

cafe

is con ..

llcuaed, and AC and GK may be found from the line ofe–

qual par": To find WhlCh,

'By CALCULATION :

F irfi, For the dlfference of longilude, il wiJl be, (by

reélangular trigonomeuy,)

:AG :: T, GAK:GK,

é .

As radius

10.00000

is to the enlarged d:ff. of lac. -

257 .9 - 2 .411H

fo is the tango of the eourfe -

33°,

45' -

9 .82489

to min o of

d.ff

. of longitude

172 .3 -

2.23634-

equal tO 2°

51'

,8", the differenee of longitude the lbi!,

h••

m.de

eallerly.

This might .Ifo have beeo found, by firll 6nding the

departure BC (by

Cafo

2. of

Plain Sailing,)

and thea

would be

AB : BC : : AG : GK, lhe d ifference of longitude

required.

Then for the direa dillaoce AC, it will be, (by red–

angular trigonometry,)

R :

AB : : Sec..A : AC,

As radius

10.00000

i.s

to the proper diff. of lat.

155

2. t90B

foi. the feeant ofthecourfe - 33° . 45' -

10 .0801~

to the direa difiance

18~

4 ...; 2 27°48

confeque~t1y

the !hip ha. failed fouth 33° 45 ' eaCl:

186.4 miles, aod

has

differed her longitude 2°

'51'

18"

eallerly.

CASE

Both latitudes, aod dillance failed, giveo;

10 find the direa courfe. anC! difference of longitude.

EXAMPLE . Suppofe a !hip from the latitude of 450'

26' north, fads

b~lween

nonh

and

can

195 miles, and

then by obfervation !he i. found to be in the latitude oí

48° 6' north; required the direa courfe aod dilfereoce

of longilude.

GEOMETRICALLY . Draw AB (No. 17.) equal te>

160 the proper difference of latitude, and from

~he

poine

B raife the perpendicular BD; then take 195 in youe

comparres, aDd feuing one foot of tbem in

with the

lher crof. the line BD in D. Produce

AB,

tilt AC be e–

quallO 233 .6 the iolarged difference of Jatitude. Thro'

C draw CK parallel to BD, meeting AD produced in K:

fo the care i. conll. uéled; and the angle A may be mea–

fured by the line of chord., aod CJe by the lioe of equa!

par.. : To fi.d which,

By CALCULATJON:

Firll, For the angle of lhe courfe BAD it wilt be, (by

rea.nguJar trigonometry)

AB :

R : :

AD : See. A .

A. the proper diff. of la!.

160

2.2°412

radius

10.00000

fo is the dillance

195

2.29001

10 the fecant of the coorfe -

34°, 52' -

10.0859 '

whieh, becaufe the fhip is faihng between north aod

e,ll, will be north 340

51'

eall, or NEhN 1° 7' caflerly.

The. for lhe difference of longitude, it will be, (by

ceélangular trigooometry,)

5 C