1000000031

to tbe trangent of courC. G -

29° ,

19' - 9 ·749,8

whieh, bee.ufe the Ihip i. Cailing between fouth and eaCl,

w.!1

be fouth 2\1° t9' eall, or SSE':' eall neady.

Then for the diClanee, we Ihall have (by rcfun!:ular tri–

gonometry) the followiog analogy,

"iz .

As radius

Io .oeoeo

;, to the dilf: of latitude

1 t

2.°569°

fa i.' the feeant of the eourfe -

29°:

19' 10.05952

to the diClance

130.8 - 2.11642

confequently Ihe lhip has fail cd on a SSE

eaCl eourfe

'1,0 8 miles .

Cus

D iClanee and departure given, to 60d courfe

dilferenee of latitude.

EX'''PLE. Suppofe. /bip at fea fails from the

latitude of 34° 24' nOrlh. bel\Veen nonh and weCl

124

mil.s, .nd is fouod

t<>

have made of welling 86 miles.

Required ,he eo..,-fe Cleered, and the dilfercnce of latitude

or nOrlhiog made g,ood.

In thi. cafe (by reéhngular trigooometry) we haYe th.

foUowiog proponion for fiodi ng tbe eou, fe ADB, (No.

S.)

"iz.

As the diClaoce AD

124

2.°9042

radius

10.00000

fa i. the departu!'e

1.93450'

tothefioeoftheeou rfeD

43°,54'

9.8'1'08

fo the Ihip's c.ourfe i. oorth

54 '

weCl, or NW6N'¡

weCl oearly.,

Then for the dilfer.nce of latÍlude, we ha.e (by

rtC–

tangular trigonometry) the foJlowing aoalogy,

"iz .;

As radiu.

10 00000

is to the diflance A D

124

2.09H2

fa is the ca fine of the courfe 43 °,

54'

985766

to the dilf of latitude BD -

89·35

1.95108

which is equal

(O 1

degree and :29 minutes nearly.

,Heoee, to find the Iatitude the Ihip is in, fioee hoth lati–

tudes are nOrln, and the Ihip failing from th.. equator;

thercfore,

To the

I..

itude failed from

add the ditrercnce of latitude

the fum is

35°,

(m:

latitude the (hip is in

nonh.

CASE

VI.

Courfe and departure giveo, to 6nd diflanee

and difrerence of latitude.

EXAMPLE . Suppofealhipat fel,

i~the

latitudeof'40

3P' routh, fail, SEbS, tiJl (he bas made of eaCling 9 6

miles. R cquired the dillance and dilferenec of latltude

made good on lhat courfe.

In this cafe, .by

Rdlangular Trigonomr/ry,

aod by

C afe ,. \Ve have ,he foJlowing proportion for finding the

diflanee, (No

9.)

"iz.

As the fine of the courfe

33°,

45'

9 .74474

is tO the departure

1.9 822 7

fa is radius

]

0 .00000

tothe d,flance

GM -

17'·8

2.23753

Then, fa, the difference of Iatitude,

have (by ree.

tangular trigonometry) the following . n.logy,

"iz.

As the tang¡;nt o( eou, fe -

33°, 45'

9.82489

t~e

departure

1 9 822 7

fo is radiu,>

0.00000

the ditferenee of Iatitude

r.H --

L¡3.7 - 2. 15738

equal tO

-2',

2ft'

nearly. Co.fequent(y, tioee th. latitude

thelhip failed trom wa. [outb, aud lbe faili.g

llill

towaNl.

the fouth,

To the latilude failed (rom

add the durereaee

latitude

a.d the furr.

i, Ihe latitude Che is come tO fouth.

6. When a Ihip lIems feveral eourfe. in 24 hours, then

Ihe redueing.1I tbefe ioto oae, ami thereby 6.ding the

courfe and di llanee made good "POO the whole, is com–

monly eaHed the refolviog of a traverfe.

'. At fe. they enmmonl] begin eaclt á.y's reckooiilg

from the noon of that day, .nd from that time tbey

fe~

down all the different courfe. aud dillances f1emllled by

the Ihip till noon next day upon the log-board; then

from thefe feveral eourfes and diflances had from the

compafs .nd log line, they compute the dilference o(

latitude and depar!ure for eaeh eourfe (by

Gafo

¡,

Plain SQiling;)

aod thefe, logether with the eourfes and

diOa.ces, are fet dowo in. table called the traverfe

table, whieh confifl, of five eolunlCc: in the 6rll of whieh

are plaeed the eourfes and diflarices

in the

" vo

next the

di¡¡'erenees of latitude belonging

thefe c.urfes, iccord–

ing as they are north or fouth; aod in Ihe two lall are

placed the departures belonging to thefe courfes, accord–

ing .. they are eafl or well. Then they fum up aH the

northings, andaH the foutbing.; and taking tbe dilference

of thefe, Ibey kDOW the ¿ ilference o( latitud. mad. good

by the Ihip in the lall '4 hours, which will be north or

fouth, aecordiDg a. lbe fum of the nOrlhings or fouthiog.

is greatefl: The rame way, by taking the fum of aH the

eallings, and liJ¡ewife o( aJl Ihe w.f1ings, and fubtraéling

th, lelfer of ,flefe from the greater, the dilfereace will

be the departure made good by the Ihip lall 24 houn,

which will be ..f1 or \Vell aecording as the fUID o f the

eaflings is greater or lefs than the fum of the weflings ;

theo from the dilference of latitud. and departure made

good by the Ihip lafl 24 hOUTl, fouod a. above, theyfind

the true courfe and dillance made good upoo tbe whole

(by

Gafo

oj' Plain SQiling),

alfo the courfe and

d i!!anee

the iotended pOrt.

EXAMnE.

Suppofe a Ihip at fe., in the latitude of

48°

24'

oonh at ooon aoy day, is bouDd to a pOr! io the

latitude of 430 4°' oonh, whofe departure from Ihe/hip

i. 144 miles eaCl; confequently the direé! courfe -,od dif–

tance of the Ihip i, SSE -} ea!!

t5 miles; but by' reafon

of the Ihirting of the winds Ihe is obliged to !!eer the

fnlJowing eourfes tilJ noon neXt day,

"iz.

SEbS 56

miles, SSE 64 miles , NW6W 48 miles, S6W

wefl

54 miles, and SE6S .;. eal! 74 milu. Required the cDurfe

and difl. nce made good the lafl 24 bours, and the bearing

and diflance of the Ihip from the inteoded port.

T he (olu, ion of .his traverfe depends oOlirely

the

and 4th

CQ!u

PIQ;n SQilinz ;

and firO \Ve mufl (by

Cafo

1 ) fiRd .he ditrertoee Df latitude and depar!ure for

caeh courfe. Th us,

Courfe SEóS dillaDee 56 miles.

For deparlure.

As radius

is to the difiance

10.00000

748 '9