1000000031

fo i, the Iinc ofBCD

56° , 15'

991 98 5

.0BD

2621 -- 1 41 84 3

¡he dillance b!{ween the

[ \\'0

headlands.

This, and lhe firfl

problc:m,

are of great

ure

drawing the plot of any harbour, or layiog dowo aoy C<a

coa(1.

•

Suppofe a !hip that makes h<r way good wilhio

6 -:–

poines of

the

wi.nd,

nonh,

is bound

pon bearing

can

miles di(la"ee from her: Required the eourCe anu

Jiflaoce upon each tac!",

gaio (he ¡ntended pert.

GEOMETRICA[)LV:

Having drawn

lhe compaJs

SW, (No.

25 .)

lel C reprefeot the n,ip's ploee, aod fet

off upon the eart

lir.e.CA

mil... fo

will be the in–

teoded port . Draw CD and CB on eaeh fide of the

north

line

at 6 {- pp:nts diHaoce (rom

¡t,

and through A

draw AB par.llel

CD meetiog CB io B ; Iheo Ihe

ENE TE lioe CS, will ue the eou"fe of Ihe nlip upoo

the fiarboaTd tack, ltod

in dillance on (hu tack ;

..Ifo the ESE

E loe Ab. will be the eou rfe 00 the

J.rboard taek, aod BA the dinaoee

that taek:

fiod

\Vbieh

CALClILATION;

lo the triangle ABC are giveo, the angle ACR, equal

16° . 5 3', tbe

dillance between

lhe ean

and ENE

lioe; the angle CBA. equal tO

1460

14',

the d¡flaoee

betweeo the ENE

E and the

WNW T W

lioe.; the

aDgle BAC equal

16°

53',

the di(laoee between the

callaDd ESE

E lioes; alfo AC

mile•.

Heoce finee the aogle at A and C are- cqual. the legs

-CB

.od BA will likewif'e be equal; tO .fiod either of

\Vhiel> (Cuppofe CB) it will be (by oblique aogled tri–

gooomeny .)

the fioe

ufB

146°, 14'

7449~

is to AC

1.93450

fó

is the fine of A

16. 53

9.463 03

44·94

,,65260

the dinaoce ,he

01ip

mun Cail

eaeh taek.

There is a great varie,y of ufeful qudlions of Ihis na·

ture that may be propofed ; but the nalure of Ihem boiog

beuer uuderllood-by pralliee at fea, we !hall lrave Ihem,

and go on

Currtnt Sailing.

Sell. 7.

Cone<rn:ng

Cu . RESTS,

and ho-w

mal"

prop(r al/o<wonctl.

CUR~EMTS

are certaio

(ertings

of the

jlr(Qm,

...hieh all bodies (as !hips,

cre.)

moving therein, are

compelled to alter theír courfe or veloci ty, or both;

and fubmit

the motion impretred upon them by the

current.

l .

the eurreot fet. jun with ,he eourfe of the

fhip,

(i .

)

moves on {he [ame rhomb with ir ; then (he

motion of the

fhip

increafed,

as much as is the

drirt

or velocity of the cunent.

EXAMPLE . Suppofe a,!hip fai ls SEbS at the rate of

6 miles

haur, in a current that feu S EbS

miles ;¡n

bour : Required her true rate of failing.

Here it is evident tbat the lhip's true rate of failing

will

miles an hour .

OASE

the eurrent felS direllly agaion the !hip's

c ourfe, theo the motioo of tile !hip is letreoed liya; mueh

as is the veloeit y of the eu"cnt .

EX"MrLE. Suppofe a Jhip fai l,

SS\V

al Ihe ro,e of

miles

hOtlr,

in a current

thót fc;ts NNE 6 miles

hour. R equi red

the

fhip's

true late

of laiJing.

Here

ít

evidem

tbar

the

lhip's

true rate

of failing

VIiI! be

iniles

hOll r. Hence ir is plaio,

CORo

the vclocity of the eurreot be lefs th.n

the veloeity of the nlip, then the !hip \ViII be, fo mueh a–

hcad

as is

lhe

difrerenec

of thé(e

velociti~s .

COR o

lflhe .t1oeityoflheeurreot be great« Ihan

lhat of Ihe !hip, th'en ,he !hip will fall fo mueh a lltrn as

is the

diff=rene~

tht-Ce

vdoci ties.

CORo

111.

Lanl y,

the veh>ci,y of the eurreot be e–

qual 'o that of ,he !hip, theo the !hip will

n.od

lIill ; the

one vcloeity denroyiog the

ol~er.

C. s

Ill.

If Ihe <urrent th\Var's the eourfe of the n,ip,

then

not only

J~crens

or au gmenrs her

vdoeity,

but

gives her a new

dircaion

eompounded of the eourfe Che!

Lteels.

and the fetting

of the

curreor, as is maoifdl: from

the íollo',l/iog

">lA.

a body at A (No.

26.)

be ímpelled by

two forces rtt the

Carne

time, the one in the

dire{lion

eapable lO carry ,hat body from Ato B io

eertain fpace

time, and

the other

the

direélion .AO

c,,:pable to

carry it

from

D in {he (ame time; complete the

parallelogram ABCD, and draw ,h. diagonal AC ; then

the body

agitated by thefe two forees together, will

move along the lioe

BC,

and will he io the poiot C at

the end of the lime in whieh it \Vould have moved aloog

AD or AB with the forees Cepar"ely applied.

Henee the folotion of the followiog 'examples will be

evident

EXA;"PLE

~uppofe

a n,ip fails (by the eempafs)

diretlly

fouth 96

miles

in 24

hours,

in a

current

that

feli

eaft

miles in Ihe fame time . Required the !h:p's Irue

eourre and d¡(lanee.

CEOMET.,C.ALLI-. Draw AD (fee No.

26.)

to re·

prefent the Couth aod oOrlh lioe of ,he !hip at A, whieh

make equal lO

96 ;

from D draw DC perpeodieular to

AD, equal lO

45;

aod join AC . Then' C will be Ihe

O,ip's

lrue

place,

her

true

dillaoee,

and

the aogle

CAD the true eourfe . To fiod whieh

By CALCULATION :

Firn, For the true eourfe DAC, it will be, (by rell–

angular trigonometry,)

As the appareot diHaoee AD

is ro

lhe current's

morioo DC

radius

the

tangent

of the

true ?

eourfe DAC --

10.00000

confequently

the

fh ip's

true cour(e

is S 25° 07' E,

3SE

2 0

37',

eallerly.

Then for the Irue dinaoee AC, it will be, (by rellao·

guiar trigonometry,)

As the line of the courfe A

25°,

07'

96278 4

i. tO the departure D C

45 - 1.65321

is radius

)

O. OOQOC

to the true dinanee AC

106 -

2 .0253

EXA>trLE. S ppoCe a !hip fails SE

120

miles in

hours, in a current that

(etS

V\T

the ra:e of:2 miles

2n hou r : R equi red the !hip's true eourfe acd dillanee fail–

ed in lhat time.