1000000031

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V ' 1 G

EXAMPL

Suppare a Chipruos at the rate af 6¡ kao..

in half a

minute ;

bUI

meafuring

tbe (pace between knot

aod koat, 1 fiod it ta be

feet : R equired the uue di–

llanee in miles .

Making it, As

feet is ta

feet, fa is

6.25

kna.. ta

7 knats; 1 find that

lhe

Hue rate af failiog is 7 miles io

lhe hOllr.

EXA '....

L~ 1I~

Suppafe a fhip ruos at the rate af 6{–

.knolS

in half

:Il

minute;

bUI

meafuring (he {pace between

I<oat aod koat, I liod it ta be anly 44 feet : R equired the

true

rate

of {¡¡iling.

Making it, As

feet is to 44 feet, fa is

6 .5

kna.. ta

5.7 2 koats ; 1 find ,Ioat

t~e

Irue r ate or CailiDg is 5.72

miles jo

lhe

hoor.

9 . Ag.i n, Cuppofing .he dillanee between knat aod

koat 00 the 10g.lioe ' 0 be exaaJy

feet, but .hat the

¡:laCs is oat 30 feeaods; :heo, ir the glaf. require longer

time

run th:\o 30 feconds, tbe dittance givcn wiU be

too gre.., ib

ima.ed

by aHawing l' mile Car even{ kaa.

run in the time the glafs

rU DS ;

and .

00 lhe cootrary,

the C1afs

requiTes

lefs time

run them 30 Ceconds,

will give the dillanee failed too [mall . Caofequentl y, ta

find the'lrue diflance in eilher cafe, \Ve mufl meafu re lhe

-time (he gLars reqhires to non out

(by

lhe method in lhe

f allo\!(iog anicle ;)

th~o

we h, .e .he Collowiog prapaniao,

'f)iz.

As Ih. number of feeondo the gl. Cs ruo" js to half •

mioute, or 30 feeaod. ; fa js the di(laoee given by the Jag,

to the true dillanee.

E XA

E!. Suppafe a fh ip runs at the rate of 7';' knolS

the ,ime .he glaCs raos ; but meafu ring , he gl afs, 1 find

ruos ; 4 feeoods: R equired the true diO. oee failed.

Makio~

it, As 34 feeoodsi. ta 30 fceaods,

i. 7. ,

ta 6.6; 1 find th. , the Ihi p lails at the r. te af 6.6 miles

an hour.

EXAMPL E TI . Suppafe a n,ip ruos at Ihe rále af

kDa.. ; bUl meaCuiíng ,he ¡¡laC., [ fiod it rUAS 00lY 2, Ce–

conds: Required the [rue

rclte

of fai Jing .

M aking it, As 2, Ceeonds is ta ,0

eoods, Ca js

6.5

k oa¡. la 7.8 knoB ; 1 fiod that the true rate af f¡¡iliog

'7.8

miles an hour.

10. lo arder ' o knaw haw maoy fceands .he glafs ruos,

you may

t,ry

bya \Vateh or clock, that vibrates feconds;

'bUI

neither of theCe be at hand, thentake a line, and to

the one end faClening a plu mmet, hang the other upon a

nail ar pego fo . s the dillaoee from the peg to . he centre

ar .the pluminet be 39i--ínches: T hen th is

pUl

ioto

mOlian

will vibrare feconds ;

every time ir pa(fes the perpen–

dicular, you are to count one (econd; cenfcquendy,

ob–

ferving lhe

number

vibrations tllar

makcs during

the

time the glaCs is running, \Ve know how many feconds [he

glaCs ruos.

11.

,here be an 'error bath io the log lioe aod ·hal f.

minute glafs,

viz.

the difhnce-bc[\veen knot and koot

and the log-line be either greatCT or lefs than

re~t,

and

{he

gl~rs

runs either mOre or lefs than

Ceconds;

then

the

finding out the

Olip's

true dillance

\ViiI

be fome–

what more comphciHe, and adIJ)it

three cares,

viz.

CA"

If the glar. rllos more ,

h.tO

reeoods, >nd

tht dinancc bctween Itnot CV"Id knot be lefs than SO reet,

~hen

the dlllaoce 8·i\·e by .he lug lioe,

viz.

by allowiog

l ·

, mile far eaeh knot the fhjp fails while the

g1.r.

'lID'

niag, will always be treater than the true dilhnee, fiD""

either of theCe erron give the dill.nee too gre.t. CooCe–

quently, ta fin<! the true rate of Cailing io thi. eafe.

we~

mu(l firll fiod (by Art. 8.) th. dia.nee,'on the Cuppofi.ion

that the log· lioe is aoly wrong, and Ihea with ,his

(by

Art. 9.)we fuall fiod the uue dillane:.

EXAMPL~ .

Suppafe a Ihip i. fouod to run at the rate

of 6 koots; but examining the glaC., I fio,f it ruos 35

feeand.; and meafuriog the lag.lioe, 1 6nd the dillaoee

be,ween kDat and kaat tO be bu, 46 feet: Required q,e

tToe difiance runo

Firll, (by-Art . .8.) We have tbefollawing.propartían.

viz.

feet : 46 feet :: 6 koa!! :

s."

kna!! . Then

(by Art. 9.) As 35 feeaods: 30 feeonds :: ,.52 koots ,

4.73 kna... ConCequently the t<ue rate of failing i, 4.73

miles an hour.

CAS E Il. If the gla[. be leCs than ;0 feeaods, .od the

place betweeD koot aod koat be more than

feet; ·then

Ihe di(laoee giveo by the log will alwayo be lefs thao .he

true di(lanee, lince ei,he, af tbere errars leíTeo the Irue

dillaoee.

EXAMPLE. Suppafe. a fhip is fouod ta run at the

r.te

af 7 koo.. ; but examiAlng the glaCs, 1 find it ruos anly 25

feeoo<\J; aod meafuring ,he fpaee betweeo koat an koo,

00 Ihe.1og line, 1 find it is

fe.. : Required Ibe true

'ate af Cailiog.

Firll, {by Art. 9 .) As 2

feeonds : 3'o feeaods :: 7 kna..,

8 '4 koats . T heo (by Art. 8. ) As

feet : , 4 feet :: 8'4

koa.. : 9.072 koo" . CaoCequently .he uue rate of fail–

ing is 9.072 miles ao haur.

CAS~

lit.

If .he glafs ruOS more thao 30feeaDd" aod

the (pace between knat and koat be greater than

feet;

or if Ihe glaC. ruos JeCs than 3<> feeaods, aod ,he Cpaee

bet lVeeo koat aod koat be lef. thao , o feet: theD, Goce in

ei.her af ,heCe two caCes the effeas of the errors are eoo–

trary, it

plain the difiance will rometimes

too great,

and

Come times

too little, according

the greaeer.quanlity

of the error lies ; as will be evidem fram th. Callowiog

examples.

E XAM PLE

Suppafe a fhip is faund to run at Ihe

ra.e of 9{- koats per glaCs; but rx.mioiog Ihe glaCo, it

is fouod to run 36 feeaod.; aod bv meafuring the fpace

betweeo kno, aod koot, it i. fauod,lO be

Sil

feer-: Re'lui–

red .he Irue rate af (ailing.

F irll, (by Art. 8 .) As ,o feet : 58 feet ::

koa..

: 11 .02 koats . Then (by Art. 9 ) As 38 Ceeands : 30

feeoods :: 11 .02 koa!s : 8. 7 knats. CooCequeDtly Ihe

fllip's true rate or

flilling

8 7 miles an

hour.

EXAMPL'

ll.

SuppaCe a fhi p ruos al the rate of 6 koa..

per glafs; but examioiog ,he 81aCs, it i. fau od

ruo

o.ly

00 feeands; . od by meafu riog .he lag. lioe, Ihe dill.n,e

bet\Vceo koot and kool i. Caunu t<\ be but 38 feel : Requir<d

Ihe IrU' rate of Ca"iog.

F irfl , (by Ar< . 8 ) As ,o feet : ,8 feet :: 6 knots:

4. ,6 knolS. T heo (by Art 9')

20 feeands : 30 fe–

eaodo : : 4.,6 koa.. : 684 kaalS. CaRfequeotly the

true r;ue orCailing is

6,83

miles

;ln

hour.

. HUI

if in

thir

cafe ie h:lppen, that

the time

lhe

glars

takes

Tun be

t O

th e diHd.nce between knot and knllt,

aS- Jo,

the Ceconds

half

minute;

S0,

the tf ae

dillaoee