1000000031

AC: CB :: AK:KD.

i .

• .

As ,he proper diff. of lali,ude

16S

2 . 2 I

748

istothedeparture

12642 . 10(75

fo i. ,he enlarged diff. of latitude -

233·3 2.3679[

10 min. of diff. longi,ude

178.7 2.252 18

equ.1 10

58'

4''''

,he difference of longitude we/ter/y.

Theo for the cou rfe it ",dI be, (by reélaogular trigo–

nornctry,)

AC : BC : : R : T, A.

' .

As Ihe prop" dij'. of latitud.

2"'748

i. 10 deparlu"

126·4

2.10175

(o is radius

10.00000

10 the langent of Ihe courfe

37°, 27

9.884'7

",.ieh, beeaufe Ihe fuip fail. b"weeo fouth and welt,

",ill b. fouth

37°

27 ' well, or SWbS 6° 30' weller/y.

. LaHly, For tbedillane. AB, i, ",ill be, (by reélangular

,rigonometry,) .

S, A :

BC : :

R :

AB .

i.,.

As ,he lioe of ,be eourfe

37°,

'7(

9.78 395

is to ,he depanure

[26'4

• .(0175

fo is radiol

10.00000

'o [he direél dill.nee

207·9

2.31780

CAl.

lX.

One lati,ude, dillance failed, and depar–

ture giveo ; to 6nd ,be olber I.,i,ude, differeoce of loogi–

tude, and courre.

EXAMPLE .

Suppofe a O,ip io the I.,i,ude of

48° 33'

lIor,h,

f.ll

. be,,,,een fou,h and eall 138 miles, and has

,hen made of depanure 11 2 6 . Required ,he la,i,ude

COnle to,

the direét

courre.

and diffcrence

Jongitude.

GEOM[TRICALLY . dl, DrawBD (No. 2 [, ) for ,he

meridian of ,he fu ip ..

and paral/e1 'o it draw FE, at

the di(lancc of 112 .6, ,he depar(ore. T ake 138, ,he

dinancc, io your compalfes, and 6xing one poio[ of thcm

in B, w¡,h .,he o,her crof. ,he line FE in ,he point E;

,hen joio B and E, and froOl E

le,

fall upon BD ,he

p.erpendicular ED; fo BD IOil/.

tbe proper differenee

of la,i,ude, and ,he angle'B ",ill be ,he courfe;

fiod

which,

calcuJation,

Fir(l. for ,he courfe i, ",ill be, (by reél.ngular trigo–

lIom'etry,)

BE: R : : DE : S, B.

' .

A. ,he dillaocc

138

radiu.

10.00000

fo i..be departure

112 .6

2.0S 'S4

(o Ihefi•• of,he courfe

54° 41'

9'9 1166

..hich, becau(e Ibe /hip (ail. bct",een fouth and eall, will

be foulb 54· 41' eall, or SE

41 ' uller/y.

TheD for ,he dilfcrence onalÍlUde, i, ",iU be, (by ree–

tan,ular "illonometry,)

R : BE:: Co·S,

B :

BD.

¡., ~.

A, radius

0 .00000

10 Ibe'dillanee

138

2. ' 3988

fo i. Ihe co fine o( ,h. eourfe

54°

41'

9.76200

,he di!fereace of Ia,ilude 79.8

1.90188

<<¡u.1 to 1°

[9',

Coofeo.¡ lIeotly,he fuip has come 10 ,he

h,ilude of 47· 13°'. Hence Ihe meridiooal dilf"eoce

of Ialilude will

117 7.

2dly, Produce

10 A, ,i" BA he equallo 117.7; and

Ihrough

draw AC p...l/ello DE, meeling BE produ–

ced in C; Ihm AC wiU be ,he dilf.renee of 10D¡i1ude ;

.&o

iod ",b.¡eh hy cal.cllla,ioD, il....il/ be,

BD : DE :

BA : AC.

r .

As the proper diff. of l' lilude 79.8

" 9° 180

is 'o Ihe depJr,u -e

112.6

2.05154

fo is ,he enlarge.! d;ff. of latitude

117 .7

2.07073

10 ,he ddf of IO:Jgi,ude

166.1

2,2204¿

<qual 10 2° 46' 0 6", ,he dilfe rence of longitude ea:

fl er/y .

9, From what ha. beco faid , il wil/ he eafy to fol ve a

tr¡verfe according

the rules ofMercator's failing.

EXAMne.

Suppofe. fui p at ,he Liurd in Ihe lati–

tude soo

00'

no(th, is bound to the Madera in the la–

tilude of

32r> ,

20'

non h, (he diffe.rence oflongitude be ...

'wceo ,hem being 11° 40" ,he well cad of Ihe Madera

Iyiog (o much 10 Ihe

wellw.rd

of ,be Lizard, and coo–

fequently Ihe direét courfe and dillanee (by

Cafo,

,his

Sdl.)

i. foulh . 6°

IS'

we(l 1181.9 miles; bu, by

re~roo

of Ihe wind. /he i, foreed to fail 00 die followiog

courres (allowance being made forlee-way and v¡riation,

&c.) "iz.

SSW

mile., S6W -} well 36 miles, SW6S

56 mile., and ShE .8 miles . Required Ihe latilude Ihe

Ihip is in. her bearing and dirtance from (he Lizard. and

her dircél courCe anl! dill.nce from Ihe Madera, a' the

end of ,hele courfe•.

The geometrical conCtruétioo of this traverfe is per ...

formed

layio& dowo ,he, 'wo por" according to con–

IIruélion of

Cafo

2. of ,hi.

Sdl.

and ,he feveral courr..

aod dillanees .ccordiog 10

Cafo

by wbich ",e J¡aveu.e.

following folulion by ealculation.

l .

Courfe SSW, dillance 44 mile._

For dllferenceofla,ilude: '

A. radiu.

10.00000

i. to Ihe dillance

6434S

fo Ihe i. Ihe eo·fioe oflhe courfe 22·, 30'

9.96562

10 Ibe dilference of lalitude

40.6

1.60907

.nd unce ,he courfe is (oulher/y, ,berefore ,he lalitude

come 10 wil/ be

49~

20' nonh, ,and confequently t be

meridional difference of latilude \ViII he 61.8. Tben

For dilfereoee ofloogilude,

As radiu.

JO.ooooo

'o ,he enlarged diff. of lat. 618

1.79099

fo is ,he tang of Ibe courfe 22·, 30'

9.61722

'o mio of diff, of longilude

256

1_4°821

2, Courfe

SbW-}

well, diOance 36 mile•.

For dlfferenee of latilude:

radiul

10.00000

is 'o Ihe dilla.nce

5563°

fo is ,he eo· fine of Ihe courf.

16°,

9'98°90

to Ihe difference of latilude

34'46

\.51720

.nd r..ce Ihe courfe is foulherly, Iherdore the lati,ude

come 10 wiJl be 48°

4S'.

Hence Ihe meridional diffe–

renco of lalitude will be 53 .4 . Then,

For dif!'er<nce of longi,ude :

As radius

i. 10 ,be enlarged diff. of lal. 53 ' 4

Ihe I.n. of,he eourfe

16°,52'

1000000

1.7 2

754

9'4 81 71

1.2°9

10 ,he dilferenee of longilude

16.19--

3. Courfe SW

bS,

dillance 56 miles.

For differeoee of 1. litude:

radiu.

is 'o the dillaoee

Ihe ca-fine of Ih. ,ourfe

1000000

1.7481 9

33 °,

45' 9 '9198,