426 / 868
N
A
v
G
:ro
¡.
Ibe fine of the courfe
)50
19'
9,915°4
"O
the depanure
-- 202 ' 3 -- 2 .3°598
L.Oly, For ,he diff<rence of longitude, it will be, by
C,,¡,
2.
of
Paral/,/ Soi/ing,
A, ,he co·fine of ,he mid o par.
42°
16' -- 986924
i. 'o ,he depanure
302.3 -- 2.3°598
Io
is radius
10 .00000
to mino of diff. of longitude
2.73·3 -- '> .n614
eq4.1 'o 4°
33',
the, difference of longitude eaOedy.
CASE
V.
Courfe and depanure given, ' o Gnd dif·
ference of lati,ude, diffelence of longitude, and diOance
hiled.
EXAMnE . .s"ppofe • Ihip in the i.lÍtude of 48°
13'
nonh , fail. SWbS, ,illlhe has
m.deof wcOing 12 3 miles:
R..equire.d
lhe
latiludc come ro, [he dilfercnce of Jongitudc,
and ,he di(lance
f.iled.
FirO, For ,he di(laDce. i, will be, by
Cafe
6.
of
J>Jain
Sailing,
As ,he (ine of .the courfe - 33°,45' -- 9.74474
is 10 the depar,ure
123
2.0899 1
fo
15
radius
10.00000
{O ,he diOance
221·4
2.34517
And forthe difference of·lati,ude il will be, by ,he fame
Coft,
As ,he ,ang. of courfe -- 33°,45' -- 9 .82489
is 'o Ihe departure
-- 123
2.08991
fo is radius
-_.
--
10.00000
to ,he diff. oHalilude -- 184
2.265° 2
equal
10
3° 04': And fince ,he Chip is failing ·,owards Ihe
equator
t
the latitude come to \.l/di be 45° 19' Dorth; and
confP.quenlly .he middle paralle! will be 46°
51'.
Then ' o find the diffcrence of longi,ude, i, will be, by
Caft
2 .
of
Paro/M Sai/ing,
A.
,he co·fine of mid o par.
46°,51' -- 9.83500
is 'o depanure
123
2.08991
fo is radius
10.00000
to mino of diff. of longit.
180 -- 2.25491
'Which is equa! to 3 0 00', the difftrence of longltude wffi·
-erly.
CA s E
VI.
D ifference of lati,ude and depanure giveD,
to find courfe, diO.nce, and difFerence of longit"de. .
EXAMPLE. Suppo(e
a
Chip in ,he l"itude of
46° 37'
nonh, fails be,ween fouth and ean, ,ill Che has made
oI
..aCling 146 miles, and is Ihen
fou.ndby obfervalion to be
,jn [he latiurde of
43°
24' north; required the: courfe, d¡[·
lance, and diffc:rence
of
longilude.
FirO, By
Col,
4' of
P/ain Sai/ing,
i, will be for ,be
c.ourfe,
ASlhc diff of lati,ude
<93
2.28556
i.
'o depa< ture
146
2.161 37
fo is radius
10.00000
to the ,ang. of ,he courCe -- 36°,
SS'
-- 9. 8]58 1
which , bec,u(e tbe Chip is failing betlVeen (ou,h and eact,
\ViII be fouth
,6°
55'
e.JIor SEbS
T
eaO nea rly.
For th. diOance, it \Vdl be, by ,he faOle
Caf' ,
A..
r<tdius
10 .00000
is 'o ,he dlff. of h,i,ude -- 193 -- 2 .28556
fo
15
the Cecaot of ,he couffe
36°,55'
--
1° ' °97 18
t o ,he diOance
24t ' 4 -- 2.38 214
Then for ,he difference of longitude, i, \Vill be, by
Caft
2 .
o(
Para/l,/ Sai/ing,
VOL.
IIl.
No. 84'
A
T
o
N.
375
As "he <oo·fine of ,he mido par. 45°, oo' 9:84949
is 'o the depanure
146 -- 2., 61
37
fo is radi us
1-0 .00000
'o mio. of diff. of longi,ude -- 205 -- 2. 31\88
equal 'o
3~
25'. Ihe difference of 10Dgi,ude ..Oerly.
CASE
VII.
Ddlanct and depan-ure given,
to
find dif·
ference of latitude, courfe, and differeflce of longitt!de.
EXAMPLE. Suppofe a O'¡p
in
the la,i,ude of 33° 40'
nonh , f.tls betwecnfoUl h and eaCl 165 mile" and has ,heo
made of ealling [12 ., miles; lequired the difference
cf
latitude, courfe, and difFt:rcnce of longit.ude.
FirCl, For!he coulfe, i, lVill be, by
Cafo
5.
of
P/ain
Sailing,
As m e diClaDce
165
2.21748
is
tO
radius
J
0 .00000
fo i, the depanure -- 102. )
2.05"5
10 the Goe of the courfe 42°,59'
9.8336,
which, becaule ,he Chip fails between fouth and eaCl, wiU
be fou,h 42
o
59' eaO or SEbE
t
eaO neady.
And for ,he diffcrence oflatitudc, il will be, by
,he
fame
Caft,
As
radios
.'O.COOOQ
is
10
the diflance
16,
2.2 1748
fo is Ihe co Gne of the courfe 4,° 59' -
9.86436
to the difference of lat o
1~0. 7
2.08184
equal to
2
0
00' ;
coofequently the latitude <ome to will
be 3,0 4'" nOrlb, and
,he
la,itude of Ihe middle 'parallel
will be 32
~
40', Hence, 10 find lhe difFerence oflongilude,
i, wlll be, by
Caf'
2 .
of
Paral/,/ Sni/ing,
As Ihe co·fine of ,he mido .par.
32",40'
-
<).92522
i.s to the depanur.
112 . 5 -- 2.0Si15
fo
is radius
IO.OOOOe.
10 mino of diff. of long.
[33. 6
2.12593
<qual 10 2° 13' nearly, Ibe diJference of longi,ude eall·
erly.
.
CASE
VIII.
U lffOfenc,e cf longi,ude and departur.
given, 'O find difFerence of l. tilude, courfe, aDd diOance
failed.
FXAMPLE. Suppore a Ihip in lbe latilude of 50° 46'
nonh, lads between foum and \VeO, till her difFereoce of
longitude is
~o
1-2', and i. Ihen found 10 have depaned
from her former meridian 1,6 miles; required the diC ..
ference of latitude. courre, :
:t.nd dil1an.cefailed.
FirO, For the latilude Che has come 'o, it will be, by
Caf'
3.
of
Para/M Sai/ing,
As Olio. ofdifF. oflnng. -- "92 -- 2.28 33°
is 10 deparlure
126 -- 2 . 10037
fo
is radius
10 .00000
to theco finenf the mid. par. -48°, 59' - 9.8'707
Now fince the middle latitude is equal tO hal( Ihe fu",
of ,he two lati,udes (by
Art .
1 .
of ,his Set!.) and fo the
fUIn of ,he two l..ilUdes equal 'o double the middle la,i.
tude
¡
it follows, rhat if flom double Ihe nliddle l..i,ude
we fubtraét any one of the latitudes, the" rcmainde"r
will
be ,he o,her. H ence from ,\Vice 48° 59',
viz .
97°
5S'
taking 50° 46'
the latitude
failed
from . there rem.lins
470
12'
lhe
latitude come
tO;
confequently
lhe
diEcrcoce
of latítude ís 3° 34', or
214
minutes.
Then for the courfe, il will be, by
Caft
4' of
P/ai~
Soilil1~ ,
As diJf. of lato
5 B
"