425 / 868
N
A
v
[
EX"-"'P"'E.
Required the dire<'t co.rfe and di(hnce
be"v«n theLizard in the latitude
DE
SOo 00' north. and
longitude
DE
SO 14' \Vefi, and S, Viocen, in <he Iati,ude
oE 17° 10'
N.
aDdloDgi,udeoE24 20
W.
Firfi, T o ,he la,itude
DE
,he Lizard -
soo, 00'
N .
add ,he la,i'ude
DE
S, Vioceo,
17 ' 10
The Cum i.
HalE ,he fum or la,i,ude
DE (
the middle paralld is
S
Alfo
.he
difference
DE
latitude is
<qual 'o 1970 mile. of fou .hing.
From ,he longi.ude
DE
St Vincent
take ,he loogilude
DE
th.. L iz-ard
AgaiD,
61 , 10
33 , 3S
N.
33 • SO
24,20
W.
OS , '4
there remaiDs
16 , 06
eq ual 'o 1146 mino of diff.,
DE
long. \Yefi.
Then for ,he miles of ""fiing, or departure, i, will be,
by
Cafi
lo
of
Para/lrl Saj/jng,
As radius
10.00000
is to the co-fine of
tht
1
middl. p.rallcl
- 33°
3S'
~o
is l1Iin. diff.
DE
long.
to ,he miles of wemng
And EGr the eourfe it will
Samng,
1146
3·
o S9 18
9S 4·1
" 979 8 7
be, by
Caft,..
of
PI"in
As the diff. of lat.
1970
3.29147
is to radius
10 .00000
fo i. ,he dep.rtu«
-
954·7
2.97987
to ¡he tango of the courfe
2So, 51' --
9 .68S40
which, beeauf. i, is be,ween fouth and wefi, it will be
SSW i-wefi neady.
For the difianee, it will be, by ,he fame eafe,
As radius
10.00000
is to the diff. of laL
1970
3.29447
fo i$ ,he feeant of ,he courfe 2So,
SI'
10.0457 9
to the di(hnce
2.89
3.34°2 6
whence ,he direét eourfe and difiaoce from ,he L lzard 'o
S, Vincent is SSW
T
W,
2
t89 miles.
CASE
JI.
One la,itude, courfe, and difiaoee failed be·
¡og gioen,
lO
fiod the otber latitude aDd difference of
longitude.
EXAMPLK.
Suppofe a Ihip in the latitude Gf 50° 00'
"Grth. C.i1. fou .h soo 06' wefi, 150 miles : Required
,he la.itude .he Ihip h.. come tG, aDd how much /he has
differed her.longi,ude.
Firrt, For ,he differeDce
DE
Ia,itude, it will be, by
Café
J •
•
r
P·/ajn Saj/jng,
A. radius
10.00000
i.
'o ,he
dirtan~e
150
2. 17609
fa is ,he c&fine of thocourfe soo, 06'
9.807 16
to the diff.
DE
Ialilude -- 96.22 -- 1.<}832S
<qual to 1°, 36'. And (ince ,he Otip i$ failing l'O\Vards ,he
equél:or;
th::rerorc,
From
Ihe
l:ttitude
(he
was in
,ake ,he dilf. of 1.,itl1de
,ROO
thcre remains
48
J
:2
4
,he IJtllude Ihe h•.s come 'o nOrlh . Confequcntly ,he
Ja,itude of ,he midJle parallc1 \ViII be
49°
12.
A
T
1
o
N.
Tbe. [or
d~parture
or welliog it wiJl be,
by
fue
fa_
cafi,
As radiu",
IO.OOO~()
jstot.bedifianc,e
150
2.176°9
[o i. ,he fioe of ,he courfe
50· 06'
9 88489
'o ,he dep.rture
115.1
-
2 .0609~
As for .he differenee of longi,ude, it will
De,
by
Café
2. 01 P/ain Saj/j1lg.
As the co (ine of the middle paralld 49
4
12'
9.815 l'
is to radius
10.00000
.fo is ,he departu«
I1S.
(
2.06098
'o ,he inin. diff. of longi,ude '76.[
-
2.24S79
equal 'o 2° 56, \Vhi<h j. ,he differeDce of longi,ude ,he
fi, 'p has made wefiedy.
CASE
lIt
Courfe and difFerence of lati,ude given; ",
lind ,he difi.nce f.i1ed, and difference of longi,ude.
EXAMPLE .
Suppofe a/hip in ,he lati'ude of n°
34'
nortb, fail. SEbS, ,ill by obfero'lioD /he i. fouod
'o
be 'in ,he lati,ude of 51 ° 12', .nd confequently has dif.
Eered her latitude
2
° 22' or [42 miles: Required ,he
difianee failed, i nd the differeoce
DE
longitude,
Firn. for Ibe departu«. it will be (by
Cal'
2.
of
PII1;',
Samng ,)
As
radiUl
10.00000
i.,o<hediff. oElatitude
142
2.15229
fo is ,he tangoof eourfe
33 ~
45'
9.82489
'o the departure
-
I
94.88
-
1.977[8
And for ,he difiance i, \ViII be, by ,he
fame.Caft,
As radius
10.00000
i$ to the diff.
DE
Ia,itude
142
2.IS"9
fo is ,he fee.n, of ,he courfe 33° 45'
10.08015
to ,he difi.nee
-
[70.8
-
2.2 3244
.Then. fince ,he latilude failed from \Vas
53°
34' no, tb.
and the latitudc come
(O
S
I
o
12'
nonh; tbereforc the
middle parrallel will be 52° 23'; and cODfequen,ly. for ,he
d,ffereoce of loogi'ude, i, \ViII be (by
Ca/<
2.
of
ParalM
Saj/jng)
As ,he co-fine of ,he !)lid. parallel
52° , 3' 9.78560
is 10 ,be depanu«
94.88 1.97718
fo is radius
10.00000
'o mio. ofdiff.
DE
longitude
IH .S 2.191S8
<qual 'o
,0
3S'
,he differcnce
DE
longi,ude e.fierly.
CA s
E
IV . Difference
DE
lati,ude and difiance failed.
given;
10
find ,he courfe and difference of longitude.
EXAMPLE.
SuppoCe a /hip io the latitude
DE
43° 26'
nOrlh. fai" be,ween fou,h and eafi, 246 miles, and ,he.
is found by obferoation 'o be in the ,he la,i.ude
DE
4 I o.
06' north : Required ,he direa eourfe and difl'erenee
DE
longitude.
Firfi, For ,he enurfe. jt \Viii be, by
Caft
3'.¡
Pll1h.
Sailing.
As ,he dirtaoce
2'01.6
'.39094
is
tO
ndius
10.QOCOQ
Co
is the diff.oflali.ude -- 140
2.146 13
'o .he eo·fine of the c&urf. H
O
19' -- 9·755'9
whieh, bce.ufe the Ihip fail, be,wcen fou,h and eafi, will
br foulh
)50
19'
e.fi. or SEbE nearly.
.
Then for depanurc. it \ViII be, by Ihe fame
c,'j<.
As
radius
10.00000
jo
.10
,he difiance
246
2.39094
• f"