420 / 868
N
A
v
G
¡te.ter than
4~
oegret., an·d fo the dilFerence of latitude
w,/1
be
,real~r
than ebe dep.rIDre; bUl if the
~Durfe
be
gre,ter
~b.n
4
poi
O",
\hen the diJf<reoee Qf latiende wiU
be kfs than
th~
depariure; and lallly, if ,he coorfe be
¡un:
4
points, the dilfereDeeof latirode " ilJ be eqo¿l
10
the
aepartur.:
5.
Sinee the ilillanc., di!rerence oT latilude, and de·
parture, form a
righl· ~ngl<d
triangle, in whieh Ihe oblique
angle oppofite to the departure is the eoorf., and. lhe
Olher its complement; thereforC', hating any two of (heCe
giveo, we can (by plain trigooomelry)
brrd
the rel! ; and
henee arif. the cafes of plain.failinz, which are as folJow.
CASE
I.
Courfe and dillaoee giren, to find dílference
oC I.,ilude and departure.
EXAMPLE. Suppofe a·Chip (aiJ, from Ihe htitude of
30° 25' north, NNE, 32 miles, (No. 4' )
Re'l0ired
the differene' of latilude and departure, and the lati·
,ude come lO.
Then (by right .ngle trigonomeuy,) we
have th. folJowing .nalogr-, for 6nding lhe departure,
vito
A,
radius
10.0000Ó
lo tbe dillanee AC -
32 -
1.5051 5
fo i, the fine o( Ihe eourfe
A
21°
30'
-
9.58284
lo the departure BC
'2 .25
1.08799
fo the Chip ha. made 12 .25 mile. of departure ear.erly,
or hos gOl fo far to the eaflward of her meridi:rn. Then
for lhe difFerenee of latilude Or oorthing 'Ihe Chip has
made, we have (by teélan!:ular trigooometry) the follow·
ing aoalou,
"iz.
A, radiu.
10.00000
i, lO ,he dinairee AC
32
1.,0, 1,
Jo
i~
the
éo~.fine
of eoorfe A-22° 30' -
9.96,62
10lhediflúenee'Oflal.
AB
29·,7
1'4i077
fo Ihe Chip has d,trered her lalitude, or made of oorthing,
29.57 minule•.
And finee her former l..i,ode
Was
north, aod her dif·
feren ce of l..itUoe alfo north; lherefore,
To lhe latitude failed from
-' 30", 25' N
add tb"e difFerenee of latilude
00°, 29.,7
aod .he fum is Ihe latitude come lO
30°,
54.57
N
By thi, eafe are e.lcul..ed .he table. of dilterenee of
la.ilude, .nd e/eparture, lo every degree, POiOl, and quar–
ler·poiOl of Ihe compaf•.
CÁH
n.
Courfe and differenee
of
latilude given, to
6nd din, nee and·deporlure.
EXAMPLE. Suppofe a Chip. io lhe latilude of 4)° 2,'
north, fails
NEbN
+
eallerly (No, .) liJl n.e Come to the
la.itu4e of 46°
SS'
nonh. Re'luired lhe diflaoce aod
departure made good upo. lblt eourfe.
Sinee both lati.udes are northerly, and Ihe eourfe alfo
nonherl
y
i
therefore-,
From the latitude come to -
fubu.éllhe latitude faiJed from
and thcir remains
the diIFerence of latilude, equal to
9ó mile,.
And (byreélangul.r tri,onometry) we have tbe foJlow.
iog aoalogy, for 6nding tbe depa",!re BO,
viz.
As radiu,
-
-
-
-
10.00000
.il to!he diff. of latitude AB
90 -
J
.95424
T
1
o
N.
3 6 9
fo is the tangent of eourfe A-39°,
22'
9.9 14°4
to ,he depanure DO
-
-
73 84
1.868.8
fo the Chip ha. got
73 84
miles 'o th. ea(lward of ber /{¡r–
tncr meridian o
.Agoin,. for Ihe
dinanc~
AD,
tVe·.have .(by .reélaoguln
tngonometry) Ihe (oJlowlIlg proporl'oo;
¡,iz.
A$ radius
10.0000 0
is· to lhe feeanl of the eou rfe
39°, 2'2'
10.11176
fo is ,he di/ferene< of lattlud.
Al:!
90 '
1.954 2
4
to ,he di/lance
AD
~
-
116' 4
2.06600
~A
lE
III.
Oilferenee of latilude and diflaoce given,
to hnd courfc: aod departurc .
EXAMPLE. Suppofe .- Chip fails from the' lalitude
oC
56° 50' nonh, on a rhomb between fOUlh and wef!, 126
mile" and !he
i,
then found by obferv.tion to be in the
latilude of
5,~
40' north . Re'luired the eou,re Che failed
0 0,
and her departure from the
me,idi~n.
No 6.
Sinee'the lati,udes are both oorth, aod lbe Chip failio)!
toward s the
c:quator
i
thercforc,
.From lh. latilude failed from
fubiratl lhe obferved la.itude
and the remail1der
-
-
-
'01°,
40'
equal lo 70 miles, is lhe dilferenee of latitude.
Dy retlangular trigonometry we have the folldwing pro.
ponion for '/inding the.angle of Ihe eourfe F,
"iz
A, the dillanee f'tled
DF
126 - 2...0037
is to radius
10.00000
fo i, the difF. of latitude
FO
70 -
.1.84516
to the eo-fine of lhe eourfe F
56°, 1,' 9.74473
whieh, becoufe Che faila belWetn fou,h aod weU,
wíU
bo
fouth ,6°
1,'
well, or SWbW. Thco, ror the departure,
we have (by reélaagulal trigonometry) the followiog pro–
portion,
viz.
As radius
]
0 .00000
is tÓ the diflance failed
DF
126 - 2.1003 7
fo i, lhe fine of the courfe F
, 6°, 15' 9 .91985.
to lh. departore
DE
t 048 - 2.02022
eonfequeotly Che has made 104.8 miles
oC
departu« wefl·
erly.
CA' E
IV.
O :/ferenee of la,ilude aod departure giveo.
10 6nd eourfe and dillanee.
EXAMPLE. Suppo(e a Chip failo froin the latitude
of
44°
, o'
oorth, between foulh and eof!, tilJ !he has
mad~
64 mile, of ealliog, .n·d is lhen found by obfervatioo lO be
in tbe lati.ude of 4.20 ,6' oOflh. Re'luired the courf.
.nd dillaoee made good .
Sinee the lati'bdes are both north, aod the Chipf.iliog
towards the equator
i
therefore,
From lhe latilude failed from
44°,
,o'N
take Ihe latilude come lO
'41°,
,6'
and their remains
01°,
54'
equal to 114 miles, Ibe differcoee of latitude or fbulh–
ing.
In thi. eafe by (teélaogular trigonometry) we have the
following proportioo to 60d the cour(e
KGL
(No. 7.)
viz.
As
lhe dilf. of latitude
GK
114
is to radius
fo
i.
the
departure
KL
2·c¡,<'9°
10 .000 00
' 1.80618
10