433 / 868
N
A
v
1
G
to the difference
oC
latitud. -- 46,6
1.66804
confequently
the'
lal iwde come to is 47
0
59, and there·
fore the eolarged d:ffcreDee of latitude wiJl be 69 .2.
TheD,
For differenee oflongitude :
h.
radius
i. tO the enlarged diff. of lat.
69.2
fa is the tango ofthe courfe
33° 4,'
10.OCOOO
1.84° tI
9. 8 '4 8 9
1.66,00
10 the differenee of longitude
46.24
4'
Courfe
SbE,
di llanee ,8 mil...
For difference of latitude :
As radius
10.00000
i.tothedillance
28
1.447t6
fa is the co·fine of the courfe
11
0, 1,'
9 ·99 t,7
to the differenet of latitude
27 ' 46
1.43873
<:onfequently the latitude come to will be 47°, 31 ' ; and
henee the meridional differenee of latitude will be 43 .2.
Tben,
For difference of longitude:
A! radius
10.00000
i. tO the enlarged dilf. of lato
43 .2
1 63548
fa i. the tangoof the coutfe
) 1°,
IS'
9.29866
to the dilf. of longitude
8 ,,9
0 .93414
Now
thert
fevc:ral
courres
and diClances,
togelher
with
·the difference
oC
latitude a.d lon¡¡itude belonging tO each
of them, being fe< down· io their proper columns io the
Traverfo Tabl.,
wiJl llaod as follow.
Courja
SSW
SbW{W
SWbS
SbE
¡Jtj/anca , DtJf. o/ La/ . ,n iJ!.
if
Longi/.
1~-S-'EIW-
44--- 4°.
6, ---
2, . 6
-
3 6 --- 34'4 6 --- 16. 19
-
,6--- 46. ,6
49. 24
- 28-
27 ' 46 8 . ,9 ---
------
---
---
Diff
if
Lat.
149· 13
8.
S9 88 '03
8'; 59
DiJ[. o/ long. 79' 44
Hence !t is plain that the Illlp has made
oC
fouthing
J49 " 3 mlOUtes, and eonfequently has come tO tlie lati .
tude of 47° 31' nortA, and fa the meridional differenee
oC
latitude bet",een that and her firll latitude will be
226. 1 ; and fince fhe has made of difference of longitude
79 ' 44 minutes wellerly; thereCore for the direél cOllrfe
aod ddlance betw<en the lizard and the fhip it will be,
( by
Cafo
2 .
if
thÍl Sdlion )
For the direé! courfe :
As the merid . diff. of latitude
226. 1
2.35430
is
lO
radius
10 .0000 0
fo i. the difference of longitude
79. 44
1.9°
00
4
to the tan¡¡ . of the courfe
-
19° 22'
9.,4593
which becaufe the differerfce of latitude is foutherly, and
the d,fference of longitude wdlerly. will be fOUlh 190
22' well, or
SbW
8° 7' wlflerly. Then,
For the direé! dillance:
As
raditU
10.00000
A
T
1
o
N.
is to the proper dilf.
oC
la,
149. 13
fo is the recant o( lhe
courre
19° 22'
'o tbe direé! d,n.nee
1,8
From the btítude the Ihip is in
fubtraé! the
loe
of tbe Madera
2. 17349
10.02 53°
2. 1\11.79
47°, 3,'N
32 , 20
N
and there remains
15
,
11
equal lO 9 11 minutes, the proper difference
of
lalitude
between tbe fhip and the M adtra.
Again. Crom the merid. parts anfwerio
g
1
tO the lati'ude the fh ip is io
3
2
4 8 . 4
Take
lhe meridional parts ao(wcriog to
"l
,he la,itude of the Madera
S
20)2 .
o
and tbere remains
1'96. 4
Ihe enlarged diRúene!: of latitud. belweeo Ibe fhip aod
the Madera.
Alfo, from .be difF. of long. be,weeo
7.
'
w
the Lizard and the Madera
5
1
[°,4°
T ake the difference of loog. b_e,weeo
7.
1,
19N.s
W
,be L izard an·d Ihe fh:p
S
and there remOlins
..
10,
'lO~W
equal 'o 620.,6 mio . of dilferenee of longilude be.ween
the fhip and .he Madera wellerly.
Then for the direé! courfe aod diClaDce belweco Ihe Jhip
aod the Madera, it wiJl be,
For .he direé! courfe:
Astlle merid. diff. of latitud.
1196. 4
3 '°7788
is to radius
fo is tbe difference
oC
longitud.
620.,6
'o tbe tango of tce courfe
27°, 2
s'
For the direé! diflance :
10.00000
2 . 792 78
9· 7
1
493
As radius
10.00000
is 'o .he proper diff. of lati,ude
911
2.9,9,2
fo is the fecant ofthe courfe
27°,2,'
10. 0,174
'0 ,he direé! diftance
1027
3. 01126
JO.
h is very common, in working a day's reckoning
at fea, to find the d,fference of latitude and departure '0
eaeh courfe and dinance; and adding all the departures
,ogether, and alJ thed,lferenees of la.itudes for ,be whole
departure, and difference of lati.ude made good that day,
from thenee (by
Caje
8 . of this
Sd/ion)
'0 find ,he dif–
C.rence
of longitude,
élc.
made goud tha, day. Now that
this method is falfe, will evidently app••r, ir we confider
thal the farne departure reckoned on two differcnt paral–
lels wilJ give unequal dilferences of longitude; aud c<¡n–
fequently, when feveral departure. are compounded .oge–
ther and reekoned on the fame parallel, tbe difference of
Jongitude reruhiog rrom that cannot
be
the fame with
,he fum of the d,lferences of longitude refulting Crom ,he
fev eral departures
00
different parallels; and therefore
we have
chofen, in ,he
Jall
~xt1l11p/~
of
a
trav~rft.
to
find
the dlfference or longitude anrwcring to
eaeh
particular
courfe and diflance, the fum
oC
whieh mufl be ,he teue
difference of longitude made ¡¡ood by the fhip on tbefe
fcveral courres
aod
diO:mces.
1
L
We fhewed, a.
Arl. S.
of this
Stfl¡on.
how tO
conOru(t
a
lJ1erco"'Dr', chorl ;
and no\V we
fhall
proceed
to
¡ts
feverdl ures,
containe-d in
,he
rollowing
probltmso
P~OB.
'. Lel il be requICed to
by
dowo a place upoa
tbe