435 / 868
N
A
v
1
G
' hrough whieh draw a paralld of latitude, ",hi,.h \vill be
t he parallcl t:" Olip is in; Iheo froOl L dr,Iw a SSW line
L/,
eUlling .he former paralld in
f,
and I!lis ",iJl be' the
fhip's place upon
lhe
chart.
,
PROB. VI. O ne lalitud., courfe, 20d din,nee, fail ed,
j!iven; tO lay down the running of the Olip, and find he.–
place. upon the ehart.
EXA.,PL E. Suprofe a Olip at
n
in Ihe latilUde of
20°
00'
norlh,
Cails nonh 37
0
'10',
ean
191
miles: Rc:qu ired
t he !hip's place upon the ehart.
H aving draIV" the meridian and pJrallel of the pl ace
o,
fel off the rhomb line
a"
making wilh
nh
an aogle of
37°
~O'i
and
llponit
relOer
191
(romato
C;
duough
e
draw
t he par.JJel
eh;
and takiog
ab
in your comp,(fes, apply it
to tlle gradu2led eq uator, and obfer"e Ihe number of de–
grees
it
contaios
j
thencount the Came f,umber
of
degrees
on Ihe gr.duatcd meridi. n from C lO
h,
aod Ihrough
h
draw Ihe
p,r~Jlel
h
_,
which wiJl cut
ae
produeed in Ihe
poin,
~,
the (h ip's place rcquired.
PR OB o VII. Bot h latiludes and dinanee f"iled, given;
t o find Ihe !hip's place upon the ehart.
EXAMPLE . Suppofe a !hip fails from
a,
in the latilude
of
20
0
oo' north. between north
~nd
ean-
19 '
miles, and
is Ihen in the lalilude of
45° 00'
non h : R equired Ihe
lh ip's place upon Ihe ehart.
Draw
d_
Ihe parallel of
45 °,
and fet, off upon Ihe me·
ridian of
a
upwards,
ah
equal lO Ihe proper dilferen« of
lalitude .aken from the equalOr or eraduated paralle!.
Through
h
d raw
be
parallel
10
d,;
Ihen wilh 19 1 in your
compalT.:s, fix.ing one (oot of them in
a,
witb [he other
cr ofs
h_
in
e:
J oin
o
and
e
wilh the right lioe
oc;
whieh
produced witl meel
d_
in _, the O,;p·S plaee requircd.
PROB
Vil/.
One lalilude, eourfe and diJfereriee uflon·
gilude, .given; lO 6nd the OlÍp', pl ace upon Ihe ehart.
Ex...t .... Suppofe a !h:p from Ihe Lizard in Ihe la ·
tilude of
50°
CO' nonh , fails SWbW, liJi her differenee
of longilude is
~
2°
3Ó': R eq uired Ihe Olip's place upon
the charro
H aving dra",n .AE the
merid~n
of Ihe L in rd at L ,
eounl from E to F upon Ihe equator
42°
36' ;' and Ihrough
F
draw Ihe meridian EG; then from L draw the SVU\V
line LK, and where Ihis mee.. FG, as at K, wiJl be Ihe
Ibip's place requi red .
PROS .
IX.
Ooe latllude, eourfe, anddeparlure, given¡
tO find Ihe Ibip's place upon Ihe ehart.
EX.HtPL E. Soppofe a !hip at
Q
in the lalitude of
200
e o' nOrlh, fails nonh 37°
20'
can, tiJi !he h.. made of
derarture 11 6 miles: Rqeuired the !hlp'S place upoo Ihe
ch;lrt.
H aving d rawn the mer:dian of
a,
at Ihe di nance of
11 6, dr .w parallel lO it Ihe meridian
/¡
l .
Draw the
rhomb line
ac,
which
",jtl
meet
J.
I
in
{ome
point
e;
lhen
t hrough
e
draw the parallel
e
h,
and
a
h
\Vdl be the pro.
per differenee of latilud., and
b
e
Ihe depanure.
T~e
11
h
in your
comp.dr~s,
and apply
it
to the cquator or gra.
duatcd paraJlel; Ihm obferve Ihe number of degrees it
contaíns , -and
COUfl(
{o nlany on the graduated meridian
{¡om C upwards lO
h.
T hrol1¡:h
h
draw Iht paraJiel
h_,
",hieh will mect
a
e produeed in fome point as
r,
whieh
;s the Chip', place upoo lhc chan,
A
T
o
N.
PR OO
X. Onc I.ltítude, di!lJncc,
an:i d~parturc,
giv:n ;
to fir,J Ihe Ih,p's rl<ee upon Ihe ,har<.
EXAMPLE.
su ppor~
a
Olip
ata
in the latitllde or
20°
00'
non h,
fails
19 1
mile, betwet:n nonh and
can,
and
[hen
is
found
tu
hi:tve
m.IJe
of deranu re
1, 6
miles :
R~·
qui red Ihe Oltp', place upon Ihe ""n.
H.I\·;n.-!
dr.Jwn the
m
:ridi.tndnd
p.tr.d ld
of the pla.:e
a,
f«
ofF
tlpon lhe pa..Jlel
Q
"'
eql111
10
lI Ó, aod
~hrough
111
draw Ihe meridian
/¡
l .
T alte Ihe givon diftanee 191
.in you r
compa(f~s;
f¡::uing one foO( of them in
a,
wa:l
the other erofs
k
IUl
e.
j lJln
ti
e,
and Ihrough
e
draw Ihe
par. lld
e h;
fo
e b
will be Ihe
depailu r~,
and
Q
h
Ihe
proper ditferencc of I.Hitude ; then proceedi ng with this,
as in Ihe for<gotng problem, you will Gnd Ihe !hip's place
to be _.
P ROS
Xl.
The' latilude
f.iled rrom, diff<renee of
la·
tilude, and depanure, given;
lO
Gnu
lhe
fhip's place upon
die chart.
EX ~"PLE.
Suppofe a Olip from
ti
in Ihe latitude
of
20° 00'
nonh, fads hetween -nonh "nd eaU, tllI !he be
in [he Lui tude of 4S c
00'
north, and is lhen found to
have made of departur. 11 6 miles: R equired the !hip's
place ':pon lhe chart .
H avi ng
dra\\
D
lhe meridian of
a,
(el
off upon it, from
ato ó,
25
degrees, (..ken from Ihe equdlor or gradua.
ted par.Ilc1,) Ihe proper dlffaenee of latitude; Ihen Ihro'
ó
dr.w the parallel
be,
and m,ke
b e
equal
10
t
16 Ihe
d ep.rture, and j oin
a e.
Counl from' the pat allel of"
on lhe gradua[ed meridil n upwa:ds
tu
h
25 degrees, and
through
h
dr.w Ihe parallel
h
_,
whieh will meel
oe
proo.,
ced in fome po:nt _, and litis win ¡'e Ihe place of Ibe !hip
rcquired.
1 2.
In Ihe fcaion of
Ploin
Stlili'~f
it is
pl.inthat lhe
terms
tnt ridional diflallu,
drparlur~,
and
diffirella
el
longil,ulr,
were fyn onymous, eonflandy
fignify.ngIhe fame
th,og: whieh evideotly follo,ved from Ihe fuppofition of
Ihe eanh's fu rf.c< bcing projrc'led on a plane, in ",hieh
the meridi;ms were made
p~r3l1c:1 ,
and lhe degrees of lati·
tude equal lO one anolher aod lO tbofe of Ihe equalOr.
BUI finee it has bcen demonHrated (in Ihis feaion) Ihal if,
in Ibe projeaion of the .earlh 's furface upon a plaoe, Ih.
meridiaos be made parallcl, Ihe degrees of latilude mol!
be un<qual, nill inereafing Ihe nearer they
e~me
to Ih.
poleo
lt.
follow, Ihat Ihefe term' mun denote Jines real–
ly dtfferent from one anolher.
Sea . 6. O/OBL1Q..uE SAIL1NG.
T ..
E
quellions Ihal may be prorofed on Ihis head beiog
innumerable, we !hall only gi,'e a few of Ihe mon ufeful:
P ROB,
1
CoaCling ,long the !hore, I fa ... a cape bear
from me NNE ; Ihen
1
flood away NWhW
20
miJes,
aod I obferved Ihe fame cape to bear from me NEhE.
R equired lhe d.nanee of Ihe !hip from Ihe cape
at
eae h
llatlDo .
GEOMETR ICALL Y, D raw the eireJe
1
WSE (No.
22 ) 10
reprefenl Ihe eompaf" NS tI,e meridian, and WE
Ibe can and \Ven lioe, and lel C be Ihe place of Ihe !hip
in her firft Ilalion: Ihen from C fel off upon the NvV
hW
line, CA
20
miles, and
A
will be the
pl.eeof lhe !hip
in Iter
r~cood !l~tioo,
Prom