427 / 868
';j6
N
A
v
j,
to r:HHus
10.00000
fo is the deporturc
116
2. 10037
to lhe tongoof Ihe eourfe
30°,
=9'
9.76996
whieh , becaufe il is between fOlllh and wert, wilJ be fOU lh
30°
29' \Vert,
or
SS\" ;} wert ncarly.
Aod for lhe d¡rtaoee, il will be, by lhe fame
Cafo,
As radius
10.00000
is
10
the diff. of lal.
2
I
4
2 .33°4 1
fo
is the feelot of
11"
eourfe
30°,
29' -
10.0646 [
' o the dirtaoee
--
248 ' 4
-
2.39S02
2
From \Vhat has beeo faid, it will be eafy tojolve
a '
traverfe, by the rules of
Middle Latitllde Sailing.
EXAMPLE. Suppofe. Ibip io the latitude of
43°
2S'
nonh, f.ils "pon the folJowiog eour(es ,
"iz.
SWbS
~3
m iles, SSW-}wcrt
15
mi"', SbE
S4
mil es , and SWbW
.74
miles: Required the latitude the Olip has COme to,
and h".v far Ib e has dilfcred her 100gilUde.
Fi rrt, B y
Cafo
2.
of this
Sdl .
fiotl the difFereoce of
h1itude aod d:fre reoee of loocitude bdoogiog to eaeh
courfe aod dinaoce, aod they w¡J1 lbnd as io the follow·
iog tableo
COllrfoJ
SWbS
SSW~W
SbE
SWHV
DiJI"nCIJI
Diff:.:/
Lat~
Di.!T
af
!::.ngit.
N
S
E
W
--- ------ ---
63 \--- 52 4 -- 47 ·SS ,
4S
---
397 ---
2S.62 '
54--- 53
°
1375 ---
741---
41.1
1---ISt oS
---o
IS7 .55
Diff. of-l..at .
IS6.2
13.7S I
Diff. of Long . 14 3.S01
H enee it is
pl.iolhe Ibip.has oi lf; redher latitllde
IS6.
2
nlinu:es. or 3° 6' and fo has come to \he latilude of
40°
19'
oOrlh, aod has made of dilferenee of longitude
143 . S
miou'es, or
2° 23' 4S"
wellerly.
3.
Tbis method of failini" though it be not llriélly
true.
ytt
it
comes very Dear
[he truth.
as
will beevident,
by eompariog ao example wrou¡:ht by lhis melhod Wilh
, be fame wrought by the method delivered in lhe neXl
Sfflion,
which is firiétly true
j
and
it
ferves, without
any
eonfiderable error, in ruooings. of
4So
miles betweep lhe
equalOr and parallcl of
30
degre.s, of
300
miles be.
'tweeD lhat aod , he parallel of
60
degr«s, and of
150
miles as
f.tras rhere is aoy occ.t.fion, and
~Drt'quently
",ull be fulJi ciemly exaél for 24 hours ruo .
Seé!.
S.
0fME.CATOR 'S SAILING.
1. TH
oue
H
the meridi:ms do a1l meet at Ihe pole.
and the parallels to lhe eq'Jalor do eooliouaJly deereafe,
aod that
iD
proportioa to lhe co·fines oT their latitudes;
yet
in old fca eharlS ,he meridian, lVere dr>wo paraJlel
to one anolher, and cohre'lueody lhe paraJlels of lalilude
inade equal tO the equator, aod ro a degree of longitude
00
any p.taJlel as large as a degree
00
the equator: alfo
in lbefe eharlS the degrees of lalilude were lliJl reprefeoled
(as theyare in tbemCelvcs) equal to eaeb olher, and
10
A
T
'O
N .
lhof. of lhe eq ualor. By lhefe means lhe degr«, or lon–
gitude bcing
incrcafed beyond
rheí r
jufl proponion, and
the more fo toe nearer
they
;:¡ppro:u.:h the poJe, the dc:–
f rees of Jatitude
al {he fame
time remaining the
fame,
it
is eviden t
pla(cs mufl be
vr!ry
erroneouOy
marked
down
upoo thefe chans wlth refpel't to thei r
I:uitude
and 1011 ..
gitude, and confeqnendy
rheir
bca riog from one another
very (aire.
2 .
To remeny this ineoo\'cnienee,
fo as
lliJl
to k('ep
the
meridians
parallel, it is
p)~'n
we
",un
protracl,
'or
Jengtlien, the
degrees of LHitude in the 'fa::ne
proponíon
as
tho[~
of
longiUlde
ue,
thar fo
toe
proportion
inealling
and
weflíng
m.IYbe rhe
'r"me with
that
of fouthing and
nonhing, and conrequ(ntly' the
bearings
of
pJaces
from
one ano[he r b(!
the
Cuue upon lhe "hart as upon tite
globe itfelf.
Let
ti
BD
(No.
11 . )
b.
a qu.drant of . meridiao,
A
the pole,
O
a POiOI on lhe equ'lOr, AC half lhe axis,
H
aoy
pOlO[
upon
the meridiem, from \l'hich
draw
BF
per.
pmdieular tO AC. and
HG
perpcodieula r to CD; then
BG
wdl be lhe fine, aod
BF
or
ce
lhe eo fine of BD
lhe: latilUde
of
lhe poine B¡
drdW
U the tangent and CE
the fecaol of lhe arch C D .
[ 1
I"s beeo demonll rated in
Se{t.
3.
lhat .oy areh of a paralld is
10
lhe ltke areh of lhe
equ&tor as the
co·fine
of
{he
);uilude of that parallel lS
tu
radius.
T'hus
any
arch
as
a minute on (he paralleJ de.
fcri bed by lhe poinl B, ..·j ll be to a
minute
on the t:C]ua.
lor as BF or
ce
is to CD; but fioco the l'riangles CeH
CDE are fimilar, [herefore
ce
\Vii i be
10
CD as CS ;,
10
CE,
i .
t .
lhe eo·fine of .oy parallel is
10
radiu.
' S
radius is to
lhe
fe cam
of
lhe
Luitude
of that
p¡¡rallel.
But
it has been jull
no\V
(hown,
t1Ut
lhe co fine of any
pa–
rallel is
to radius,
as
the
leng,h of
aoy
arch a!
a minure
011
thac parallel is
to
the
lenóth
of
the
'Ike
arch on lhe
equator :
Therefore the
lenglh
of aoy areh as a minute
00
-any paralJel,
is
to lhs: Jength' of
lhe
like: areh
on
the
(quaror,
as
radius
is
te
lhe {ec,lOl of
lhe Jatitude
of
that
paraJlel; and fo the
length
of 3ny
areh.
as a minute
on
the equator, is looger thao the like .reh of any parallel
in the falOe proportion, as the recanl of the
Ia.titude
of
that parallel
i,
to radius. llu! fince in
lhis
projeétion the
",eridians are par.llcl , aod eoofequend y e. eh paraUd of
latilude equal tO the cquator, it i. -plaio lhe leoglh of .ny
arch
as
a minute on aoy
paraJlel, ¡s
iocreared beyond
Í\s
jun
proportion,
at {ueh
rélte
as
thc Cecant of
the:
latitude
of tbar
paralJel is greater lhan
radius; and therefore
10
keep up lhe prOpOrtioD of oonhine and foulhing
10
that
of ed.fiiog
and wefiiog. upon
Ihis ehan, as
it
is upon the
glube
itfdr,
the
Jength of
a minute
upon
the
O1eriaian
at
aoy paraUel mull alfo be iocr'eafetl beyond ilS iull propor·
tion
at
the
fa me
ra((',
i.
~
.
..-as the fecant of
the Jatitude
of thal par.lId is grea"r lh.n radius. Thus to 60d the
length of a minute
upoo
the meridian
al
lhe Iatilude of
75
degrees.
(ince a
minute
of a meridian is
every
where
equal
00
the globe, aod alf" equal
10 •
minUle upon lhe
equator, let it be reprefeoted by uoily: theo making il
as
ndius
is
tO
the fecant
of
75 degrees:, fo is unity
to
a
founh Dumber, whiehis
3.S64
nearly; anp confequently,
by whatever
lin'" you
repreft!n,
one minute on
the
equ3tor
of lhis eharl, lbe leoglh of one minute
0 0
,he eolarsed
meridiao