423 / 868
A
v
'1
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Sea. 3.
Oí
PARALLEL S"ILING.
l .
SINeE the parallels of latitude do .
lwa.ysdecr••fe
the nearer tbey approach (he paJe,
it
¡s plclin a
aegrce
00
aoy of them mu(1 be lefs thao a degree upoo the equator.
N ow io order to koow the leoglh of • degree
00
any of
them. let PE (No.
10.)
reprefeot half the eareh's axis,
PA a quad"ot of a meridiao, and coofequeody A a poiot
011
the equator,
e
a
POiOl 011
the meridian.
aadeD
a per·
pendicular from
lhat
point opon tite axis, which plainly
will be [he fine of CP the dillaoce of [hat poiot from [he
pole, or [heco-fine of CAits diCl:rlnce (rom
lhe
equator; aod
C'D will b. tO All, as [he Goeof cr, or eo·fioe of CA,
is [O Ihe radius . Agaio, if [he quadrant rAB is [uroed
Tonnd upon the axis PS,
it
is pJ.tin rhe paiol A will de·
faibe lhe drcumference of lhe
eqllator
whofe
radius
is
AB , and any other
paiOl
e
uponlllt: mcridi:\D
will dercribe
(he circumferencc
oC
a
pnallel
whofe radius is CD.
Ca
R.
I.
H ence (becaufe the circumfe rence of cireJes
are as their radii)
it
follo",s, thal lhe
clrc'Jmfereoce
of
any parallel
is
tO
the circumference of the t:quator, as
the co fine of its latitude
is
to
radius.
Ce • .
n.
And fio« [he 'I holes are a. [heir fimilar
parlS, i[ wiU be, As [he leog' h of a degree
00
any p"aUcI
is
to the length
of a
degree upon the equator, (o
is
lhe
eo fioe of [he lati[ud. of [h'at parallel [O radius.
COR olII. Heoce, as radius is [O [he eo·fine of any la·
titude,
Co
are the minutes
of
diffcrence of 101gitude be–
tween two meridians,
or
their dillance in miles
upon the
equator,
to
the diílaoce
of
theCe
two
meridians on lhe
p."Uel in miles.
Co R. IV. And as the eo·fine of aoy parallel is [O radius,
fo is [he leng[h of any areh on thal p. raUel (in tereepted
betweea twO
meridian~)
in mile"
tO lhe length of
a
fimilar
lirch on the equalOr, or minutt:s of difference of longitude.
COR oV. Alfo,as theeo. fioe
of.oyooeparaUeli, [o[he
eo fioe of aoy o[her p.raUel, fo i. the leng[b of any areh
00
A
T
o
N.
the firfl, io miles, [o theicng,h of [he f.:ne areh
00
ilie
other in miles .
2 .
Fro", wha[ has beeo fai<l, arifes [he folu[ioo of th,
feveral eafes of paralld railing. wh,eh are as follow.
CASE
l.
G iven
the difE:rence
of longiwde
betWttD
two pl.ees. bo[h lyiog
0 0
[he fam: parallel;
[O
fiod ,he
difl.n ce be[weeo tbofe places.
EXHIPLE
l.
Suppofe a Ihip io [he lati[ude of 54°
20'
noreh. fail, direélly wefl on [hat p.raUel [iU fue has dif·
fcred her loogi[udc
12° 45' ;
required the
di
fla ace failed
on [hat paraUe!.
Firfl, The differeoee of longi[ude reduced ioto minutes,
or nautical m les, i9
,65',
which is the difhnce between
the
meridi,lO Jailed from,
ano the meridian come to,
up–
on the eq ualOr; then to find
the
dittan:.e betweeo
there
meridians on [he par.Uel of
54° ?O',
or [he diflance
f.il·ed, i[ wiU be, by
C".
3. oC [he laH artiele,
As
radiu5
"Jo.OOQOO
i, [O[he co·fine of [he lal. --
54°,20' -- 9 76572
fo are [he minutes o( diff. long. --
765 -- 2.88366
[O Ihe diflaoee on Ih. parallel --.-
446.1--2.64938
EXAMPLE
11.
A degre<
00
Ihe equator beia&.
60
minates
or
namical
miles;
re~ui red
the length
of
a
d!–
gree on ,he l'a..11cl of
510 32 .
By
Cor o
3. of [he
1~ILarticJe,
it will b.
As radius
10.00000
is 'O [he eo·(,oe of [he lati[uJe
5,° 32' -- 9.7938 3
fu are [ne minutes io
1
degree
00
[he equa.
60 1.77815
[O
-- -- --
37.32 1.57198
[he miles aofw.riog [O a degre< on [he para11el of
510 32'
By [his problem ,he following u ble i, eooOruéted,
fhewing
tha geographic miles anfwering to a degree
00
any
paralld of l. <il ude ; io whieh you may obfene, [hat the
columos marked at
tbe
top
wi,h
D .L.
contaio the
deg,rees
of'"I.<ilUde beloogiog
[O
eaeh para11el; aod [he adjaceot
colurnos
marked
at (he tOP,
M'¡o ,
contaio
the
geograpbic
miles anfweriog [O a degre< upon [befe parallels.
A T.ble
lhewiD~
how
m.oyM ile. aofwcr to a D egree of L ongi[ude, a[ every D egree of La\itude.
¡p .I
M i/o
f)
L.
Mi/",
D.L.
Mi/a
D .L / ¡'¡'¡" D.L.
M il,)
--1--------
1 5999' ' [9 5 6 '73 37 479 2 1 55 134'4 ' 73
17~54
2 5997: 20 56'38 38 4728 56 33·5 5 74 16·53
3 59.9 2 2' 56 .
0
1 39 46.62 57 32 6E 75 15 52
4 59. 86 1 22 55 .63 40 45 .95
58131 ' 7 ~
76 14 ·5'
5 59 77 , 23 55 . 2 3 4' 45.28 59' 30'90 77 13·50
6 5967: 24
~4
81 P 4495 60 30.00 78 1248
- 1--------
7 59.5 6
1 25 54:3 8 43 143.88 61 129.09 79 1[ 45
8 59'42, 26 53 93 44 43. 16 62 28. 17 80 10.42
9 59 26 , 27 53 '46 45 142 . 43 63 27 ·24 81
9.38
10 59 081 28 52 .97 46 ;51.68 64 126 30 82 8 35
11
5889' 29 5247474092652 1.36 83 7.3
'
12 5868' 30 5' .96 48 14015 66 12441 84 6.28
--1----
---- ,--1-- ----
l i
58 4 6 3 1 5' ·43 49 39.36, 67 2345 8 5 5. 2 3
14 58.22 32 5088 50 38.57 68 1'2248 86 4·,8
15 5795 33 5°3 2 ' 5[ 37·76 69 2 1.50 87 3. 14
16 57 6 7, 34 49·74 52 36.94 7° 120521 88 2.09
17 57·37 35 49. 15 53 36.11 7' '9,54 89 1.05
18 57.06 36 '48.51 54 35 .26
,2
18 .55 90
O,O?
Tbough