1000000031

424 / 868

N A v 1 G
T houg1\ tbi. lable does <lnly 1bew tbe mile. anfweriog
10 a degree of aoy paraJld, wbofe btitude confiO. of a
Wlhole Dumbcr of degrees 1- yet it may be made tO ferve
for ~ny paralleJ wbofe 'Iatitude is fo~e oumbe~ of
degree. and mioutes, by OIakiog tbe followmg proporuoo,
~iz.
As t d!gree, or 60 minuus, is difFereoce be–
tweeD (be nllJes anfwering tO a degrce iD (he next greatcr
'snd oex, lef. t.bular Iotitude tbao tba, propofed; fo i.
the excefs of the propofed latitude above the next tabular
J¡titude, to a proponional part j which, fubtrallcd (rom
(he miles iofwcriog lO a degree óf JOogilude in (be ncxt
Jef.· tabular latitude, will give tbe mil.. aofweriog to a
degr<e io tbe propofed latltude.
EXA MPLt , Required to find ,he mile. aofwering to a
degree on the paral/e1 of 56° 44'.
Fir(t, The oex' I.f. parallel of laritade io the table
Ihao Ihat propofed, i. tha. of 56° , a aegree of which (by
.he .able) i. equat to 33 .55 mile.; aod tbe oex' greater
parallel of latitude in the table. thao that propoled. is
thal of 57°. a degree of which is (by tbe uble) equal to
3' 68 miles ¡ lbe diCIerence of thefe is 87. and the
dillance betwcen theCt parallc::ls is I degrce or 60 minutes;
alfo Ihe diOance be.",eeo the par. UeI of 56°. and the
propofed paraUd of 56° 44', i. H miou«s : theo by Ihe
precedi0l: proportioo it wiU be. As 60 i. to 87. fo is
44 to 638, the diIFerence betw..n a degree on the paral·
Id of 56° aod a degree o~ lhe parallel of ,6° 44'; which
Iherefore t. keo from 33.55, the milesanfwering tO a de·
greo on the paraUel of 56°. leaves 3'.9". the mil..
anfwering to a degre. on tbe paraJlel of 56° 44' . as was
rcquired.
CA SE Ir. The diOance failed in any p.raUd of lati·
lude, or lhe dWance between any two places on that pa·
ralle!. being given; tO find the diIFereDce of longitude.
EX'MPLE. Suppofe • Chip in the Iatitude of 15° 36'
nonh fails direélly ean 685 6 miles: required how mucb
Ibe has dlIF.red her longitude.
By Coro4 . Art. l . of this feélioo. il wiU be
Asthcco fioeof the lal. -- 15° 36' -- 9.75202
is to radius 10.00000
fo is the diO,oce f.iled -- 685 6 -- 283607
10 ,,!in. of ditf. of long. 1213 -- 3..08405
"hich rtduced into degree., by dividing by 60. mak..
20° 13'. the d,IFerence of longi,ud. the Chip has made.
This may alfo be folved by help of the foregoiog
table, viz. by finding from it lhe miles anrwering to
a degree on ,I¡e propofed par.llel, aod diVJdiog with
this che giveb number o( miles, the quotient will be
' lje degree. and minule. of dilference of loo¡itude re·
qoired.
Thu, io Ihe I.n example ¡ 1 find. from the fo.-going
table. that a degree on the paralle! of 55° 36' i. equal
lo 33 89 miles; ' y this 1 di.ide Ihe propofed number of
mil.. 685.6 aod tlle quotieot i. 20.13 degrees; i. e. 20°
) 3', the dífFertnce of longitude required.
CAS E IIl. The diIFereoce of loogitude I\VO
place. 00 the fame paralle!. aod Ihe diOance belweeo
tbem. being given; 10 find ,1" latilude of thal p.raUel.
EXAMPLE . Suppofe a Chip fail. on a c",tain paraUd
direélly wcll 6.24 miles, aod then Iu. differed her loogi.
A T 1 o N. 37 3
lude 18° 46' or I 126 miles·: Requircd Ihe of
Ihe paraUd Che f. iled upoo.
By Coro 3. Art. l . of ,hi. feélion, il will be,
A"be minoef . long. 11 16 3.oPH
is to ,he diO.nce failed 624 2:795 18'
fo is radius J 0.00000
10 Iheco fine oflbelal. 56° 21' - 9.743 64
confequeotly the latitude of the Ibip or par.Uel Che 'failec!
upon was .5 6° 21'.
From wh.. bas b«o faid, m.y be [olved Ibe foUo'Ning
proble., ..
PROB o 1. Suppofe Iwo Chips in theJatitUde of 46° 30'
oonh. .funder 654 míle._ fail both direélly no"h
256 miles, and confeque.ntly are come tO Ihe lalitud.
of 50' 46' oonh : R equired their d;n.o~e on Ibat paraJltI
By Cor. 6. Art. 1, of Ihi. Seétioo, il will be.
As the ro fine of 46' 30' 9.8 37 81
is to the co·lioe of 50° 46' 9,80105
foi. 654 2,81158
to 601 2.77882
the diOance betweeo the Chips \Vheo on the paraUeI of
50° 46' .
PRO'. Il. Suppofe IWO Chip. io the latitude of 45 0 4 8'
north. 846 miles. f,iI dircélly north tiU Ihe dif,
tance bel""'eo Ihem is 624 miles: Required the lalitudc
come 10. ond I~e diOance failed .
By Coro 5. Art. l . of this Seélioo, it wiU be,
A. Iheir firll diOance 846 2 '9 2 737
i. to their fecood diOance - 624 2.79$18
fo i. the co·fine of - 145 o 48' 9.84334>
tO Ihe co·fine - 59. 04 - 9.711 IS
lhe latitude of Ibe paraUd the Ibips are come 10.
Confequently tO find th';r dillaoce failed,
From [he huitUde come tO
the I.tilude f.iled from,
2nd there remaini - - 13 t .6
_qual to 796 mile., Ihe d¡IFereDce of L .. ilude or dlllaoce
f.,led.
Seft. 4. Oj'MIDDLE'LAT'TUDE SAILINC.
WHEN tWO places lie both on the fame ",rallel. we
(hewed in the laO feéliQn, how, from the diIFerence of
longitude given. tO 60d Ihe miles of e.Uing or welling
between lbem, & e con/rll. But when two places lie not
on the fame par.Uel. then tbeir diIFerence 'of longilude
canoOI be rtduced to miles or ea(liog or werting onthe pa.
r.U<I of eith.. place: for ifcounled on the par. lid of tb.l
place that has Ihe greateO it would be loo fmall ;
~tn;~~I~o~~~::~~~:~.o~~~~~ltahc: ~~,i;~~~~~;·o(lflr:I~~Uc~:~
the difl'ereoce of longitude belw«n IWO places: l)'ing on
diIFerent p.rallds. 10 miles of c.Oing or wemog, & ~
t Ol1lra·, is by counting ir 00 the middle paralJel between
the places,. which is found by adding Ihc latitudes of Ihe
IWO together. aod taking half ,he fum, whicb ",iII
be Ihe I.tilude of the middle par.Uel required. Aod
hcnce arifes <.he folution of Ihe following cafes.
CA! E 1. The latiludes of two places. and their dif,
ference of longitude, giveD; 10 find Ihe direél courfe aDd
dill.oce.
EUMPU.