An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

f(2 "'T' 4 nARTIf.
1. lad co s.A:::::cos. cos:tS.
t-ad sin AIrt
2. Rad sin AlIt:: tan RS cot A..~. cot A:.: d in Al..t...
t..............
ffHence the computation for.AS and A is ass follows:'For thce Lfongit ude AS. For the Obliquity A.
cos Alt'1 530:38' o00" 9.7730185 silt A.X 990592247
cos l:S 1.9 15 57 9.9749710 tal0n.S, at. corn. 0.4565209
cosAS 55 57 4t3 9.747 9895 cot A. 23f 27' O5' 10.36244 G
It will be recollected that iln Napier's rule for the solution of ra ight-angled
spheric'al trilc, 1by' mlealns of the Fve Ctircul Parts, wte proceedl as follows
tIn a right-angled sphericallt triangle we are to recognize btnt five larts, viz., tthe
three sidets anltd the two obliquce angles. If twe take any one of these as a middle?prt, tlhe two which lie nlext to it oin each side will b1e a.ait f-ehnt prts. Thus (in
Fig. 21), takintg A for a mtuldle part, b and c will )be tie adjaCent parts; if we
take c for the middle part, A anid BI will
be the adj:acent parts; if ywe take B for 21
the lniddtlc part, c and a till be the adacenlt parts; hut if we take a for t c,,..
middle part, then as thtc angle ( is not A
considered as onut of the ceircular parts, 1I
andl b are the adjicent p-arts; and, lastlty,
if b is thle middl partt, thein the -adjacent C
parts are A and -a-'the two parts imimnediately beyond the adjaicentt parts on
each side, still disregardingl the right angle, are called tite (~oppet'tt parts; thuis,
if Ais the middle pat-t, the opposite parts art a antd I. Napier's rule is as
follows:
Rat'dius itto the sine flt iou/die - lpart, etal f e prodc! f i the ktanget:r of the tiwaceot:?parts, or of the cosittes of the Oppoite t t;rtus.
('the orrestpotidting vowels are marked to aid thle meno( r)I fIl tl use of tlhis
trule, it,lnltist. tie undcrstood that the coimpttement/!fs f the ll-tles:rd the htypoteinuse art usid, instead of those parts tlthetlSelv s. T'huls, if A is middle part,'we
say trad X coS,'not tadl X Sitn A,'ad so of B; or, if A0 l i s ad jacenlt part, ywe use
cot All, not tan All; if opposite, sint.Al, ot cos All, &c.
Exarmples. I. In the righlt-angled triangle, AC, are giiven the two perpetndicular sides, ivizd, a::::8~ 24' 10",:::5'9~ 38' t7", to find the hipotemt se c. The
hlypotctise bexing timade the middle part, the othe sides becotme tthe oppotsit
parts, being separated from the middle ipartl by the angles A a.lt 1. I[tncc,
cos a cosm b
Iiad cos c:.:cos a cos b.'. cos c......-...............::Q:::..0~ 23' 40".
2. In th1e splherical triangle, rightt-angled at C,, are given two perpendicular
sides, viz., a:::I6 30' 43'", 4b2'9~ -t1' 32', to fint the angle A.
H:ere the required angle is edfacentl to one of the gi ven parts, viz., b, whichI make
the middle Imrt.'hen,
Rad Xsin b4:::cot A tan a' cot A a, h:........' 13"1
talLc a