438 Demonstration of the rule for finding the place of a meteor. 
5 * sine Cwa 
another form by observing that cosine Cwa= re ary and that the 
plane triangle Cwa gives — — = aa, Then the plane coe 
Cag gives ag=Ca x sine aCw = Ca x sine ACW=Cax sine AW, and 
Cg=Cax cosine AW. Whence we= Cw 2Ca x cosine AW, and 
l we Cw Ca X cosine AW 
iang.Cwa ag Pee, dae This substituted gives ang 
py % CO 
AVR tone. Cores erame aw” > ane RW ie 
sine AW). 
The spherical angle MWB is equal’to the plane signin and 
the plane triangle ewd gives we: be :: sine ebw : sine ewb ort: cosine 
AWB : sine MWB, because _ angle ebw = = chw = comp. ew or 
AWB, | Hence; e sine ¥ MWB =— — x cosine AWB. Now in the plane 
Cm, the triangles Cmw, so are > simailar: whence Cm: Cw. me. 
ef ; and in the plane Cam, the similar triangles Cam, en les 
Cm::: de: me, whence by. composition of ratios Ca ; Cwi:4 de: ef (and. 
by substituting the above rules of de, ¢f,) :: be x cotang. Gas: : WEX COP, 
fs Ca ., cotang, Cwm bem Overs dog ne Com 
sia. Cwii; whietice! =—* cotang. Cis Cas 3 pie a 
x tang. Cas, which Soa 0 oy gives sine MWB= = = je = or is 
2B epee 
Cwmxtang. Casxcosine,A WB, as in page 218.. The’ rest oft the york 
(depending on t the common rules of f spherics) requires no explanation. 
‘i 7 er 
Leen? “oppeetce?  euygi’ = 
S35). 2RiG. Sai 4 
