54 2 A/r. Wild bore on 
if CC 2 be greater than Aa 2 ; but if Car 2 be lefs than AsC it will 
make two whole ofcillations. In like manner it will be found, 
that if SC =:r — fuch bar will make whole revolutions 
when A3 2, is greater than CC , and ofcillations when A3* is 
lefs tlian C£ 2 ; and we are at liberty to make either the one 
iuppofitipn or the other. 
Cafe 3. But if A3" = C&\ and the track that paffes under Z 
x*" “ 
be a great circle of the fphere, then A*~ =Cs 2 , — = — , By 2 = 
AS* - Ax z ~ A a 2 — Cz\ and the velocity under Z=: 
AC 13 C J 
m 
^ ~ = JL V^ACr - a* - ** X c'AM 
SLx 
+ a acr = -=v/f’AB + a'BC = 
BC 
m3.b z x I A 
which is therefore 
B \c 
o when ^=0, or B is under Z, fuppofing that to be poffible. 
But then t 
-y 
Vac ^cb 
A3 2- 
~b 
2 A 
X 23 
4 
—y 
-y 
A3 2 
and t = 
VcB 
23 
B 
a \lr~ y 
lxhyp.log. of a ; therefore, when at the firft inftant 
a 
Vr 
+y 
jy=o, to have the motion poflible, y muft be a negative 
quantity; which is agreeable to what was obferved before, 
that y muft be negative within the angle ACV / ; but in 
this cafe Z can never come over V', for then t would be 
infinite. And if the motion be fuppofed to begin when Z 
is fomewhere within the o&ant ABC, where y the firft 
inftant is equal to a given quantity 315, then the fluent muft 
be fo corrected as that t = x hyp. log. of 
3 
