CM w 
Spherical Motion 
with which the track paffes under Z, but 
BY ,J '"" 
53/ 
Xjy% and x z == 2L“ — a ^° % ^ 
BT , BC 2 
C + A 
x/'4»g ? C\ 
B *V , af€ z 
cP A 2 
+ 
b*y 4 £ 4 /» 2 
B 2 
C ' 4 JJ, 2 C 2 
BC AB 
rn'b'Q SC 
£V<r ^itxr 
+ 
ba> 4 - tya’ 
» rr 1 
^ rx 
which fubftituted for their equals give the v elo city 
— — . — : , \~rrz?y 7 a" IT -A lA i z ,<r'z Tft A . 4 . , 4 -,! 
m s j- 
IA 
m sj~ 
£t = -x('? 
C*A AC V B 
AC AC *\ B 2 
a 4 X \ B 
A 
2 
AC 
becaufe A - 
c 2 X 
— i- and nici& + b‘c (f£ —!• 
AC 
rr-«x _ 0 l_ _ A- _ A and fflVS 1 + »VC = i • Now, 
fuppofing as above, the motion to begin when W is under Z 
and y — o, the track muft crofs CA at right angles, and with a 
velocity under Z ~z a~ ~ c X — 
a - c z xM 
. that velocity be- 
ins; then the fwifteft poffible, 3, C> and \/3 4- 
/- .1 _i O A * Vi dl 
C* being 
the then velocities of the poles C, A, and B, along their 
proper tracks in abfolute fpace, the velocity x being then - 
3 and z = €, which are their greateft values ; ^ and then 
2 becoming without the odant ABC, the velocity y mu. 
be negative or in a contrary fenfe to what it would be 
if Z were within the odant ; that is, fince within the 
odant, y, as we have feen, is in the fenfe from C towards 
A, it muft now be in the fenfe from A towards C^; # and 
% frill continuing to be in the fame ienle as if Z v '' e ‘^ 
within the odant, -till the great circle BCV' comes under 
2 A. 31 — ' 
which then touches V', and confequently x = o, y = 
- LVvV&Air* 9A ma& 
~C 
T’ 
% = 
€ 
and yj — 
^a 2 c 2 
B 2 
a- 
BC 
v 2 ABC 
v/CC 1 - A A = the velo- 
city of the track under Z, which is then the flowed, the 
correfpondent velocities of the poles A, B, and C, along 
Vol. LXXX. 4 A tneir 
