lx e~ + a* in like manner 
Spherical Motion. 
«£ 2 — AB/I 2 — A 2 BV 
555 
2 v-2 
a o 
A + and 
A*C z xe- = x / + hence the velocity 
* z y* • * 
VC 
@7$ 
ABC 
B 3 CV , A 2 BV 
+ + 
A’CV 
p 
+a*-B(V 
+ AC x £ 4- 
^ — If 
' ABC \ l 
b 2 c 2 2 
-+ 
A*BV 
+ 
BC» 2 + €* — AB x / + k* 
— — — «*) (becaufe 
p 2 1 $ 2 
i -i- AC - BC - AB = o, and + € 2 = £ 2 ) which may be farther re- 
duced to 
ey 
VC 
c 2 , a s 
+ 
A + CxW l 3M 2 
+ 
} = thevelo- 
A 2 BC ‘ ABC 2 AC A 2 BCV B> 2 
with which the momentary pole O fhifts its place along its propet 
track ; but it fhifts its place in a diredion perpendicular to the 
great circle ZO at O with a velocity whofe fquare is equal to 
'ZjO 
the fquare of that laft found minus the fquare of — 
which is 
the velocity along ZO 
x * x cof.ZO 
«j 3y<l 
ts z x f. ZO “ * ABC X tang. ZO $ 
hence then the velocity perpendicular to ZO at O 
//B*c* . A’B 1 . A’ C* 
I 
t3@y$ 
ABC 
I — 
W( 
r 
A*C 2 
B 2 C* A 2 B 2 
~+-y- + V 
f. ZO' 
„ , ) this drawn into i gives 
tang. ZO / G 
J = the elementary fpace perpen- 
dicular to ZO; hence the angular velocity with which O 
fhifts its place about Z in abfolute fpace = XbcxTzo “J ( + - 
2^q-2-2. — -2L- V and the elementary fpace divided by f. ZO 
gives the meafure of the elementary angle, and the - track of 
O in abfolute fpace may hence, concejjis quadraturis, be con- 
ftrufted by points. But this is unneceflary after the path of 
one of the angles C of the oft ant has been found ; lince the 
track of O is thence given by the projection of points ad 
libitum of the now known triangle ZOC. 
4 C 2 
Hence 
