538 Mr. Wildbore on 
To that after all the pains bellowed upon the problem, the refuit 
is as firnple as could be wilhed for ; and the motion, though 
not quite fo regular, is as eafy to be conceived as that in the 
particular cafe of the folids of revolution. For the fpherical 
lurface, concentric with the body, moves with an uniform and 
conftant angular velocity V about an axis IZ at reft: in abfolute 
{pace, whilffc the track WV \V / V upon that lurface always 
pafies Z, the pole of that axis, with a velocity = 
k* y 
- - which, though not conftant, recovers its 
B 'lutf + i'i* AC' 
firft value again and again in equal times, as the body revolves 
for ever. 
6. I fhall only juft add, that if P, Q, and R, be any three 
external motive forces fuppofed to afl upon the body in the 
direflions of the three great circles BC, CA, and AB, then 
mu ft 
Ma 
x 
i 
P-c 1 
a 
y- 
Nik 2 i 
P — a 1 
x zx, and 
R 
Me 1 
• 2 2.5 
a —b 
, 2 . 
X xy exprefs the values of the external accelerating 
& L> 
forces that aft upon the body to alter its velocity about the 
three permanent axes of rotation. And when the relations of 
thofe external forces to the internal perturbating ones are given, 
a folution will hence be obtained to the more general problem, for 
determining the motion of the body, when, belides the pertur- 
bation arifing from the centrifugal force of its own particles, 
it is alfo a fled upon by any external difturbing forces what- 
ever. And, if P, Q, and R, be equal to, but in contrary di- 
reflions to Myz x b 2 - c\ Max x c - a, and M xy x a 2 - by the 
perturbations vanilh, and then about whatever axis the body is 
firft impelled, it muft continue to revolve uniformly round it 
for ever. 
