Mr . YVildbore an 
516 
✓g + aAf + g . ^ or of v/a^ + a+D* x /3 2 -: A/3 ; therefore, 
the times being inverfely as the velocities, as A/3 : 
</A z -f- 2 AIT 4- /3 2 : : the time of one revolution of A' round 
Z : the time of one revolution of the furface round A 7 , that 
is, round the axis whofe pole is A', which time is given be- 
caufe xzzefi, and confequentiy the time of one revolution of 
eb3 
A' round Z is given. Again, e x f. OZ = ~ the 
velocity with which the furface pafles under Z (at reft). The 
angular velocity round the axis whofe pole is 0 = e, and the 
velocity round O in a circle whofe radius is bzz be^ O fliifts 
its place in a circle of the fame radius b with a velocity = 
— ; the time therefore in which O fliifts through the lefler 
A 
circle eO is to that of one revolution round O (which time 
may be fuppofed given) = T as eb :: or as 1 : that is, as 
- : 1 :: T ; — — the time in which O makes one revolution 
A £ 
T 
upon the furface. And as e/3 : T :: e : — =the time in which 
the furface makes one revolution round A\ or the axis whofe 
pole is A' ; and from the analogy above, the time of one revo- 
lution of A" round AT - Alfo, as 1 : f. AZ :: 
eB : — — = the velocity with which the furface would 
V A z + 2 A& z -\-$ z 
pafs under Z, owing to the motion only round the axis whofe 
pole is A\ and in a fenfe from W towards C ; whereas, owing 
to the compound motion it really moves under Z in a contrary 
fenfe with the velocity - ; this is, however, only a 
J VA z + 2A& z -\-8 z 
neceflary conference of the centres of the circles whofe radii 
are. 
