the Rotatory Motion of Bodies. 
269 
* *! 
vity) adted at a fig. 3. and at the new poles a , a, See. as 
they become fuch by a fucceffive change caufed by fuch 
continued adtion of the force f urging the fphere at 
i i if // 
every inftant to revolve about the diameter de y or de i 
i a 
Sec. of the contemporary mid-circle, the new pole ( a , 
See.) would not inftantly be at a finite diftance from the 
primitive pole a, but fome finite time would be requifite, 
that by fuch fucceffive change, the pole might be varied 
to. a finite diftance from a: and the force F continuing 
invariable, the velocity ( v ) wherewith the pole changed 
its place would be exprefled by y, t being the time elap- 
fed whilft the pole is varying from a to a, and z the 
length of the arc a a. Therefore the velocity wherewith 
the pole will change its place during fuch adtion of the 
force f will be exprefled in the fame manner as the ve- 
locity (v) of a body moving uniformly from a to a in 
the time t may be exprefled ; that is, in both cafes v will 
be = - . But there is a material. difference, between the 
i 
motion of a body fo moving from a to a and the change 
/ // 
of place of the pole a, a, &e. the former. is permanent, 
and will continue to carry the body forward without the 
adtion of any force whatever ; whereas the latter will 
inftantly ceafe, and the axis will keep its pofition, if the 
force 
