the Rotatory Motion of Bodies. 2 73 
to the tangent to the curve which m will defcribe ; that 
point it is obvious will, in confequence of the adtion of 
that force, defcribe a leffer circle of the fame radius (y) 
as that defcribed by the particle ni when faftened to a 
firing and acted on by the force F as above-mentioned; 
and the center of the fphere being always confidered as 
at reft, one of the momentary poles of the fphere will 
defcribe a circle whofe radius will be — V r* - q z parallel 
to, and 90° diftant from, that defcribed by the point ?«, 
For if the faid force were to ceafe adting, that point of 
the iphere would defcribe a great circle, as would the 
particle m at the firing in the like cafe ; and therefore 
both the faid particle and the point m of the fphere at 
every inftant having the fame tendency, and being adted 
on by -equal accelerative forces, the effedt will be the fame 
with refpedt to the motion of each. Gonfequently, v being 
put to denote the velocity wherewith the momentary 
pole changes its place in the circle which it will defcribe 
whilft the motive force producing the accelerative force 
F adts on m as juft now mentioned, v will be = — , the 
fame as in the preceding article, e here denoting that 
velocity which we there denoted by c. 
5. Referring the point of adtion of the perturbating 
force to the mid-circle we have not hitherto confidered 
Vol. LXVII. 
that 
N n 
