XVII. dA general Demonstration of the Principle of 
Virtual Velocities. 
By THe Rev. J. POWER, A.M. 
FELLOW OF CLARE HALL, CAMBRIDGE, AND OF THE CAMBRIDGE 
PHILOSOPHICAL SOCIETY. 
{Read March 21, 1825.] 
Conceive a machine, of any description whatever, to be 
kept at rest by forces P, P’, P’....., and let m, m’, m’..... 
denote the points of their application. 
Call ayaa’... any indefinitely small spaces, subject to 
the conditions. of the system, which these poimts are at liberty 
to run over in the same instant; and £#, pf, B’..... the cor- 
responding spaces estimated in direction of the forces. Then 
ashi ak cel will be the cosines of the angles at which P, 
" 
Pee are inclined to the spaces a, a’, a’..... ; so that 
if we resolve these forces into others, a part tangential, and the 
remainder normal to the above spaces, the former will be ex- 
pressed by 
for which we may substitute the following: namely, 
