Principles of progrejfve and rotatory Motion. 555 
and B (fig, 1.) are refpedtively ax ac and bxbc ; alfo 
the centrifugal force of the point g, confidering it as 
having both bodies to move in the diredtion of the rod, 
is a + bxgc, but from mechanics axac + bxbc=a+bx 
gc : hence the centrifugal forces of the bodies a and b 
give the center of gravity a centrifugal force equivalent 
to its own centrifugal force, which, as the latter would 
caufe that center to move in the tangent Gg, the lever 
not being fixed at c, it is manifeft that the former will 
caufe the center of gravity to continue its motion in the 
feme direction. 
That this motion of the lever,, in a direction from 
the center c, is the only motion which is communicated 
to it from the effect of the bodies A and b is manifeft from 
hence. The bodies begin to revolve freely about the 
point c, and confequently if the point c had been fixed, 
the bodies would have moved on with a uniform angular 
velocity about c ; if therefore we fuppofe the lever not to 
be fixed ate, as the efficacy of the centrifugal force which 
a<Sts in the direction of the lever is now fuffered to take 
place, and no new external force is imprefied on ei- 
ther of the bodies, it is manifeft, that if in the former 
cafe the bodies had no efficacy to difturb the angular ve- 
locity of the lever, they cannot have any in the lat- 
ter, confequently the angular velocity, and from what 
Vol. LXX. 4 D has 
