MOVING FORCE. 
es 
motion by tbe pressure of ibe atmosphere on the pistons P and Cases of Jiffi- 
Ci acting upon m and n, by means of the levers G I and A B j joctrine^of 
A F being equal to B F, but G H=2 H I, and the area of the moving force, 
cylinder E twice that of C ; suppo.sing these cylinders and the 
fulcra F and H to be immovable, and the .space under each 
piston to be a vacuum. Then P and Q will move through equal 
spaces in equal times, and m will acquire just twice the velo- 
city of n. 
Here the force of P is twice that of Q, but the effects of 
these forces, if estimated by the product of each mass into its 
velocity, arc equal. 
3. In treating of rotatory motion; — in finding, for example, 
the centre of gyration of a mass revolving about a fixed point, 
the rotatory force of each particle is universally understood to 
be as the square of ils distance from that point, or as the square 
of its velocity. If a body. A, (fig. 3 ) be made to revolve about 
the centre C, by a force acting at P ; four times that force, 
(applied at the same point, P, will be required to make a body, 
B, equal to A, placed at twice the distance of A from C, re- 
volve with the same angular velocity, that is, with twice the 
absolute velocity of A. If both the bodies be disengaged 
from C, they will each continue to move with the same velocity 
as before, but in rectilinear directions ; and then the force of 
B is said to be only twice that of A. But it is not alleged that 
'A can gain, or B lose force, by the mere circumstance of being- 
disengaged from C. How then is this change in their relative 
forces to be accounted for ? 
4. Let the lengths of the arms A F, F B, (fig. 4.) of the 
balance beam, A B, be in the proportion of l to 2, and let the 
jweight of the ball, m, be to that of n, as 2 to one. If they 
/ibrate about the fixed fulcrum F, the quantity of motion of 
■71, will be equal to the quantity of the motion of n. Let C D be 
I mother balance beam, and let C G and G D be each equal to 
aA F, and the weights of o and p be each equal to that of m, 
' tnd let A and C move with equal velocities. If the quantity of 
motion of m be equal to that of n, the quantity of motion of p 
must also be equal to that of n ; and the sum of tbe quantities of 
. motioa 
