Revolving about Fived Aes. 267 
to obviate those difficulties, we will consider the circle ST as 
passing through the centre of the rim of a fly-wheel connected 
by arms with the small circle AB, representing a nave working 
onan axle atc. If the rim be supposed to weigh 150 lbs. it might 
easily be revolved at the rate of two entire revolutions in a se- 
cond by a handle at A, which is four inches from the cent 
so considered for illustration. When the winch A is moved about 
the axis, the force may be considered as acting by repeated slight 
impulses, as if it were applied at right angles to the radius of the 
circle, at each instant of time along the side of a polygon with 
an infaite number of sides, drawn within the circle. - If the 
sides of the polygon be one hundred in number, they would be 
one fourth of an inch long, and then one and a half inches in 
the larger circle S'T, will be the length of each side of a polygon 
along which the centre particles of the rim may be supposed to 
move. As the proportion of the circle ST is to AB as six is to 
unit, a moving power acting on the latter at the winch A, witha 
given force, through g, h, one fourth of an inch, will move the — 
tim through i, &, equal to six times that space, with one sixth of 
the force applied; but as the moment of rotation is equal to force 
multiplied by leverage, the whole amount of force upon the rim 
through that space must be exactly equal to the power applied 
through the fourth of aninch upon A. And so of each side of the 
two polygons respectively. But they are considered infinitely small 
and ultimately become parts of the two circles ; the power therefore 
must be applied in a circle, and the particles of the rim must be 
propelled in circles with a force exactly equal to that power. Con- 
sequently, the moving power, applied to a fly-wheel or to any 
other revolving body, cannot be expended in pressing the parti- 
cles of such bodies from the centres nor in the direction of tan- 
gents to the circles in which they revolve. And this is evident 
from the fact, that such moving bodies cannot give out nor im- 
part, in any manner whatever, more force than is applied to re- 
volve them. And that force is not only equal to the power ap- 
plied, but it is always returned in the circle in which the body 
moves, and in a direction contrary to. that in which tt was 
received. ‘If a wheel spinning on its axis with a certain velo- 
city be stopped by a hand seizing one of the spokes, the effort 
which accomplishes this is exactly the same, as, had the wheel 
been previously at rest, would have put it in motion in the oppo- 
