Revolving about Fixed Axes. 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 

 on an axle at c. 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 centre, or 

 so considered for illustration. When the winch A is moved about 

 the axis, the force may be considered as acting by repeated sHght 

 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 infinite 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 ST, 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, with a 

 given force, through g, A, one fourth of an inch, will move the 

 rim through «, A;, 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 an inch 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 

 m.oves, and in a direction contrary to that in which it loas 

 received. " If a wheel spinning on its axis with a certain velo- 

 city be stopped by a hand seizing one of the spokes, the eflbrt 

 which accomplishes this is exactly the same, cis, had the wheel 

 been previously at rest, would have put it in motion in the oppo- 



