Revolving about Fixed Axes. 271 



ed to an arm revolving in a circle of eight feet in diameter, and 

 let EF be an arch of that circle, touching the straight line Ag at 

 B. As the velocity of the bar and the circumference of the circle 

 are equal, the bar, after being attracted by the magnet at B, would 

 move on with the same uniform velocity and perform one entire 

 revolution in a second, friction and the resistance of the atmos- 

 phere being considered equal to nothing. And its deflection from 

 the straight line, or its centripetal force for j\ of a second, would 

 be equal to the square of the arch B^r, which is six inches, divi- 



ded by the diameter of the circle, that is = Q- = .375 = f of an 



inch, or only one eighth of the deflection caused by the smaller 

 wheel ; and in the same ratio for any other spaces through which 

 the bar would have passed whilst moving through equal spaces 

 in the circle. And hence it is that the central forces are inversely 

 as the diameters of the circles in which a body is made to move 

 with a given velocity. The increment of deflection for an en- 



25.142 



tire second being = — ^ = 632 feet per second in the smaller 



25.142 

 wheel, and in the larger one = — ^ — =79 feet per second only ; 



and yet the bar has precisely the same velocity, and consequently 

 the same force in the latter that it had in the former. Therefore, 

 aside from friction, it would, if welded to m, require no more 

 force to revolve it in the former than in the latter case. 



For the same reasons, with a given velocity for the particles 

 of the rims, the smaller a fly-wheel is, the greater will be the 

 amount of centrifugal force, other things being equal. This will 

 appear obvious upon inspecting the figure ; for it will be seen that 

 a particle of iron at v in the rim of a small wheel would be de- 

 flected from the straight line eight times as many inches in a given 

 unit of time as a particle would be at the point z of the large wheel. 

 The measure of the deflection from that line must therefore be 

 the measure of the centrifugal force for any instant of time : and 

 consequently the aggregate amount will be proportionate to the 

 curve in which the body moves. This deflection takes place 

 when a body is moved in a curved line, and the tendency to resist 

 it and move in a straight line is excited in such a mass of matter 

 in obedience to the important law of inertia, with as much cer- 

 tainty as electricity would result from the action of sulphuric 



