St LECTURE IV. 



Standing its weiglit, to the sling which is above it, in consequence of the ex- 

 cess of the centrifugal force abo\e the force of gravitation. 



It is also a centrifugal force that is thp foundation of the amusement of a boy- 

 driving a hoop. A hoop at rest, placed on its edge, would very quickly fall 

 to the ground; but Avhcn it is moving forwards, a slight inclination towards 

 either side causes the parts to acquire amotion towards that side, those which 

 are uj)permost being most affected Iry it; and this lateral motion, assisted 

 sometimes by the curvature of the surface of the hoop, causes its path to de- 

 viate from a rectilinear direction, so that instead of moving straight forwards, 

 it turns to that side, towards which it began to incline; and in this po- 

 sition, its tendency to fall still further is counteracted by the centrifugal force, 

 and it generally makes several complete revolutions before it falls. The mo- 

 tion of a bowl, with its bias, is of a similar nature; the centrifiigal force 

 counteracting the tendency to curvilinear motion, so as to diminish it very con- 

 siderably, until the velocity is so much reduced, as to suifer it to describe a path 

 evidently curs'ed, and becoming more and more so as the motion is slower. 



When a body is retained in a circular orbit, by a force directed to its centre^ 

 its velocity is every where equal to tliat which it would acquire, in falling, by 

 means of the same force, if uniform, through half the radius, tliat is, through 

 one fourth of the diameter. This proposition affords a very Convenient me- 

 thod of comparing the effects of central forces with those of simple accele- 

 rating forces, and deserves to be retained in memory. We may in some mea- 

 sure demonstrate its truth by means of the whirling table: an apparatus which 

 is arranged on purpose for exhibiting the properties of central forces, although 

 it is more calculated for showing their comparative thati their absolute magni- 

 tude; for accordingly as we place the string on the pullies,, the two horizontal 

 arms may be made to revolve either with equal velocities, or one twice as fast 

 as the other. The sliding stages, which may be placed at different distances 

 from the centres, and which are made to move along the arms with as little 

 friction as possible, are in a certain proportion to the weights, which are to be 

 raised, by means of threads passing over pvdlies in the centres, as soon as the 

 centrifugal forces of the stages with their weights are sufficiently great; and 

 the experiment is to be so arranged, that when the velocity, having been gra- 

 dually increased, produces a sufiicient centrifugal force, both stages may raise 



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