274 Dynamies. 



two currents of water, moving with different velocities and driv- 

 ing two wheels, one of which is placed at each extremity of the 

 axle. When the wheels have begun to move, by the joint action 

 of these falls of water, its motion will at first be slow, and each 

 fall of water will perform its part in giving motion to the axle ; 

 but if the greater fall is capable, by the continuance of its action, 

 of giving its wheel a velocity either equal to, or greater than the 

 velocity of the smaller fall, then it is manifest that the smaller 

 fall ceases to iuipel its wheel, and that the whole effect is produced 

 by the action of the greater fall. Hence it will be perceived from 

 this statement, not only why a diminution of the impelling power 

 accompanies an increase of velocity, but why there is a certain 

 velocity of the machine, which is necessary before we can gain 

 all the useful effect which we wish to have from the powers which 

 we employ. 



392. In order to illustrate this in the case of a real machine, 

 let us suppose that the power of a man is to be employed in rais- 

 ing a load by means of a walking crane. This machine consist's 

 of a large wheel placed upon an axle, round which is coiled 

 a rope, having a weight r attached to its lower extremity ; the 

 man walks upon the interior of the wheel, and by his weight 

 gives it a rotatory motion, aftd thereby coils the rope round the 

 axle, and elevates the weight r. Let us suppose the wheel or 

 drum so constructed, like the fusee of a watch, that the man 

 can walk at different distances from the axis ; and let p be the 

 power or weight of the man, r the weight to be raised, and tf the 

 distance of the latter or radius of the axle, and D the distance of 

 the former or the radius of the wheel ; then 



r$ 

 p : r : : o : D = , 



the distance from the centre of the wheel, at which the man must 

 place himself, in order to be in equilibrium with the resistance r. 

 But as the machine must be moved, and the weight raised, the man 



must go to a greater distance from the axis than ; the motion of 



the machine will therefore be accelerated, and the acceleration 

 would increase as he moved to a greater and greater distance 

 from the centre of the wheel. Hence it is obvious, that as the 

 acceleration increases, the man must walk with greater and 



