the Comervation of Force. 85 



ratio of the squares of the distances. Where abides the force 

 which is here destroyed ? The reply is : — If the mass A be left 

 to itself, it moves back towards B, and when it has arrived at its 

 original position, it will be attracted by B with the same force 

 as before ; besides this it has attained a velocity, half the square 

 of which, multiplied by the mass of A, is exactly equal to the 

 work which was formerly expended in removing it from B. 

 There is therefore no force destroyed by the change which the 

 external cause has wrought; but just as much force appears at 

 the end as was expended in producing the change. Let us look 

 a little more closely into the matter with which we have here to 

 deal. What is our measure of the force of attraction ? It is 

 the augmentation of velocity which a body experiences in the 

 unit of time by the action of the force. In virtue of inertia, 

 the impulses of gravity are accumulated in the body, the velo- 

 city augments in the same proportion, and the quantity stored 

 up in the unit of time serves as a measure for the magnitude of 

 the attractive force. This is the only true and direct measure 

 of a force ; for as the very notion of a force has been derived 

 from the concrete phaiuomena of motion, the measure of a force 

 must also be derived from the same thing. 



It is this augmentation of velocity which follows the law of 

 the inverse square of the distance, and this stands in no con- 

 tradiction, but in the most complete harmony with the principle 

 of the conservation of force. This principle affirms, that in every 

 system which is abandoned to itself the sum of the tensions 

 added to the sum of the vires viva:, gives at all times the same 

 quantity. In other words, that in every such system the quan- 

 tity which is obtained when the moving masses arc multiplied 

 by half the squares of their velocities has a maximum, which is 

 given once for all, which cannot be overstepped, and of which 

 moreover nothing can be lost. j\Iotion can never be destroyed 

 so as to be incapable of regeneration, because motion disappears 

 only in consequence of a change of place of the masses, which 

 change in due time again appears as a cause of motion, and on 

 the return of the masses to their original position, reproduces the 

 motion which was consumed during the change. It is here of 

 course assumed that the measure of the motion is always the 

 product obtained by the multiplication of the single masses with 

 the half-squares of their velocities. Let us take the simplest 

 system of all, the vibrating pendulum. The maximum above 

 referred to is the vis viva obtained when the mass is multiplied 

 by the half-square of the velocity with which the ])cndulum 

 passes its position of equilibrium; at every other point the vis 

 viva is less, and at the turniMg-])oiiits it is zero. But at these 

 points the whole force, as a cause of motion, is stored up ; and 

 when the pendulum again attains its position of equilibrium, the 



