VOL. LXVI.] l-HILOSOPHICAL TRANSACTIONS. 81 



conclude, that tliis is the universal law of nature, respecting the capacities of 

 bodies in motion to produce mechanical effects, and the quantity of mechanic 

 power necessary to be employed to produce or generate different velocities, the 

 bodies being supposed equal in their quantity of matter ; that the mechanic 

 powers to be expended are as the squares of the velocities to be generated, and 

 vice versa ; and that the simple velocities generated are as the impelling power 

 compounded with, or multiplied by, the time of its action, and vice versa. 



We shall perhaps form a still clearer conception of the relation between 

 velocities produced, and the quantities of mechanic power required to produce 

 them ; together with the collateral circumstances attending, by which these 

 propositions, seemingly 'i, are reconciled and united, by stating the following 

 popular elucidation, which indeed was the original idea that occurred to me on 

 considering this subject ; to put which to an experimental proof gave birth to 

 the foregoing apparatus and experiments. 



Suppose then a large iron ball of 10 feet diameter, turned truly spherical, 

 and set on an extended plane of the same metal, and truly level. Now, if a 

 man began to push at it, he will find it very resisting to motion at first ; but, 

 by continuing the impulse, he will gradually get it into motion, and having 

 nothing to resist it but the air, he will, by continuing his efforts, at length get 

 it to roll almost as fast as he can run. Suppose now, in the first minute he gets 

 it rolled through a space of one yard ; by this motion, proceeding from rest, 

 similar to what happens to falling bodies, it would continue to roll forward at 

 the rate of 2 yards per minute, without further help ; but supposing him to con- 

 tinue his endeavours, at the end of another minute he will have given it a 

 velocity capable of carrying it through a space of 2 yards more, in addition to 

 the former, that is, at the rate of 4 yards per minute ; and at the end of the 

 3d minute, he again added an equal increase of velocity, and made it proceed at 

 the rate of 6 yards per minute ; and so on, increasing its velocity at the rate of 

 2 yards in every minute. The man therefore in the space of every minute 

 exerts an equal impulse on the ball, and generates an equal increase of move- 

 ment, correspondent to the definition of Sir Isaac Newton. But let us see 

 what happens besides ; the man, in the first minute, has moved but one yard 

 Irom where he set out ; but he must in the 2d minute move 2 yards more, in 

 order to keep up with the ball ; and as he exerted an impulse on it, so as at the 

 2d minute to have given it an additional velocity of the 2 yards, he must also 

 in this time have gradually changed its velocity from the rate of 2 yards per 

 minute to that of 4, and the space that he will of consequence have actually 

 been obliged to go through in the 2d minute, will be according to the mean of 

 the extremes of velocity at the beginning and end of it, that is, 3 yards in the 

 2d minute : so that being i yard from his original place at the beginning of the 



VOL. XIV. M 



