PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 979 



or diminution of the associated force in precisely the same pro- 

 portion. 



We accordingly find that gravity, which, at the surface of the 

 earth, is considered to be virtually a uniformly acting force, at 

 least for such comparatively small distances as fall under our obser- 

 vation, produces equal accelerations or retardations of velocity, in 

 equal times. A falling body, freely acted upon by gravity, acquires 

 twice the velocity in two seconds that it had at the end of the first ; 

 three times the velocity in three seconds, and so on for any num- 

 ber of seconds, until a distance is traveled which sensibly afiects 

 the force of the earth's gravity. The actual velocity at the end 

 of the first second is about 32 feet ; at the end of the second, 64 

 feet ; at the end of the third, 96, etc. 



Again, if two equal inelastic bodies, rigidly attached together, 

 meet in space a third similar body, equal to each of them in 

 weight, and moving in the opposite direction with twice their 

 velocity, all three will be brought to rest, i. e., the moving force 

 of the latter just equals that of the two former. And so if any 

 two unequal and inelastic bodies having the same momenta, i. e., 

 product of mass into velocity, meet in space while moving in oppo- 

 site directions, they will be brought to rest. 



This is in accordance with Newton's third law, namely: "That to 

 every action there is always opposed an equal reaction ; or the 

 mutual actions of two bodies upon each other are always equal, 

 and directed to contrary parts ; " and the ratio of the quantity of 

 force in a body to the quantity of its motion, or to the product of 

 its weight into its simple velocity, is a corrollar}^ of this law.* 



Let us now examine the views and arguments of those who 

 maintain that the force of a moving body is as the square of its 

 velocity. Instead of the imparted velocity, another element of the 

 efiect of force has been introduced by them, as its proper measure, 

 namely^ the space through which the body acted upon is carried 

 during the action. An unretarded moving body will continue to 

 move forever, and will, therefore, pass over an infinite distance in 



* I have attempted, in another paper read before the Polytechnic Association, to show 

 that there is no actual contact, or rather no clashing of atoms in the collisions of bodiea- 

 (See page 818.) An explanation of the equality of action and reaction is offered, which is 

 widely different from that usually given, and it is also shown that material atoms are 

 detached from each other, movable and not impenetrable even, so that in the collisions of 

 inelastic bodies, here cited, the force apparently lost, is retained among the atoms, increas- 

 ing their relative motion among each other; in other words, their temperature. The 

 mutual destruction of the motions of the bodies, as bodies or aggregations, however, is 

 none the less a proof of the equality of the moving forces. 



