with reference to the Measure and Transfer of Force. 339 



the plane of revolution, no force is introduced, the sum of the 

 motions being always 10. 



If we inquire what is the function of the absolute velocity 

 which, being multiplied by the mass of each globe respectively, 

 shall give a sum that is constant, whatever may be the direction 

 of the motion of the common centre of gravity, we shall find 

 that the square velocity is the only function that answers, and 

 that although the absolute velocities are continually changing 

 through a cycle, the sum of the products of the mass of each 

 body by the square of its respective absolute velocity, is a con 

 stant quantity, and equal to the sum of the rectilineal and rota- 

 tory vis viva taken separate. 



§12. 

 Distinction between momentum and motion. 



In our educational treatises, up to the present time the idea 

 continues to be inoculated into the student of physical science, 

 that the natm-al standard measure of motion in the abstract is 

 the product of the mass of a body or system by the velocity of 

 its centre of gravity. The ambiguity and contradictions that 

 this involves when he extends his studies, might be avoided if 

 such definition was confined to the word momentum, and the 

 word motion taken to mean the product of the mass by its square 

 velocity. The following instance will serve to make this appre- 

 ciable. 



In the use of the Ballistic pendulum, the same velocity is 

 communicated to it by the stroke of a 2 lb. ball moving 100 feet 

 per second as by a 1 lb. ball moving 200 feet per second; the 

 momentum or velocity of the centre of gravity of the system com- 

 posed of the bullet and pendulum being in the two cases the 

 same, or veiy nearly so. Suppose the 1 lb. ball to be hollow, so 

 as to have the same diameter as the 2 lb. ball, its penetration 

 into the timber of the pendulum would be found to be double 

 that of the 2 lb. ball, because its quantity of motion is double. 

 Its working power or efficacy is double. The definition of mo- 

 mentum would thus conform to the condition of inelastic impact, 

 where the force of impact disappears in molecular disruption or 

 production of heat, or both combined. The definition of motion 

 confined to the natural standard of living force would conform 

 to the causal relation of dependent action. 



§ 13. 



Newton and Laplace's arguments in favour of the simple ratio 

 of the velocity being the natural standard of motion. 



Newton employed the word motion to denote the velocity of 



