DISCOVERY OF THE LAWS OF MOTION. 45 



Product of the weight and the velocity is the same 

 for the two balancing weights ; and if we call this 

 Product Momentum, the Law of Equilibrium is, 

 that when two weights balance on a machine, the 

 Momentum of the two would be the same, if they 

 were put in motion. 



The Notion of Momentum was here employed 

 in connexion with Virtual Velocities: but it also 

 came under consideration in treating of Actual 

 Velocities, as we shall soon see. 



Sect. 5. Attempts at the Third Law of Motion 

 Notion of Momentum. 



IN the questions we have hitherto had to consider 

 respecting Motion, no regard is had to the Size 

 of the body moved, but only to the Velocity and 

 Direction of the motion. We must now trace the 

 progress of knowledge respecting the mode in which 

 the Mass of the body influences the effect of Force. 

 This is a more difficult and complex branch of the 

 subject; but it is one which requires to be no- 

 ticed, as obviously as the former. Questions belong- 

 ing to this department of Mechanics, as well as 

 to the others, occur in Aristotle's Mechanical Pro- 

 blems. "Why," says he, "is it, that neither very 

 small nor very large bodies go far when we throw 

 them ; but, in order that this may happen, the 

 thing thrown must have a certain proportion to 

 the agent which throws it? Is it that what is 



