SEQUEL TO THE EPOCH OF GALILEO. 59 



the Third Law of Motion in its most general sense ; 

 namely, that the Momentum (which is proportional 

 to the Mass of the body and its Velocity jointly,) 

 may be taken for the measure of the effect ; so that 

 this Momentum is as much diminished in the strik- 

 ing body by the resistance it experiences, as it is 

 increased in the body struck by the impact. This 

 was sometimes expressed by saying that "the Quan- 

 tity of Motion remains unaltered," Quantity of Mo- 

 tion being used as synyonymous with Momentum. 

 Newton expressed it by saying that "Action and 

 Reaction are equal and opposite," which is still one 

 of the most familiar modes of expressing the Third 

 Law of Motion. 



In this mode of stating the Law, we see an 

 example of a propensity which has prevailed very 

 generally among mathematicians; namely, a dis- 

 position to present the fundamental laws of rest 

 and of motion as if they were equally manifest, and, 

 indeed, identical. The close analogy and connexion 

 which exists between the principles of equilibrium 

 and of motion, often led men to confound the evi- 

 dence of the two ; and this confusion introduced an 

 ambiguity in the use of words, as we have seen in 

 the case of Momentum, Force, and others. The 

 same may be said of Action and Reaction, which 

 have both a statical and a dynamical signification. 

 And by this means, the most general statements of 

 the laws of motion are made to coincide with the 

 most general statical propositions. For instance. 



