SEQUEL TO THE EPOCH OF GALILEO. 348 



when we say that it requires more force to throw a stone one hundred 

 paces than fifty." 4 Reasoning upon this difference, he comes to the 

 conclusion that " the Momentum of percussion is infinite, since there 

 is no resistance, however great, which is not overcome by a force of 

 percussion, however small." 5 He further explains this by observing 

 that the resistance to percussion must occupy some portion of time, 

 although this portion may be insensible. This correct mode of re- 

 moving the apparent incongruity of continuous and instantaneous force, 

 was a material step in the solution of the problem. 



The Laws of the mutual Impact of bodies were erroneously given by 

 Descartes in his Princrpia ; and appear to have been first correctly 

 stated by Wren, Wallis, and Huyghens, who about the same time 

 (1669) sent papers to the Royal Society of London on the subject. In 

 these solutions, we perceive that men were gradually coming to appre- 

 hend 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 striking 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 Quantity 

 of Motion remains unaltered," Quantity of Motion being used as 

 synonymous 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 

 disposition to present the fundamental laws of rest and of motion as if 

 they were equady manifest, and, indeed, identical. The close analogy 

 ano 1 connection which exists between the principles of equilibrium and 

 of motion, often led men to confound the evidence 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 dynam- 

 ical 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, Newton deduced from his principles the 

 conclusion, that by the mutual action of bodies, the motion of their 

 centre of gravity cannot be affected. Marriotte, in his Traite de la 



* Op. iii. 210. 6 iii. 211. 



