22 I. KINEMATICS OF A POINT. LAWS OF MOTION, 



the path is a straight line, and since 



it is traversed with constant velocity. We may on the other hand 

 interpret the statement as giving us a means of measuring time. 

 Intervals of time are proportional to the corresponding distances traversed 

 ty a, material point not acted on by forces. 



Obviously this statement gives us an absolute definition neither 

 of time nor of force, but only a relation between them. It is 

 difficult or impossible for us to realize experimental conditions in 

 which a body shall be withdrawn from the influence of all force. 

 However we may approximate toward this condition, which must at 

 any rate give us the ideal measurement of time. However we find 

 in nature angular motions which, by an application of the first law, 

 give us a practical means for the measurement of time. 



The second law gives us in a move positive manner than the 

 first a measure of a force. 



Lex II. Mutationem motus proportionalem esse vi motrici im- 

 pressae, et fieri secundum lineam rectam qua vis ilia imprimitur. 



Change of motion is proportional to force applied, and takes 

 place in the direction of the straight line in which the force acts. 



By change of motion is meant acceleration. If all our experiments 

 were made with a single body, there would be no advantage in the 

 introduction of the term force over that of acceleration, the mul- 

 tiplication of names being useless when no new ideas are thereby 

 introduced. The convenience of the term force arises from the 

 consideration of the third law. In the case of more than one body 

 , the factor of proportionality mentioned above requires separate defini- 

 tion for the diiferent bodies. 



Lex III. Actioni contrariam semper et aequalem esse reactionem: 

 sive corporum duorum actiones in se mutuo semper esse aequales et in 

 paries contrarias dirigi. 



To every action there is always an equal and contrary reaction: 

 or, the mutual actions of any two bodies are always equal and 

 oppositely directed. 



If we have a certain action between two bodies 1 and 2, and if 

 the actio were proportional only to the accelerations, we should have 



dt* ~dt^ ~dt*~ ~dt*~ ~dt^ ~ dt* 



which is not found to be the case. We must accordingly introduce 

 a factor of proportionality, or (for symmetry) two factors, so that 

 we write 



