158 Dadourian — Progressive Development of Mechanics. 



nomenon is not satisfactory until we can apply it to the New- 

 tonian system of Mechanics. In fact we may state that the 

 extent to which the Newtonian system can be applied to a 

 group of phenomena is a measure of the clearness with which 

 we understand them. 



It is therefore of the utmost importance for the develop- 

 ment of physical science to have the principles which underlie 

 the Newtonian Mechanics as clearly stated as possible. The 

 fact that so many eminent scientists have severely criticized 

 Newton's laws of motion indicates that these laws are not the 

 best possible foundation upon which Newtonian Mechanics can 

 be based. Some of the important points raised by the critics 

 of Newton's laws are contained in the following extract from 

 Hertz :* 



" We swing in a circle a stone tied to a string, and in so doing 

 we are conscious of exerting a force upon the stone. This force 

 constantly deflects the stone from its straight path. If we vary 

 the force, the mass of the stone, and the length of the string, we 

 find that the actual motion of the stone is always in accordance 

 with Newton's second law. But now the third law requires an 

 opposing force to the force exerted by the hand upon the stone. 

 With regard to this opposing foi-ce the usual explanation is that 

 the stone reacts upon the hand in consequence of centrifugal 

 force, and that this centrifugal force is in fact exactly equal and 

 opposite to that which we exert. Now is this mode of expression 

 permissible '? Is what we call centrifugal force anything else 

 than the inertia of the stone ? Can we, without destroying the 

 clearness of our conceptions, take the effect of inertia twice into 

 account, — first as mass, secondly as force ? In our laws of motion, 

 force was a cause of motion, and was present before the motion. 

 Can we, without confusing our ideas, suddenly begin to speak of 

 forces which arise through motion, which are a consequence of 

 motion ? . . . These questions must clearly be answered in the 

 negative. The only possible explanation is that, properly speak- 

 ing, centrifugal force is not a force at all. . . . But, what now 

 becomes of the demands of the third law, which requires a force 

 exerted by the inert stone upon the hand, and which can only be 

 satisfied by an actual force, not a mei'e name ? " 



" I do not regard these as artificial difficulties wantonly raised : 

 they are objections which press for an answer. Is not their 

 origin to be traced back to the fundamental laws? The force 

 spoken of in the definition and in the first two laws acts upon a 

 body in one definite direction. The sense of the third law is that 

 forces always connect two bodies, and are directed from the first 

 to the second as well as from the second to the first. It seems to 

 me that the conception of force assumed and created in us by the 

 third law on the one hand, and the first two laws on the other 

 hand, are slightly different. This slight difference may be 



*Heinrich Hertz, Principles of Mechanics, p. 5. 



