680 SCIENCE AND HYPOTHESIS 



these values so that the motion of the centre of gravity is uniform and 

 rectilinear. This will always be possible if Newton's third law holds 

 good, and it will be in general possible only in one way. But no sys- 

 tem exists which is abstracted from all external action; every part 

 of the universe is subject, more or less, to the action of the other parts. 

 The law of the motion of the centre of gravity is only rigorously true 

 when applied to the whole universe. 



But then, to obtain the values of the masses we must find the motion 

 of the centre of gravity of the universe. The absurdity of this con- 

 clusion is obvious ; the motion of the centre of gravity of the universe 

 will be forever to us unknown. Nothing, therefore, is left, and our 

 efforts are fruitless. There is no escape from the following definition, 

 which is only a confession of failure: Masses are co-efficients, which 

 it is found convenient to introduce into calculations. 



We could reconstruct our mechanics by giving to our masses differ- 

 ent values. The new mechanics would be in contradiction neither with 

 experiment nor with the general principles of dynamics (the principle 

 of inertia, proportionality of masses and accelerations, equality of 

 action and reaction, uniform motion of the centre of gravity in a 

 straight line, and areas). But the equations of this mechanics would 

 not be so simple. Let us clearly understand this. It would be only 

 the first terms which would be less simple i.e., those we already 

 know through experiment ; perhaps the small masses could be slightly 

 altered without the complete equations gaining or losing in sim- 

 plicity. 



Hertz has inquired if the principles of mechanics are rigorously 

 true. " In the opinion of many physicists it seems inconceivable that 

 experiment will ever alter the impregnable principles of mechanics; 

 and yet, what is due to experiment may always be rectified by experi- 

 ment." From what we have just seen these fears would appear to be 

 groundless. The principles of dynamics appeared to us first as ex- 

 perimental truths, but we have been compelled to use them as defini- 

 tions. It is by definition that force is equal to the product of the mass 

 and the acceleration; this is a principle which is henceforth beyond 

 the reach of any future experiment. Thus it is by definition that 

 action and reaction are equal and opposite. But then it will be said, 

 these unverifiable principles are absolutely devoid of any significance. 

 They cannot be disproved by experiment, but we can learn from them 

 nothing of any use to us ; what then is the use of studying dynamics ? 

 This somewhat rapid condemnation would be rather unfair. There is 

 not in Nature any system perfectly isolated, perfectly abstracted from 

 all external action; but there are systems which are nearly isolated. 

 If we observe such a system, we can study not only the relative motion 

 of its different parts with respect to each other, but the motion of 

 its centre of gravity with respect to the other parts of the universe. 



