FOECE 679 



the inverse ratio of their masses. Thus is the ratio of the two masses 

 defined, and it is for experiment to verify that the ratio is constant. 



This would do very well if the two bodies were alone and could be 

 abstracted from the action of the rest of the world; but this is by no 

 means the case. The acceleration of A is not solely due to the action 

 of B, but to that of a multitude of other bodies, C, D, . . . To apply 

 the preceding rule we must decompose the acceleration of A into many 

 components, and find out which of these components is due to the 

 action of B. The decomposition would still be possible if we suppose 

 that the action of C on A is simply added to that of B on A, and that 

 the presence of the body C does not in any way modify the action of 

 B on A, or that the presence of B does not modify the action of C 

 on A ; that is, if we admit that any two bodies attract each other, that 

 their mutual action is along their join, and is only dependent on their 

 distance apart ; if, in a word, we admit the hypothesis of central forces. 



We know that to determine the masses of the heavenly bodies we 

 adopt quite a different principle. The law of gravitation teaches us 

 that the attraction of two bodies is proportional to their masses; if r 

 is their distance apart, ra and in their masses, Jc, a constant, then their 

 attraction will be Jcmm'/r 2 . What we are measuring is therefore not 

 mass, the ratio of the force to the acceleration, but the attracting 

 mass; not the inertia of the body, but its attracting power. It is an 

 indirect process, the use of which is not indispensable theoretically. 

 We might have said that the attraction is inversely proportional to 

 the square of the distance, without being proportional to the product 

 of the masses, that it is equal to f/r 2 and not to Tcmm. If it were so, 

 we should nevertheless, by observing the relative motion of the celestial 

 bodies, be able to calculate the masses of these bodies. 



But have we any right to admit the hypothesis of central forces ? Is 

 this hypothesis rigorously accurate ? Is it certain that it will never be 

 falsified by experiment? Who will venture to make such an asser- 

 tion? And if we must abandon this hypothesis, the building which 

 has been so laboriously erected must fall to the ground. 



We have no longer any right to speak of the component of the ac- 

 celeration of A which is due to the action of B. We have no means of 

 distinguishing it from that which is due to the action of C or of any 

 other body. The rule becomes inapplicable in the measurement of 

 masses. What then is left of the principle of the equality of action 

 and reaction? If we reject the hypothesis of central forces this prin- 

 ciple must go too; the geometrical resultant of all the forces applied 

 to the different bodies of a system abstracted from all external action 

 will be zero. In other words, the motion of the centre of gravity of 

 this system will be uniform and in a straight line. Here would seem 

 to be a means of defining mass. The position of the centre of gravity 

 evidently depends on the values given to the masses; we must select 



