III. 



THE NEW MECHANICS AND ASTRONOMY. 



I. 



Gravitation. 



Mass may be defined in two ways — firstly, as the 

 quotient of the force by the acceleration, the true 

 definition of mass, which is the measure of the body's 

 inertia ; and secondly, as the attraction exercised by 

 the body upon a foreign body, by virtue of Newton's 

 law. Wc have therefore to distinguish between mass, 

 the coefficient of inertia, and mass, the coefficient of 

 attraction. According to Newton's law, there is a 

 rigorous proportion between these two coefficients, but 

 this is only demonstrated in the case of velocities to 

 which the general principles of Dynamics are appli- 

 cable. Now we have seen that the mass coefficient of 

 inertia increases with the velocity ; must we conclude 

 that the mass coefficient of attraction increases 

 similarly with the velocity, and remains proportional 

 to the coefficient of inertia, or rather that the 

 coefficient of attraction remains constant? This is a 

 question that we have no means of deciding. 



On the other hand, if the coefficient of attraction 

 depends upon the velocity, as the velocities of bodies 



