MECHANICS AND OPTICS. 227 



that their real mass, if it exists, is not constant, but 

 varies with the velocity, following the same laws as 

 their fictitious mass. 



2, That all forces are of electro-magnetic origin, or 

 at least that they vary with the velocity, following the 

 same laws as forces of electro-magnetic origin. 



It is Lorentz again who has made this remarkable 

 synthesis. Let us pause a moment to consider what 

 results from it. In the first place, there is no more 

 matter, since the positive electrons have no longer 

 any real mass, or at least no constant real mass. The 

 actual principles of our Mechanics, based upon the 

 constancy of mass, must accordingly be modified. 



Secondly, we must seek an electro-magnetic ex- 

 planation of all known forces, and especially of gravi- 

 tation, or at least modify the law of gravitation in the 

 sense that this force must be altered by velocity in 

 the same way as electro-magnetic forces. We shall 

 return to this point. 



All this appears somewhat artificial at first sight, 

 and more particularly the deformation of the electrons 

 seems extremely hypothetical. But the matter can 

 be presented differently, so as to avoid taking this 

 hypothesis of deformation as the basis of the argu- 

 ment. Let us imagine the electrons as material points, 

 and enquire how their mass ought to vary as a function 

 of the velocity so as not to violate the Principle of 

 Relativity. Or rather let us further enquire what should 

 be their acceleration under the influence of an electric 

 or magnetic field, so that the principle should not be 

 violated and that we should return to the ordinary 

 laws when we imagine the velocity very low. We 

 shall find that the variations of this mass or of these 



