RELATIONS TO OTHER SCIENCES 137 



(22) Longitudinal Mass and Transverse Mass. We find under these 

 conditions that the force of inertia is proportional to the acceleration 

 with a coefficient of proportionality analogous to mass, but which is 

 here a function of the velocity, and increases indefinitely, like the 

 kinetic energy, as the velocity tends to approach that of light. 

 Moreover, this electromagnetic mass differs for the same velocity, 

 according as the acceleration is parallel or perpendicular to the 

 direction of the velocity. There is, corresponding to the direction, 

 a longitudinal and a transverse mass. Mass is then no longer a 

 scalar quantity, but has the symmetry of a tensor parallel to the 

 velocity. No experimental fact yet allows us to verify this dis- 

 symmetry of the mass of the electrons, which becomes evident only 

 when the velocity is of the same order as that of light, but the vari- 

 ation of the transverse mass with the velocity has been proven by 

 Kaufmann for the ft rays of radium, which consist of particles 

 identical with the cathode rays. It is sufficient to compare the 

 deviations of these rays in the electric and magnetic fields perpen- 

 dicular to their direction in order to deduce, by application of 

 the equations of the dynamics of the electron, their velocity and the 

 ratio of the charge to the transverse mass of the particles which 

 compose them. This ratio decreases as the velocity increases, and, 

 if we consider as fundamental the principle of the conservation of 

 electricity, we conclude from it an actual increase of the transverse 

 mass according to a law easy to compare with that which the theory 

 gives for the electromagnetic mass. 



(23) Matter of the Philosophers. But before discussing the result of 

 this comparison, I wish to point out a logical difficulty raised by the 

 course which we have followed: we are accustomed to consider as 

 fundamental the ideas of mass and force, built up in order to repre- 

 sent the laws of motion of matter; we, a priori, conceive of mass as 

 a perfectly invariable scalar quantity. 



Now, let us suppose the possibility of a material representation of 

 the ether: we apply to it the equations of material dynamics, and 

 we are led to admit for the electrons, which form a part of matter, 

 and consequently for matter itself, a dissymmetrical mass, tensorial 

 and variable. 



To what, then, should the equations of ordinary dynamics apply, 

 and what are the ideas considered as fundamental which they imply? 

 To an abstract matter, the matter of the philosophers, which could not 

 be ordinary matter, since it is inseparable from electric charges, and 

 which is probably made up of an agglomeration of electrons in periodic 

 motion, stable under their mutual actions? Or to the ether? But 

 we have no idea of what can be its mass or motion. 



It is, indeed, rather the ether which it is necessary to consider as fun- 

 damental, and it is then natural to define it initially by those proper- 



