( 826 ) 



eorrcspoiidiii.u', in llio lu.iiiiier S[>eciüed in § iO, to the circular paths 

 descrihod iji the other ease. 



§ 12. Jt remains to say some words about molecular motion. We 

 may conceive that bodies in which this has a sensible influence or 

 even predominates, undergo the same deformation as the systems of 

 j)articles of constant I'elative position of whicii alone we have spoken 

 till now. Indeed, in two systems of molecules 2£' and ^, the first 

 without and the second with a translation, we may imagine molecular 

 motions corres[)onding to each otiier in such a way that, if a particle 

 in ^"' has a certain j)Osition at a definite instant, a particle in -^^ 

 occupies at the corresponding instant the corresponding position. This 

 being assumed, we may use the relation (33) between the accelera- 

 tions in all those cases in which the velocity of molecular motion 

 is very small as compared to ir. In these cases the molecular forces 

 may be taken to be determined by the relative positions, indepen- 

 dently of the \elocities of molecular motion. If, finally, we suppose 

 these forces to l)e limited to such small distances that, for particles 

 acting on each other, the ditfei'ence of local times may be neglected, 

 one of the particles, together with those which lie in its sphere of 

 attraction or repulsion, will form a system which undergoes the 

 often mentioned deformation. In virtue of the second hypothesis 

 of § 8 we may therefore apply to the resulting molecular force 

 acting on a t)article, the equation (21). Consequently, the proper 

 relation between the forces and the accelerations will exist in the two 

 cases, if we suppose that the masses of all particles are influenced 

 by a translation to the same degree as the electroniagnetie masses of 

 the eJectrons. 



§ 13. The values (30) which I have found for the longitudinal and 

 transverse masses of an electron, expressed in terms of its velocity, are 

 not the same as those that have been formerly obtained hj Abraham. 

 The ground for this difference is solely to be sought in the circnm" 

 stance that, in his theory, the electrons are treated as spheres of 

 invariable dimensions. Now, as regards the transverse mass, the 

 i-esults of Abraham have been confirmed in a most remarkable way 

 by Kaufmann's measurements of the deflexion of radium-rays in 

 electric and magnetic fields. Therefore, if there is not to be a most 

 serious objection to the theory I have now })roposed, it must be 

 ])Ossible to show that those measurements agree with my values 

 nearly as well as with those of Abraham. 



1 shall beuin bv discussing two of the series of measurements 



