318 B. Rosing on the Participation of Matter 



a mathematical fiction, representing the conditions of the propa- 

 gation of lines of induction in the space occupied by the particles 

 of matter, namely the conditions of their reflexion at the surface 

 of these particles. 



Formula (3) or (8) shows that neither of the hypotheses, 

 when excluding the participation of matter, can explain para- 

 magnetic phenomena: the first, because the magnetic moment 

 of induced currents always appears in a direction opposed to 

 the magnetic field ; the second, because the presence of abso- 

 lutely impermeable matter always lessens the magnetic per- 

 meability of space. Consequently we are obliged to introduce 

 a supplementary hypothesis expressing this participation in 

 some way or other. 



We introduce it here by supposing that the matter, when 

 in a magnetic field, is itself put into some motion ; and con- 

 sequently, besides the system of coordinates representing 

 molecular electric currents, coordinates also exist which fix 

 this magnetic motion for each particle. As these new coor- 

 dinates, we suppose, are of kinosthenic character, the new 

 terms, appearing in the magnetic energy of a substance, are 

 of the form 



XI J and ^vJ 2 ; 



where J is the vector defining in every point the velocity of 

 magnetic motion of matter, and the coefficients X and v depend 

 on the nature of a substance, and denote — the first, X, the 

 connexion between the motion of magnetic induction and the 

 magnetic motion of matter, and the second, v, the inertia of 

 this latter motion. 



Thus the magnetic energy of unit of volume will be repre- 

 sented by the following expression : — 



W 



= ^(j+l)l 2 + IH + XlJ + ivJ 2 . . . (10) 



By applying to this expression the principle of Least Action, 

 we obtain Lagrange's equation in a new form : 

 for coordinate I 



d /4tt/2 

 dt 

 for coordinate J 



J(XI + ,J) = (12) 



Hence, after integrating and putting the initial conditions 

 I = J = H = 0, we have 



(t(7 + 1 ) i+xJ + h )=°> • • • (") 



