316 B. Rosing on the Participation of Matter 



2tt 



W -3 



(J+l)'P+IH, .... (2) 



where e is the aggregate volume of the particles in unit of 

 volume. 



At the same time, by applying Lagrange's equation to the 

 expression of the energy of molecular currents, we get the 

 following relation between the magnetization I and the mag- 

 netic force H : — 



£(|+l)l + H=0 (3) 



It is evident that this equation can be got by applying 

 Lagrange's equation directly to formula (2) and by regarding 

 I as a velocity. 



Formula (3) represents a case of diamagnetism, 



i= " H 



47T/2 



C-0 



From it we find the coefficient of magnetization tc to be 



t(;- +1 ) 



and, lastly, that of the magnetic permeability to be 



,-*=*. ...'.... (5 ) 



1 + 2 



The formula (5) of magnetic permeability is found by 

 assuming the hypothesis of molecular currents, excited by 

 the magnetic field on the surface of particles which are 

 themselves absolutely impermeable. It is remarkable that 

 the same formula can be found by assuming another hypo- 

 thesis, namely that which takes magnetic induction to be a 

 flux, propagating through media of different conductivity. In 

 reality, as is known, the problem of distribution of magnetic 

 induction in space corresponds exactly with that of electric 

 currents*. But we know from Electrok haematics that the 

 conductivity of a medium consisting of spheres of conduc- 

 tivity /jL 2 , disseminated through a medium of conductivity fi l9 

 is t 



* See Maxwell's ' Treatise on Electricity and Magnetism,' 1892, vol. ii. 

 p. 54. 



f Ibidem, vol. ii. p. 57. 



