518 M. E. Jochmann on the Electric Currents induced 



rents induced in the conductor, since, with the exception of a 

 constant factor, the second terms in the expressions for L, M, N 

 give obviously the rectangular components of this action upon 

 an external point. 



If we take the axis of rotation for axis of Z, and denote by n 

 the angular velocity of rotation, we have 



u=—ny, b = n%, fo = 0, 



and the equations (15) become transformed thus : 



a=K {_g + n,N}, 



-Kf-jg-MyN}, 



w=E.\ -|^- n(xL+yM) } . 

 *» nz J J 



(15*) 



4. In the particular case when the given magnetic distribu- 

 tion is symmetrical with respect to the axis of rotation — in other 

 words, when P is a function of z } and r= s/x^ + y* — the equa- 

 tions (15*) may be satisfied by assuming 



u=0 } v=0, w = 0. 



That is to say, a distribution of free electricity within and upon 

 the surface of the conductor may always be assigned so that its 

 potential shall at every point of the conductor equilibrate with 

 the electromotive force induced by the magnetic distribution, 

 and thus prevent the production of currents. In this case, in 

 fact, the expressions (11) are reducible to 



L=2*|? 

 0# 



M=2k 



By' 



N=2*|?, 



whereby the equations (15*) become 



s- — =)lnk3c^—> 

 ox oz 





(21) 



J~K*g+€> 



It is readily seen that when P is a function of r and z alone, the 

 expressions on the right of these equations satisfy the conditions 

 of integrability of the system. By the introduction of polar 



