522 M. E. Jochmann on the Electric Currents induced 



This done, the equations (15*) are reduced to the 



very small, 

 following: :• 



m = K \ — ^- \-2nkx ^— r , 



and the equation (16) becomes transformed thus : 



(26) 



a*v.3*v.a«v , .3P 



dy 02 d« 



0* s 



(27) 



This equation, therefore, has merely to be integrated, subject to 

 the limiting condition 



^-- cos X + =-- cos a 4- -^— cos v 

 0% oy oz 



2/i^(a7COsX-fycosyLt) ^ 2nk cos v (^<— 



MY I 

 3y/' J 



I 



(28) 



after which u } v, w will be found by simple differentiation. 



As an example, we will treat the case of a disc of arbitrary 

 thickness, bounded by two parallel planes, which rotates,, under 

 the influence of an external magnetic pole, around an axis per- 

 pendicular to those planes. Let 2S be the thickness of the disc, 



z = 8 and z= —8 



the equations of the limiting planes, and a, b, c the coordinates 

 of the inducing pole, so that 



P = 



(29) 



provided 



denote the distance of this pole from any point of the disc. 

 The limiting condition will be fulfilled if, for z= ±8 } 



= 0, 



or 



ay 



OZ 



—**('%+'%)■ ■ 



(28*) 



We will now show that the equations (26) and (27) may be 

 satisfied by assuming that everywhere w = 0, — in other words, 

 that the currents flow in planes parallel to the two by which the 



