516 M. E. Jochmaun on the Electric Currents induced 



and from the same conclude that the total electromotive force 

 arising from the several inductive actions is everywhere perpendi- 

 cular to the direction in which the ^ conductor-element moves. 

 By differentiating the expressions (11) and employing (7) and 

 (9), we deduce the relations 



Id* oy 



3 .r— =4-77^ Y 



OX oz 



oy o% J 



o% oy oz 



(13) 



(14) 



On substituting the values (12), the equations (10) assume the 

 forms 



w; = k|-^-+uM-1,lT. 

 From these three equations, in combination with the condition 



|!l + !? + !?f! = 0, (16) 



ox ay oz 



which is to be fulfilled at every point within the conductor, the 

 functions u, v, w, and V must be so determined that, at the same 

 time, the equation 



UCOSX + V COS /jL + W cos v = . . . . (17) 



will be satisfied at every point of the surface. By means of the 

 equations (13), we may eliminate from the equations (15) either 

 u } v, w or L, M, N. In the first case we obtain 



- ^ =47r*K*f - |X +bN-fa)>lT," 

 oy L o% 



> • (18) 



oM. 



3N 



oz 



3y 



0% 



"a* 



47r*K-f -|^ +faL-«N"V, 



|L_|M =47r , K (_|V + „ M _ bL -l J 

 oy o* I oz J J 



