524 M. E. Jochmann on the Electric Currents induced 



(28*), but that it also possesses the above-mentioned properties 

 so long as f differs from zero, — that is to say, so long as the in- 

 ducing pole remains at a finite distance from the limiting sur- 

 face of the conductor. On the other hand, the value of V which 

 corresponds to the negative sign is discontinuous when f = 

 and r) = 0. 



Taking into consideration the equations (29) and (31), it 

 follows from (26) that 



which values may obviously be written thus : 



3ABy p+U r ^yp{p+Z) 



d*V>x p + Z J ^xp{p + Z) 



or, by reintroducing the coordinates x y y, z, thus : 



7 Tr "d ay — bx 



u = 2nku,K ^ t-^ : , 



dy p{p + c— z) 



n 7 rr B Ix — aV 



v = 2nkfjuK 



(35) 



~dx p(p + c— z)' 

 The differential equation of the current-curves is consequently 



vdx— udy=0j 

 which by integration gives 



bx-ay =CQDst 



p(p + c-z) 



The differential equation for V being linear, the solution of 

 the problem contained in the equations (34), (35), and (36) may 

 be at once extended to any number of poles whatever. We have, 

 in fact, 



1 <- p p(p + c—z) J 



u=-2nkK 



.] 



By 

 B*' j 



v=+2nkK^. 



