526 M. E. Jochinann ou the Electric Currents induced 



either both positive or both negative. When C=0, then 17 = 

 for all values of £, and the curve corresponding to this value of 

 C coincides with the axis of f . The curves corresponding to 

 equal and opposite values of C are symmetrical with respect to 

 the axis of £. Every curve is symmetrical also with respect to 

 the axis of tj, since its equation involves £ 2 solely. All curves, 

 with the exception of the one for which C = 0, are closed; for 



since for real values of £ the fraction - is always a proper one, 



the value of the quotient (38) must diminish, when p increases, 

 beyond any assignable magnitude. It is also manifest that for 

 a given value of C, the ordinate 97 cannot sink below a determi- 

 nate limit. The greatest and smallest admissible values of rj 

 and p correspond to £=0; consequently every curve cuts the 

 axis of 7] perpendicularly in two real points, and all curves 

 circulate around two points situated upon this axis at equal dis- 

 tances from the axis of £. These points, which for brevity we 

 will call whirling -points (Wirbelpunkte), correspond, as curves of 

 the system, to a maximum value of C, or to w=0 and v = 0. 

 Their coordinates are given by the equations 



^(2p + ?)=0, 



Hence, since p is always positive, 77 according to the second equa- 

 tion can never vanish. From the first equation, therefore, it 

 follows that f=0, and hence p 2 =?7 2 + f 2 ; so that the second 

 equation takes ultimately the form 



whose real roots are 



V=±^ 



1+ */5 



2 



The maximum value of C, corresponding to the whirling-points, 



is 



V 5 ? V H + 5^5 



To greater positive or negative values of C correspond no real 

 current-curves. 



The whirling-points of the current-systems situated in the 

 several planes lie on two right lines which intersect in the indu- 

 cing pole, and enclose an angle of about 103° 39'. In the limit- 

 ing case, where the pole approaches infinitely close to the surface 

 of the disc, that is to say, when ?=0 is the equation of one of the 

 limiting planes of the latter, the two whirling-points approach 



