by a Magnet in a Rotating Conductor. 525 



provided we make 



q, = v A*(fa-gy) 



p{p + c-zy 

 in which case 



^= const (36*) 



will be the equation of the current-curves. 



6. In the case of a single inducing pole, the axis of X may 

 for simplicity be made to pass through the same so that £ = ; 

 and on introducing the coordinates f, rj 3 f, 



»- ***** » -0,^ ^+0-^+0 i 



*= -2n*/*K«^ -r^r =2»^Ka ^? P *\l 



wherein « denotes the distance of the pole from the axis of rota- 

 tion. The equation of the current-curves is now 



P jpwr c (38) 



A noteworthy result, immediately deducible from this, is that 

 the form of the current-curves induced by a single pole is indepen- 

 dent of the distance of the pole from the axis of rotation ; whilst, 

 as shown by the expressions (37), the current-density is pro- 

 portional to this distance, and vanishes when a = 0. The equa- 

 tion (38) represents a system of curves of the fourth order, 

 of which, however, only those branches correspond to the pro- 

 blem for which 



has a positive value. The currents are situated in planes parallel 

 to the two by which the disc is bounded ; the parameter f cha- 

 racterizes the whole group of current-curves which belong to the 

 plane f=c — z ; whilst the constant C changes from one curve 

 to another in the same plane. The system of curves correspond- 

 ing to one and the same plane, constructed according to the 

 equation (38), is represented in Plate V., wherein the distance 

 of the inducing pole from the plane of the figure is shown by 

 the line AB, whose length, according to the arbitrary scale 

 adopted, is equal to 0'5. 



Since v vanishes for ?? = 0, it follows that no curve cuts the 

 axis of f . The denominator of the expression (38) being always 

 positive, the corresponding values of 77 and the constant C are 



