by a Magnet in a Rotating Conductor. 523 



disc is bounded. Since 



it follows from (27) that 



^ + W =2nk ^i 2V+x ^ +y TyJ- • (30) 



This equation is satisfied by the value 



V=2n*/»!p (31) 



provided W be understood to be a solution of the equation 

 d 2 W yw _ 2 _ 3?(3?-a)+y(y-5) 



and the value of P be taken into consideration. On observing 

 that 



we deduce at once the relation 



y(W-p) , B'(W-p) «(*-«) + %->) ,,„> 



If, now, for simplicity, the origin of coordinates be removed 

 to the inducing pole by the substitutions 



a?— a=g, y—h—7], z—c=%, 



it will be readily seen that to the equation (32) corresponds the 

 integral 



W= P + a ±^>, ..... (33) 

 whence we deduce the value • 



The upper sign is alone admissible in the present problem, since 

 V must possess the characteristic properties of a potential func- 

 tion, and consequently remain finite and continuous throughout 

 the interior of the conductor, and vanish, together with its dif- 

 ferential quotients, when £=co or 97 = go . For it is easy to see 

 that the value 



*= 2 *H + £t§} • ; ■ ■ < M > 



not only satisfies at every internal point the equations (27) and 



