Electricity and Magnetism. 431 



and therefore, if v = v at time t Q , 



l_ 

 P 



lm(r^V)=h 2 (41og^+l) 5? . . . (9) 



where 5 is the distance traversed by the slider in time t— t Q . 

 But we have also 



and therefore 



and 



*=£( 4i °4 +l ) ; (10) 



-<-o=£(41og^+l)(*-<„); .... (11) 



s= Vi{ t-t )+tJ±\o g l +i)(t-t y. (12) 



£m 



Hence we can write (9) in the form 

 I 



(« 2 -% 2 )-i7 2 ^og- +l^-i )| %+ X(41og- + l)(«-* )}.(13) 

 L-L =(41og-+l) 5 . . . . (14) 



We have also T T / . i 1 



P 



The rails and slider illustration though apparently very 

 simple is not really so, and is inferior to the arrangement, 

 sometimes substituted, of a metal disk rotating across the 

 lines of force of an impressed magnetic field, and touched at 

 its centre and circumference, or at the circumference and 

 at some concentric circle nearer the centre, by the terminals 

 of the external part of the circuit. If the field be main- 

 tained constant and the disk rotate at a uniform rate, and 

 there be no variation of contacts of the wire with the disk, 

 a constant current will be maintained. This of course is the 

 arrangement of a disk magneto-machine, and of the Lorenz 

 apparatus for the determination of the ohm, except that in 

 the latter case the electromotive force in the disk circuit is 

 balanced. 



In this arrangement there is no change of self-induction, 

 inasmuch as the configuration remains unchanged as the 

 rotation proceeds. For total magnetic induction, I, through 

 the area of the disk between the circles of contact, and angular 

 speed co, the electromotive force is Ico/27r. If the field be of 

 uniform intensity H, and a, a' be the radii of the circles of 

 contact, the value of I is 77- (a 2 — a /2 )H and the electromotive* 



2G2 



