﻿288 Lord Rayleigh on the Minimum Current 



enormous, and was in fact about 12 megohms * as indicated 

 by a galvanometer. It was evident that the coil was acting 

 principally as a leyden rather than as a resistance, and that any 

 calculation founded upon results obtained with it would be 

 entirely fallacious. 



It is easy to form an estimate of the point at which the 

 complication due to capacity would begin to manifest itself. 

 Consider the case of a simple resistance R in parallel with a 

 leyden of capacity C, and let the currents in the two branches 

 be x and y respectively. If V be the difference of potential 

 at the common terminals, proportional to e ipt , we have 



x = Y/R, y = C dV/dt = ipYC ; 



so that 



x + y _ 1 + ipRO 



v ~ r • 



The amplitude of the total current is increased by the 

 leyden in the ratio >/ (1 +//R 2 C 2 ) : 1 ; and the action of the 

 leyden becomes important when pRC= 1. With a frequency 

 of 640,/> = 4020 ; so that, if R = 10 14 c.G.s., the critical value 

 of C is 4 -^ x 10 -1 ° c.G.s. , or about ^ of a microfarad. 



It will be seen that even if the capacity remained unaltered, 

 a reduction of resistance in the ratio say of 10 to 1 would 

 greatly diminish the complication due to condenser-like 

 action ; but perhaps the best evidence that the results obtained 

 are not prejudiced in this manne" is afforded by the experi- 

 ments in which the principal resistance was a column of 

 plumbago. 



The revolving magnet was of clock-spring, about 2^ centim. 

 long, and so bent as to be driven directly, windmill fashion, 

 from an organ bellows. It was mounted transversely upon a 

 portion of a sewing-needle, the terminals of which were carried 

 in slight indentations at the ends of a U-shaped piece of brass. 

 As fitted to the wind-trunk the axis of rotation was horizontal. 



The inductor-coil, with its plane horizontal, was situated 

 so that its centre was vertically below that of the magnet at 

 distance B. Thus, if A be the mean radius of the coil, n the 

 number of convolutions, the galvanometer-constant G of the 

 coil at the place occupied by the magnet is given by 



G = 2 -^, (1) 



* Doubtless the insulation between the wires should, have been much 

 higher. 



