212 



Mr M'Connel, On the effects of 



[Nov. 24, 



He neglects the self-induction of all the resistances. Now one of 

 these resistances is the galvanometer, and the coefficient of self- 

 induction of a galvanometer of 11,000 ohms resistance is by no 

 means small. My first impression was that the total quantity of 

 electricity, that passed through the galvanometer in the transient 

 current which charges the condenser, would be considerably 

 diminished by the self-induction. Although this proved to be not 

 the case, the results I obtained seemed to me to be of sufficient 

 interest to be worthy of your notice. 



To prevent the physical peculiarities of the motion from being 

 obscured by the length of the algebra, let us first consider a simple 

 case which has very similar characteristics. 



A charged condenser is permitted to discharge itself through 

 two resistances placed in parallel arc, only one of which has 

 appreciable self-induction. 



Let g be the resistance which has self-induction L, 



R the other resistance, 



x the current through g, 



y the current from the condenser of capacity C. 



E the potential to which the condenser is initially charged. 



or 



We have the equations 



Lx + gx — R (y — x) = 0] 

 {y-x)R = E-!L\ 



Lx + (g + R)x-Ry = 0) 

 Rx-Ry-?t + E=0t 



(1), 



(2). 



At first sight I thought that since the self-induction delayed 

 the current through the branch g, the greater part of the discharge 

 would pass through the branch R and thus the whole current 

 through g would be diminished. 



But the investigation below shews that though the self-induc- 

 tion prevents the current from attaining its full magnitude at 



