Coefficients of Self-induction and Mutual Induction. 227 



H =i (g +...), ..... (3) 



C being the capacity of the condenser whose charge is u. The 

 general equations of the system are of the form 



d t \dk ) d'x dx d'x ' 



To find the impulsive currents at the instant of making or 

 breaking circuit we may integrate (4) once for all. We thus 

 obtain 



w 



dk\ 



+ 1^-^=0. 



The first term of this equation involves the initial and final 

 currents of the system, w r hich may in most cases be written 

 down at once : the second term 



= a n x + a 12 y + . . . , 



where x, y . . . are the total flows of the currents round the 

 several meshes. In any particular case, therefore, we may 

 easily write down this equation if we know the expressions 

 for t, F. 



The equation of the type 



d_/d%\ dF , ^5 = q 



dt \du) du du 

 must be treated differently. Suppose, for example, that we 

 are considering the effect of making the battery-current. 

 When the currents are steady and the condensers have re- 

 ceived their full charge, 



dt ' du > 

 and the equation becomes 



dii du ' 



the symbols x, y, u . . . denoting the final values of these 

 magnitudes, and u being put =0. 



§ 3. To Balance tlie Current of Self-induction by a Condenser* . 



Method I. — Suppose the resistances in AB, BC, CD, DA, 

 AP be a, 6, d, c, R ; that in the battery B ; L the coefficient 



* Since this paper was placed in the printers' hands I have seen Mr. 

 Rimington's paper in the July number of the Philosophical Magazine, 

 from which it appears that he has anticipated me in some of the results 

 of this article. 



Q2 



