Prof. Thomson on Transient Electric Currents. 395 

 current, and tliis is all that is required to be known for the pre- 

 sent investigation. Let then ^ Ay^ denote the actual energy of 



a current of strength, 7, in the linear conductor which serves for 

 discharger in the arrangement which forms the subject of the 

 present investigation, A being a constant which may be called 

 the electrodynamic capacity of the discharger. The work spent 

 in exciting electrical motion during the time dt will be 



Again, the work done in generating heat in the same time is, 

 according to Joule^s law, 



if k denote the " galvanic resistance ^' of the discharger, or the 

 mechanical equivalent of the heat generated in it, in the unit of 

 time by a current of unit strength*. Now the loss of potential 

 energy from the principal conductor, in the time dtj being 



— c?(^~-j, is entirely spent in producing these effects; and 

 therefore _,gf j^.g^^.)^^.,, . . . . (^. 



This equation and (1), with the conditions 



g = Q, and 7=0, when t=0 .... (3), 



are sufficient for the determination of q and 7 for any value of 

 /, that is, for the complete solution of the problem. 

 By (1) we have 



and (2) becomes 

 from which we find 





Substituting for 7 its value by (1), we obtain 



§4l^c^^=« • • • • (^)- 



The general solution of this equation is 



* See a paper entitled " AppHcation of the Principle of Mechanical 

 Effect to the Measurement of Electromotive Forces and Galvanic Resist- 

 ances," Phil. Mag. Dec. 1851. 



2 D 2 



