THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE, - 



[FOURTH SERIES.] 



JUNE 1853. 



LXV. On Transient Electric Currents. 

 By Prof. William Thomson*. 



THE object of this communication is to determine the motion 

 of electricity at any instant after an electrified conductor, 

 of given capacity, charged initially with a given quantity of elec- 

 tricity, is put in connexion with the earth by means of a wire or 

 other linear conductor of given form and resisting power. This 

 linear conductor, which, to distinguish it from the other or prin- 

 cipal conductor, will be called the discharger, is supposed to be 

 of such small electrical capacity that the whole quantity of free 

 electricity in it at any instant during the discharge is excessively 

 small compared with the original charge of the principal con- 

 ductor. Now any difference that can exist in the strength of 

 the current at any instant in different parts of the discharger 

 must produce accumulations of free electricity in the discharger 

 itself, and therefore must be very small compared with the actual 

 strength of the current depending on the discharge of the prin- 

 cipal conductor. The strength of the current throughout the 

 discharger will therefore be considered as the same at each 

 instant, and, being measured by the quantity of electricity dis- 

 charged per second, will be denoted by 7. Again, the conduct- 

 ing property and extent of surface of the principal conductor, 

 and the resistance of the discharger, will be considered as so 

 related that the potential throughout the principal conductor is 

 uniform at each instant. Hence if q denote the quantity of 

 electricity which the principal conductor possesses at any time t, 



* Communicated by the Author, having been read at a meeting of the 

 Glasgow Philosophical Society on the 19th of January, 1853. 



Phil Mag. S. 4. Vol. 5. No. 34. June 1853. 2 D 



