Prof. Thomson on Transient Electric Currents. 403 



which agrees with conclusions arrived at by Helmholtz and 

 others. 



This result shows how, when a linear conductor, initially in a 

 state of electrical equilibrium, becomes subjected to a constant 

 electromotive force V between its extremities, a current com- 



. . V 



mences in it and rises gradually in strength towards the limit -r . 



This limit cannot be perfectly reached in any finite time, although 

 in reality only a very minute time elapses from the commence- 

 ment in ordinary cases, until the current acquires so nearly the 



full strength -j- that no further augmentation is perceptible*. 



The equations (6), expressing generally a continuous discharge, 

 assume the following forms when A is infinitely small. 



g=Q6 kC 



(17), 



which show how, when anything like electrical inertia is insen- 

 sible, the current commences instantly with its maximum strength, 

 and then gradually sinks as the charge gradually and perma- 

 nently leaves the principal conductor. 



One of the results of the preceding investigation shows a very 

 important application that may be made of Weber's experimental 

 determination of the "duration" of a transient current, to enable 

 us to determine the numerical relation between electro-statical 

 and electro-magnetic units. For if a denote the quantity of 

 electricity in electro- statical measure which passes in the unit of 

 time to constitute a current of unit strength in electro-magnetic 

 measure, the strength of a current expressed above by 7 will be 



-7, in terms of the electro-magnetic unit; and if K denote the 



(T 



resistance, in absolute electro-magnetic measure, of a linear con- 

 ductor of which the resistance measured as above in terms of the 

 electro-statical unit is k, we have 



<?)■=''•. 



which gives z._ ^ 



K — —5 



<.^ (18). 



* See a paper by Helmholtz in Poggendorff's Anndlen, 1852, which 

 contains valuable researches, both theoretical and experimental, on this 

 subject. , . . 



