INVESTIGATION OF CURRENTS IN THE VARIABLE STATE. 293 



If R is the resistance between the two points A and B, k the 

 constant of the instrument, and 8 the deflection observed, the mean 

 square I? n of the intensity is given by the expression 



The only condition to be fulfilled is that the coefficient of self- 

 induction of the interposed resistance R may be disregarded. 



The method employed in (869) for measuring the energy ex- 

 pended between the two points A and B also applies to alternating 

 currents. The difference of the deflections a and j3 gives 



906. INVESTIGATION OF CURRENTS IN THE VARIABLE STATE. 

 Ordinary galvanometrical methods enable us to measure variable 

 currents whose variations are slow in comparison .with the time 

 necessary for the damping of the needle, but they are not suf- 

 ciently so in the case of rapid variations like those which accompany 

 the effects of induction. The methods to which we should have 

 recourse depend greatly on the conditions of the experiment. We 

 shall restrict ourselves to a few general conditions and to some 

 examples. 



The most direct means of knowing the state of a circuit at a 

 given time /, is to put two points in connection with an electrometer 

 during a very short time 0, and then to insulate the electrometer. 

 The permanent deflection, or the initial swing, of the galvanometer 

 is proportional to the charge of the instrument that is to say, to 

 the difference of potential E between the points A and B, or to 

 the intensity I of the current at the time t. We may also substitute 

 for the electrometer a condenser of capacity C, the charge of which 

 is then measured by a galvanometer. 



The charge, however, which is acquired by the instrument in 

 the latter case is not, strictly speaking, independent of the duration 

 of the contact If the effects of self-induction can be neglected, the 

 difference of potential E of the armatures at the time is given (242) 

 by the formula 



E = E n I I - e Kcr I , 



J .AJ 



V- 



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