290 MEASUREMENT OF CURRENTS. 



The deflection 8 gives then the mean square of the intensity by the 

 same expressions as if it were the case of a uniform current. 



Such, for instance, would be the case of a sinusoidal current. 

 When a circuit contains a sinusoidal electromotive force of the form 



E = E sin27r-, 



the current is also sinusoidal, and of the same period T. The in- 

 tensity may be represented by the equation 



= A 



A 2 

 and the mean square of the intensity is equal to . It is useful 



to remember that the resistance, and the coefficient of the electro- 

 dynamometer, occur in the expression for the maximum amplitude 

 and of the phase of the current. 



903. If the coils are traversed separately by sinusoidal currents 

 of the same period, but different in intensity and in phase 



I = Asin27r-, 



I' = A sin27r ( --\j; \ , 



as in the case in which these coils are shunted in respect of each 

 other (548), we should have for the permanent deflection 



S'GAA' C 9 . t . ft \ 

 tan 8 = -- sin 27r - sin 27r ( --^ ) dt. 



c e J o \ T / 



The integration being made for any given time 0, which con- 

 tains a whole number of periods, we have 



(56) tan 8 = AA' ( - - sin 2 



C \2 



If we suppose that the coefficient of mutual induction may be 

 neglected, which is almost the case with the arrangement of the 



