480 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



the mean value of the square of such a quantity is one-half the 

 square of its amplitude, and the mean of the product of two such 

 quantities of the same period and a difference of phase equal to a 

 right angle is zero. 



The quadratic mean, or square root of the mean square of a 

 variable current or electromotive-force is called the effective or 

 virtual current or electromotive-force. Its value in the case of 

 a harmonically -vary ing quantity is accordingly the amplitude 

 divided by V2- 



The activity, or power absorbed by the circuit, is 



E 2 



El -~ cos cot cos (cot a), 

 J 



and its mean value, by the above formulae, 



To the solution (5) is to be added, in order to obtain the 

 general solution of ( I ), the solution of the equation with the right 

 hand member equal to zero, obtained in the preceding section, but 

 as the current thereby represented rapidly dies away, the resulting 

 state of the alternating current is that which we have found. 



A number of circuits in parallel, to which a single harmonic 

 electromotive-force is applied, receive virtual currents inversely 

 proportional to their respective impedances if the frequency 

 is great enough the distribution is almost independent of the 

 resistances of the branches, the impedance being sensibly equal to 

 the reactance. 



(2) Two CIRCUITS. Suppose fchat we have two circuits, one 

 of which, the primary, contains a harmonic electromotive-force, 

 while the secondary contains no impressed electromotive-force, 

 except that due to induction. The equations then are 



