USE OF SINUSOIDAL CURRENTS. 397 



The resultant current being of the form 



we deduce from it 



sn 27T-, 



27TAL / 



E l= ^ COS21T-, 



AT / 



The constant of integration is null in the last equation, for, from 

 symmetry, the charge of the condenser is null when the current 

 is at its maximum value. The two electromotive forces have the 

 same period, and a difference of phase equal to TT. They are 

 then represented by two sinusoids with the same nodes, and ordi- 

 nates of opposite signs, and their sum is null if the amplitudes 

 are equal in absolute values that is to say, if equation (53) is 

 satisfied. 



994. Let T denote the value of the period which corresponds 

 to this condition. For any greater or less value of T the apparent 

 resistance is greater than the true resistance, and the intensity of the 

 current is less. The velocity T is then that which corresponds to 

 the greatest intensity for a given circuit. 



This property may be utilised in measuring the resistance of 

 liquids. If x is the resistance of the liquid, R that of the principal 

 circuit, the maximum current would be observed ; replacing then 

 the liquid by a metal resistance r, the velocity is varied so as to 

 obtain the same current. We shall have then 



from which is deduced 



To get the maximum current it would be necessary to measure 

 the period T, and ascertain the coefficient L, or eliminate it by a 

 second experiment. 



