PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 803 



Whence equation (3) becomes 



<ii 



= {E-RY)C+ Cydt. (6) 



Jo 



With n charges of the condenser per second, we have for the galva- 

 nometer current-reading Ii in the charge circuit Ii = nqi ; whence 



/i = nC{E - BY) + n Cydt. (7) 



In this equation R is the resistance of the charge circuit from the 

 source of e. m. f. up to the point at which the charge is deposited on 

 the condenser. This includes the resistance of the galvanometer, the 

 resistance of the contacts of the electrodes with the conducting laminae, 

 and the resistance of these laminae up to the point of leak. 



Equation (7) is an exact expression for the current-reading of the 

 galvanometer in the charge circuit when the commutator is driven so 

 as not to exceed the speed at which the charge of the condenser at each 

 impulse is complete. 



Equation (7), therefore, holds for 



in which T is the time during which the condenser is in charge relation 

 to the circuit during one cycle of the commutator, and r is the interval 

 required for practically complete charging of the condenser. Let us 

 now break up the last term of equation (7) into two integrals, one from 

 zero to T and the other from t to T. During the first of these intervals 

 the leak current y =. y-^ (say) is variable, and during the second interval 

 the leak current y ^ Y (say) is constant. Then we have 



/i = nC{E - nY)-\-n {\j^dt + n j Ydt, 



in which yi is the variable leak current during the short interval for the 

 potential of the condenser to attain substantially its final value, and Y 

 is the steady current through the crystal and the leads under the steady 

 e. m. f £J during the remainder of its connection with the charge circuit. 

 The steady-leak term may be integrated, and we have after integration 



