PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 805 



of the condenser at the beginning of the discharge is less than E the 

 applied e. m. f. for two reasons ; first, because on account of the leak, 

 the crystal was not charged to the applied e. m. f. ; and second, because 

 there has been a small loss of charge during the insulation time while 

 the commutator was changing from charge to discharge. 



As may be seen by reference to equation (5) the deficiency of poten- 

 tial due to the first of these causes is R Y. The fall of potential due 



1 C^^ 

 to the second of these causes is -^^ I y^dt, in which yz is the leak 



current during insulation, and T^ is the length of time of the insulation 

 period during each cycle. Therefore the current reading of the galva- 

 nometer in the discharge circuit is 



l2 = n\CE-RYC- / \j,dt - / y^dtl (13) 



Jo Jo 



This is the exact equation on discharge. 



As an approximation let us suppose that the leak current during 

 insulation was constant and equal to its value at the end of the pre- 

 ceding charge. This is approximately true, because the insulation 

 time was short. With the approximation we have 



S\dt = nYT^ (14) 



Jo 



Y . . 1 . 



= — , in which — is the part of the com- 

 m m 



mutator circumference occupied by the insulation segment. With this 



approximation equation (13) becomes 



/2 = - ^ + w {CE -EYC- j yodt} , (approx.) (15) 



in which the first term Y/m is a little too large. 



Examination of the Data of Experiment I. 



In order to compare the data of Experiment I. with the theoretical 

 equations for charge and discharge current derived above, let us write 

 the charge equation (11) in the form 



J, = ^-{-nEC\, (16) 



n 



