804 PROCEEDINGS OF THE AMERICAN ACADEMY. 



7i = nC{E - RY) + n Y{T - t) + nj\j^dt. (8) 



Now it should be noted that the quantity nTh independent of the 

 speed, since the geometrical dimensions of the commutator, which is of 

 the rotating type, are fixed. The value oinT'i^ l/^j>, — this quantity 

 1/p being the part of the whole circumference of the commutator occu- 

 pied by the charge segment. Replacing nThj its value 1/p, we have 



I, = — + n\CE-IlYC-Yr+f\j,dt}. , (9) 



P Jo 



In equation (9) r is arbitrarily defined as the time for a practically 



complete charge. Let us be a little more specific and suppose that t 



is of such value that when substituted for t in the exponential expres- 

 t 



sion e "^ it reduces this exponential to .006. This would make the 



charge complete so far as measurements of the accuracy of the present 



experiment would show. If 



T 



g-Rc= 006, 

 T = 5BC (by tables of exponentials). (10) 



With this definition of t equation (9) becomes 



I^ = — -\-n\CE-^BYC+ / y^dt\. (11) 



P I/O 



This is the equation of current-reading of the galvanometer in the 

 leads to the crystal during charge. 



Let us next examine briefly the theoretical problem of the discharge 

 of the crystal condenser. 



A mathematical treatment similar to that of the charge shows that 

 the current-reading of the galvanometer in the discharge circuit, if 

 there are n discharges per second, is 



J'^bRC 

 y^dt, (12) 







in which y^ is the leak current during discharge and Eq is the poten- 

 tial of the condenser at the beginning of the discharge. The potential 



