PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 335 



for values of current between 1 and 6 milliamperes, when the current 

 is from copper to molybdenite, e r is approximately a linear function of 

 the current, with the equation 



(5) e r = q + ri, in which q = .60 volts, r = 183 ohms. 

 With this approximation equation (4) becomes 

 (6) 



i?sin wt — q = (r + R c ) U + L -jr. 



Integration of this equation gives 



(7) 



E . ( _, L(u 



i 2 = — -= ^ , ., „ sin I wt — tan 



dt 



) 



+ ce 



-{ Rc+r)t 

 L — 



TABLE VI. 

 Computed Values of the Rectified Cycle. Upper Loop 



lie + r 



in which c is a constant of integration. If we substitute known values 

 in this equation, namely, 



(8) r + i2 c = 183 + 436 = 619 J 2ao = 584, #=5.0, ? = 60, 

 we have 



(9) i 2 = 5.87 X 10~ 3 sin (orf - 43.3°) + or™** - .97 X 10" 8 . 



For the determination of the constant c, we have the relation i 2 = 0, 

 when Esin wt = q. This gives c = 5.1. 



From equation (9) values for the current in the upper loop of the 

 rectified cycle for various values of wt were computed and are given 

 in Table VI. 



The lower loop of the rectified cycle was obtained in a similar manner. 



