PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 333 



(3) F(fi 2 rdt, Cidt). 



The terms (1), (2), and (3), when put into the differential equation for 

 the current through the circuit and integrated (if possible), would give 

 in the result a shift of phase of the current with respect to the voltage- 

 phase cycle. 



Let us, therefore, attempt to determine whether there are any phase 

 differences between the rectified cycle and the voltage-phase cycle that 

 are not accounted for by the conditions existing in the oscillographic 

 apparatus. In doing this we shall make use of the current-voltage 

 characteristic of the molybdenite rectifier, as obtained with the current 

 and voltage in the steady state and recorded in Table III and Figure 

 5. This table of data was obtained with the same molybdenite recti- 

 fier in practically the same adjustment as in the oscillograms Nos. 1 

 and 2 of the Plate. 



Let us derive, first, the numerical equation for the " voltage-phase " 

 curve. In ,the case of oscillogram No. 1, an ohmic resistance of 400 

 ohms was in series with the deflecting coils, which had a resistance of 

 436 ohms, making a total resistance of 836 ohms. Let the inductance 

 of the coils be L. The value of L can be calculated from the voltage 

 and current of the cycle. The R. M. S. voltage impressed on the cir- 

 cuit was 3.54 volts ; the maximum voltage was therefore 5.00 volts. 

 The maximum current, taken from oscillogram No. 1, was 4.9 x 10 -8 

 amperes, whence we have 



4.9 X 10- 3 = 



a/836 2 + XV 

 Therefore 



(1) Zo> = 584, 



(2) tan" 1 -^ = ^ = 35°, 



and the equation for the current i t of the voltage-phase cycle becomes 



(3) h = t 5 '° sin (wt - 35°). 



V836 2 + 584 2 



