PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 337 



This means that if there are any terms contingent upon heating or 

 other effects which involve an integral of a function of the current 

 with respect to the time, this integral attains its final value in a time 

 within the limit of error of measuring the oscillograms, which is about 

 1/6000 second. This time corresponds to 3.5°, and is about 1 mm. on 

 the original photographs. 



It might seem that the approximation made as to the analytical 

 expression for the steady current- voltage curve would not warrant the 

 accuracy here claimed ; but if we draw the straight line through the 

 points for which the current is 1 and 6 milliamperes, this line will 

 depart from the observed values only for values of i below 1 milliampere, 

 where the departure will have the following values : 



In the negative loop of the rectified cycle the departure of the approxi- 

 mation from the observed current- voltage curve is still smaller. How- 

 ever, apart from the specific assumption as to the analytical function 

 representing the current-voltage characteristic of the rectifier under 

 the action of a steady current, the theoretical discussion given above 

 permits a ready qualitative understanding of the lead that occurs in cer- 

 tain parts of the rectified cycle, which may be summarized as follows : 



(1) The case of the advance of the rectified cycle on rising from the 

 axis of no current is seen to be due largely to the fact that after a dor- 

 mant half period the current in the circuit follows the ordinary expo- 

 nential "building-up " curve for a time before coming into coincidence 

 with the sine curve. This building-up curve starts from the axis with 

 zero lag, and is, therefore, in advance of the sine curve. To this effect is 

 to be added the effect due to an apparently higher resistance of the rec- 

 tifier for small currents than for large currents. This apparently higher 

 resistance brings the building-up curve a little nearer to the sine curve. 



(2) The slightly quicker descent of the rectified cycle on approach- 

 ing the axis after having traversed the upper half of the curve is also 

 due to this apparently higher resistance of the rectifier when traversed 

 by smaller currents. 



VOL. XLIV 



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