464 Mr. W. E. Sumpner on the Variation 



for steady currents. If the discharge Q produces a throw 0, 



Q = kd, 

 where k depends, among other things, on the time -constant of 

 discharge, and therefore varies with the self-induction and 

 with the resistance in the battery branch. AVe may, however, 

 regard k as being approximately constant, and we may 



accordingly take the values of 



to represent the 



(Ji— C 2 



values of the coefficient for the current ^(Cx + Co). In a 

 series of experiments the currents were changed by successive 

 steps from a small value to about 13 amperes, and decreased 

 through the same stages in inverse order. The cycle was 

 repeated many times, both for positive and for negative 

 currents ; and the numbers given in the following table are a 

 fair sample of the results obtained. L; and La are the values 

 of 0/(C l — G 2 ) for increasing and decreasing currents respec- 

 tively. A is the value in amperes of 2(^1 + ^2)' 



A. 



Iv 



I* 



0-21 



98 



137 



069 



115 



143 



113 



118 



133 



1-65 



126 



131 



227 



126 



128 



2-75 



131 



132 



304 



132 



137 



339 



113 



111 



3-91 



113 



111 



4-60 



104 



100 



5-60 



106 



101 



7-15 



78 



72 



9-70 



61 



51-5 



The numbers obtained, although not altogether satisfactory, 

 leave no doubt about the way in which the coefficients change. 

 For increasing currents L; at first increases and then dinii- 



Lrf begins at a lower 

 of Lj and continually 

 This is exactly what is 

 that the value of L is 



nishes, while for decreasing currents 



value than the corresponding value 



increases as the current is decreased. 



to be expected when it is remembered 



represented by the slope of the curve of magnetization If 



the curve connecting 53 with $ be like that indicated in fig. 1, 



the curve connecting dSb/d$ or L with $ will be such that. 



for increasing values of «£) the ordinates L will at first increase 



and then diminish, while for decreasing values of *V> the 



ordinates will continually increase. It is noteworthy that u 



discontinuity will occur at the cusp K, and the value of L 



