of the Coefficients of Induction. 469 



columns of the annexed table. The first two columns give 

 the values obtained respectively for increasing and decreasing 

 positive currents ; the last two columns indicate those obtained 

 for increasing and decreasing negative currents. 



A. 



Values of L c , 





 2 

 4 

 6 

 8 

 10 



•0231 

 •0221 

 •0167 

 •0150 



•0231 -0231 



•0193 



•0134 -0194 -0147 



-0141 -0119 



•0105 



•0090 -0099 



The values obtained are slightly lower than those obtained 

 by the swing-method. This is accounted for by the fact that 

 the amplitude of the cycle is less. With the secohmmeter the 

 test-current was only "01 ampere, while it was *037 ampere 

 with the former method. The value of L c will be smaller, the 

 smaller the amplitude of the cycle. The secohmmeter is so 

 sensitive that it would have been easy by means of it to 

 measure L c for cycles of very small amplitude. 



Shape of Current Waves. 

 14. It is a matter of both theoretical and practical interest 

 to determine the way in which currents change when the , 

 impressed electromotive forces are given at every instant 

 of time and when the coefficients of self-induction are given 

 in terms of the currents which are flowing. In calculations 

 concerned with alternating-current problems it is usual to 

 assume that the impressed electromotive forces are pure sine 

 functions of the time, and that the coefficients of induction 

 are constant quantities. These assumptions are more con- 

 venient than true. The coefficient of self-induction can be 

 at once deduced from the curve of magnetization, and there- 

 fore can no more be expressed as a mathematical function of 

 the current than electromagnetism itself. It therefore appears 

 as if, in the treatment of such problems, graphical methods are 

 to be preferred to analytical ones. If, in a simple circuit, the 

 curve connecting the impressed electromotive force with time 

 be given, together with the curve connecting magnetization 

 with current, it is perfectly easy by purely graphical processes 

 to obtain the curve connecting current with time. For we 

 have 



E0 + f 



at 



E, 



Phil Mag. S. 5. Vol. 25. No. 157. June 1888. 2 I 



