dt 



dNdC 

 dG dt' 



tent of self-indue 



E 

 ,_ R' 



T- L 



dC_ 



dt ~ 



c -c 



T ' 



470 Mr. W. E. Sumpner on the Variation 



where E is the impressed electromotive force, N is the number 

 of lines of force enclosed by the circuit, E is the resistance of 

 the circuit, C the current flowing, and t the time at which 

 the different quantities are evaluated. 



Now, if we can neglect Foucault currents, or possible mag- 

 netic lag, or anything analogous which would make N directly 

 dependent on time, we may put 



, dN . 

 where -^- is 

 dG 



we obtain 



Now C is the value of the current which would be flowing if 

 there were no self-induction ; and since E and R are given, 

 it is possible to plot a curve having C for ordinates and time 

 for abscissae. Moreover, since the curve connecting N with C 

 is given, it is possible by graphical processes to find another 



connecting ^ -^ or T with C. This curve (see Plate III. 



fig. 3) should be plotted, with the values of C for ordinates 

 and the values of T as abscissas. It will be found convenient 

 to plot T in the negative direction. The time-ratio T will 

 be in seconds if L is in secohms and R in ohms. The two 

 curves should of course be plotted to the same scale for 

 current and time. 



The construction follows immediately from the equation 



^C_ C -C 

 dt ~ T ; 

 and is as follows: — 



Suppose P x (see PI. III. fig. 3.) be the given initial point on 

 the curve connecting C with time. Project it parallel to the 

 axes to T x on the curve T and to Q x on the curve C . Project 

 Q x parallel to the axis of abscissas to R^ on the current axis. 

 Draw from P t a line parallel to R^, and choose a point P 2 

 on it not far from P x . P 2 may be regarded as the next point 

 on the current curve, and the process (which is indicated in 

 Plate III.) may be repeated to obtain a third point P 3 , and so 

 on, until the whole curve connecting current with time is 

 obtained. 



