PEIRCE. — CIL\.NGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 



543 



and to represent the value (X) of the inductance at any time < ^ < 7', 

 by the expression 



(1) 



Xo + (^-Xo)/(|), 



where/(0) = 0,/(l) = 1, and for < ^' < 1,/ (x) > 0. 



The line OK in the i? 7' plane (Figure 1) has the equation t — T, and 

 after the value (7 = OF) has 

 been fixed for T, the course of 

 the current during the change 

 of inductance may be shown by 

 a GnTve(HQS) in a plane (FRS), 

 the equation of which is T= T'. 

 FH, which measures the ordi- 

 nates of the line AG in the CT 

 plane represents the initial cur- 

 rent (Co) at the time ^ = 0, and 

 the ordinates of the curve MB 

 in the plane COK represent for 

 different values of J' the inten- 

 sities of the current at the end 

 of the change in inductance, 

 when the form of the function 

 /is the same. The vertical dis- 

 tance AB shows the magnitude 

 of the sudden change in the 



current strength when the change in L is supposed to be instantaneous 

 and is the same whatever form/' has. 



During the interval < # < 7", the current is to be found, of course, 

 by solving the equation 



Figure 1. 



E- 



dt 



rC, 



— where L has the variable value given above — and making the con- 

 stant of integration such that C =■ Co when ^ = 0, After the epoch 

 t = T, the intensity of the current satisfies the equation 



E- 





(3) 



in which the coefficients are constants, 

 in the form 



Equation (2) may be written 



