PEIRCE. — CHANGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 549 



inductance without an increase of the resistance usually involves a 

 change of the conformation of the circuit, and this generally retiuires 

 a considerable fraction of a second, at least, to bring about, so that the 

 formula (9) cannot be used to determine the current strength at the 

 end of the inductance change. To illustrate this fact we may assume 

 that the change from Xq to Ly, in the time T is brought about at a 



Figure 7. ODE shows the current in a simple circuit of fixed inductance, 

 4L. If at the time OW, when the current has attained half its final intensity, 

 the inductance is suddenly reduced to L, the course of the current will be 

 ODBST. 



constant rate so that L = Lq + t (Li — Lo)/T, and the strength of 

 the current at the time t is given by the equation 



where 



c'=g^)".(e. 



+ 



ET 



m — 



m{Li — Lo) 

 U ~ L, • 



L'^-L 





(15) 

 (16) 



If, now, C = E/r amperes, Lq = 2 henries, Li = A henries, then, ac- 

 cording as 7' is one second, half a second, one tenth of a second, or one 

 hundredth of a second, the value (C'l) of the current at the end of the 



interval T is G.980-C;, 0.962 -Cn, 0.836 • C'„, or 0.569 



Cq, whereas C\ 



