PEIRCE. — CHANGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 561 



In the case represented by Figure 21, vi = 80, r^ = 40, M = \/'2, 

 Li = 2. At the beginning Li = 2, but at the time OA this is su(hlenly 

 changed to 4. Before the change in Li the currents are given by the 

 equations 



C, = 4 - 2.4 e-io' - 1.6 e" 



C,= ^(e-'^'-e-^^'), (29) 



V2 



Just before the impulse, Ci = 2.465, and C^ = — 0.945 ; just after, the 

 current in the primary is about 0.822 and the secondary current has 

 the small positive value 0.217. The new currents satisfy the equations 



C"i = 4-2.634 e-20'/ 3-0.543 e-3% C"2= -0.932 6-2°'/ 3+ i,i 49^-30*^ (30) 



very nearly. C2 is plotted below TQ. 



Figure 22 shows the manner of growth of two neighboring currents, 

 when ?• = 30, r = 40, L = 2, L = 2, and when 31, which is at first 



Figure 20. OJR and MFQ represent the forms of the primary and second- 

 ary currents in a certain induction coil without iron when the primary circuit 

 is closed at the origin of time. If at the time OG, the self-inductances of 

 both circuits and the mutual inductance of the two are suddenly doubled, the 

 currents take the forms OJAZ and MFKY. 



V2, is suddenly changed to zero at the time A. When 31 is changed, 

 the current in the primary circuit suddenly falls from 2.465 to 1.797, 

 and the current in the secondary circuit, which has been negative, 

 rises from —0.945 to -fO.798. After the change, the currents are 

 given by the simple equations 



C'l = 4 - 2.203 e-^« C'2 = 0.798 e'^O'. (31) 



Figure 23 exhibits the effects of a sudden change in the value of the 

 mutual inductance between the two circuits already described under 

 Figures 21 and 22, from \/2 to 1.9, while the other inductances remain 

 unaltered. The primary current is shown by the curve OKRGS, and 



VOL. XLVI. — 36 



