554 PROCEEDINGS OF THE AMERICAN ACADEMY. 



LxU^r:^ + [(»' + n)U + (r + rn) Zi] 



dt 



dt 



4- (riro + rrx + rrs) Cg = r^E, 



and it is clear that if the inductances are suddenly changed, the prod- 

 ucts L\(Jx and LiCi are continuous, and if, in particular, only one of 

 the inductances is altered, the current in the parallel branch is itself 



• Figure 12. The lines OTW, OSM, show the forms of the currents in two 

 parallel inductive resistances which connect the terminals of a storage battery. 

 When at a given instant, the inductance of one of the parallel branches is 

 suddenly doubled, the current in it changes its value abruptly and takes the 

 course OTPVY, while the current in the other (OSED) suffers no sudden 

 change in strength. 



continuous. Figures 12 and 13 are drawn to scale for two typical 

 cases which indicate well enough what is usually to be expected. In 

 both diagrams L^ = 1, Zs = 1, r = 12, n = 20, r^ = 30, E = 120 (or 

 these quantities are to be in the proportions here given). The final 

 values of Ci and C^ are 3 amperes and 2 amperes. 



In the case which corresponds to Figure 12 the battery circuit is 

 closed at a given instant, and 0.02 seconds afterwards, when Ci has 



