556 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



and C2 instantly acquire equal and opposite values, and the subsequent 

 course of Ci is given by the equation 



Vi — 1^ ; e ^\-r^i , 



(23) 



See in Figure 13 the line GRXZ. 



If the terminals of an open battery circuit of inductance L and of 



resistance r be connected by a number of inductive conductors in par- 

 allel, of resistances ri, r^, 

 Tz, Ti, etc., and of induc- 

 tances Zi, L2, Ls, Li, etc., 

 and if sudden changes be 

 made in the inductances, 

 the quantities 



LO+UCs, 



H 



H 





® 



t%-f 



etc., will be continuous. 

 If L is negligible, and if 

 only some of the other 

 Figure 14. inductances be impul- 



sively changed, the cur- 

 rents in the other branches will be continuous. 



If, in the arrangement shown in Figure 14, the masses P, Q, R are 

 numerically equal to Xi, L, L^, respectively, if the velocities of P and 

 R in the direction of the bottom of the page are Ci, C2, and if the 

 dimensions of the vanes attached to the masses are such that the air 

 offers resistance of ri, r, 7\ times the velocities to the motion of P, Q, 

 and R, the equations of motion of the masses are identical with the 

 current equations for the electrical circuit shown in the figure. 



The currents in two neighboring circuits (Figure 9c) of self-induc- 

 tances Xi, Z2, and mutual inductance M, which contain the electro- 

 motive forces El, E^, are given by the familiar equations 



^'-^■f-^^^f-'-'^- = «' 



^'-^^f-^^f-''^» = «' 



(24) 



