526 PARTICULAR CASES OF INDUCTION. 



of an electrometer, which determines the difference of potential. 

 Experiment has shown that the phenomena are in complete agree- 

 ment with this theory. 



If we detach the condenser at the ends of the wire, the 

 electricity set in motion by the electromotive force of induction 

 charges the wire throughout its entire extent, especially near the 

 ends, and the intensity of the current is not at each moment the 

 same throughout the entire length of the wire. It may also happen 

 that the electricity thus accumulated on the surface of the wire 

 escapes across the surrounding medium by a series of branch 

 circuits. These two circumstances complicate the problem, and 

 the preceding equations no longer present an exact solution, but 

 the difference of potentials at the end of the wire is in most cases 

 still represented by a periodical oscillation of decreasing amplitude. 



547. LAWS OF BRANCH CURRENTS IN THE VARIABLE STATE. 

 The law which in a closed polygon connects the strengths of the 

 currents with the electromotive forces (211), also applies in the 

 variable state, provided that to the ordinary electromotive forces 

 we add those arising from the effects of induction. 



We shall first examine the case in which the current bifurcates 

 between two points A and B, along conductors r and /, which 

 contain no electromotive forces. To define our ideas, we shall 

 assume that these conductors are wound as coils, and we shall 

 call L, L', and M their coefficients of induction. If, at a given 

 time, we denote by i and /' the strengths of the currents in the 

 two branches, we have 



(L-M)*WY' + -(L'-M)*'. 

 dt dt 



Let us first consider the case in which the second wire is 

 uncoiled ; the coefficient L' is very small, as is also the coefficient 

 of mutual induction M (540). Equation (44) reduces to 



(47) -r7' + Ly = 0. 



at 



As long as the general current is increasing, we see that the 

 strength { in the rectilinear branch is greater than it would be 

 in the permanent state. The branch which contains a coil has 

 therefore an apparent resistance which is greater than its real 

 resistance. The difference is greater the greater is the coefficient 



