Maintenance of Electric Currents by Mechanical Work. 477 



tity, being the coefficient of self-induction of the whole circuit, 

 ln—m-, and therefore LN — M, must be positive. When the com- 

 mutator is of the first kind, the ratio r is greater than unity, provided 

 pm is greater than qn ; and when 





* (12) 



and 



which is the maximum value of r. 



When the ratio of p to q lies between that of n to m and that of m 

 to I, r lies between +1 and — 1, and the current must decay; but 

 when pi is less than qm, a reciprocating current may be kept up, 

 and will increase most rapidly when 



When the commutator is of the second kind, the first step is to close 

 both circuits, so as to render the currents in them independent. 

 The second circuit is then broken, and the current in it is thus 

 stopped. This produces an effect on the first circuit by induction 

 determined by the equation 



L#+My=L#' + My. '. - (14) 



In this case M=— M , y=x, and y'=Q ; so that 



(L-M>=La/, (15) 



where x is the original, and x the new value of the current. 



The next step is to throw the circuits into one, M being now 

 positive. If x" be the current after this operation, 



(L + M)ar'=(L + 2M+N>". . . . (16) 



The] whole effect of this commutator is therefore to multiply the 

 current by the ratio 



L 2 -M 



L(L + 2M + N) 



The whole effect of the semirotation s to multiply the current by the 

 ratio 



L + 2M + N 



L-2M+N* 



The total effect of a semirevolution supposed instantaneous is to 

 multiply the current by the ratio 



= L 2 -M 2 

 r L(L-2M + N)* 



Up and q be the number of windings in the first and second coils 



