MAINTENANCE OF ELECTRIC CURRENTS BY MECHANICAL, WORK. 83 



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 



I .,\ 



}-\ 



V In] ' 

 and ^-(l.-S' 1 (13). 



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 



Lx + My = Lx' + My' .............................. (14). 



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



(L-M]x = Lx ................................. (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, 



" ....................... (16). 



The whole effect of this commutator is therefore to multiply the current by 

 the ratio 



The whole effect of the semirotation is to multiply the current by the ratio 



L + ZM+N 

 L-2M+N' 



The total effect of a semi re volution supposed instantaneous is to multiply the 

 current by the ratio 



D-M* 

 ~L(L-2M+N)' 



