Electric Currents in Networks of Conductors. 253 



Theorem. — To compare the induction between one pair of 

 coils and any other two. 



Let a, /3, 7, 8 be four coils of wire. 



It is required to compare the mutual induction of a and y 

 with that of /3 and 8. 



Join up a and /3 coils in series with a galvanometer, and 

 join up y and 8 coils in multiple arc with a battery, as shown 

 in fig. 18. 



Place the coils in position. 



Let S and R be resistances of the primaries 7 and 8 ; let 

 be resistance of the two secondaries and of the galvanometer. 



Let L l3 L 2 , Ni, N 2 be the coefficients of self-induction of 

 the coils, and M x , M 2 the coefficients of mutual induction of 

 a and 7, and 8. Let V be the coefficient of self-induction 

 of the galvanometer. 



Call x the cycle current of y, y that of 8, and z that of the 

 circuit formed of a, /3, and the galvanometer. 



The kinetic energy T of the system is 



2T = x 2 N x + xzM x + z 2 (L x + L 2 + r) +f$ 2 + 2yzM 2 , 

 and the dissipation function F is 



2F = x 2 TL+y 2 S + z 2 Q. 



Then, by the formula 



E= f^ + JL^i 

 dtdx 2 dx y 



^N 2 + 0M 2 +yS=-E. 



iM 1 +^M 2 -i(L 1 + L 2 + r) + 2Q=0. 



Now x— y is the current through the battery; hence if we 

 put x+y for x in the above, we shall get x as the battery- 

 current. Hence, making the change, we have 



gave this method of obtaining the equation for the currents in a network 

 of conduction. In the last lecture of all he applied the method to cases in 

 which self and mutual induction was taken into account, and gave the two 

 illustrations in § 19. At the conclusion of this lecture he had ended his 

 professorial duties for the term, and a melancholy interest attaches to the 

 subject which occupied his mind on the last occasion on which, uncon- 

 sciously to himself or his pupils, he was to perform them. Those who 

 enjoyed even for a brief period the privilege of being taught by him, ever 

 cherish a vivid remembrance of the intellectual treat afforded by Professor 

 Maxwell's lecture-teaching, and the profound suggestiveness and interest 

 of it. 



The two examples in § 19 and § 20 are taken from my notes of Prof. 

 Maxwell's lectures, with some little alterations to make them clearer. 



Phil Mag. S. 5. Vol. 20. No. 124. Sept. 1885. T 



