and Conductance Operators, 493 



flux, in the wire ; so that the current is Ke, if K be the con- 

 ductance of unit length. 



These examples are mostly selected from a paper I am 

 now writing on the subject of electromagnetic waves, which 

 I hope to be permitted to publish in this Journal. 



If the electric and magnetic energies, and the dissipation of 

 energy, in a given system be bounded in their distribution, it 

 is clear that the resistance-operator is a rational function of p. 

 But should the field be boundless, as when conductors are 

 contained in an infinitely extended dielectric, then just as 

 complete solutions in infinite series of normal solutions may 

 become definite integrals by the infinite extension, so may the 

 resistance-operator become irrational. We may also have to 

 modify the meaning of the sinusoidal H' from representing 

 mean resistance only, on account of the never-ceasing outward 

 transfer of energy so long as the impressed force continues. 



9. Returning to a finite combination represented by V = ZC, 

 there are at least three kinds of induction-balances possible. 

 First, true balances of similar systems, where we balance one 

 combination against another which either copies it identically 

 or upon a reduced scale, without any reference to the manner 

 of variation of the impressed force. Along with these we may 

 naturally include all cases in which the Z of a combination, in 

 virtue of peculiar internal relations, reduces to a simpler form 

 representing another combination, equivalent so far as V and 

 C are concerned. The telephone may be employed with great 

 advantage, and is, in fact, the only proper thing to use, espe- 

 cially for the observation of phenomena. 



There are, next, the sinusoidal current-balances. These are 

 also true, in being independent of the time, so that the telephone 

 may be used ; but are of course of a very special character 

 otherwise. Here any combination is made equivalent to a 

 mere coil if L' be positive, or to a condenser if S' be positive 

 [§§3 and 4], and so may be balanced by one or the other. 

 But intermittences of current cannot be safely taken to 

 represent sinusoidality, and large errors may result from an 

 assumed equivalence. 



In the third kind of balances it is the impulsive inductance 

 that is balanced against some other impulsive inductance, 

 positive or negative as the case may be ; or perhaps the 

 impulsive inductance of a combination is made to vanish, by 

 equating the electric and magnetic energies in it when its 

 state is steady. The rule that the impulsive balance in a 

 Christie arrangement without mutual induction between the 

 four sides is given by equating to zero the coefficient of p in 

 the expansion of Z 1 Z 4 —Z 2 Z 3 in powers of p, where Z 1 &c. are 



