Resistance of Compound Conductors. 487 



one of them (N) can be neglected. The formulae for the re- 

 sistance and self-induction of the combination then reduce to 



R+S[ E(R+S) 2 +/L 2 J' * ' W 

 S 2 L 

 n -(R+8) 2 +p 2 IP W 



in which SR/(R+S) represents the resistance to steady cur- 

 rents (j? = 0). The peculiar features of the arrangement are 

 brought out most strongly by taking a case in which S (the 

 resistance of the induction-less component) is great compared 

 with E. It is then obvious that steady, or slowly alternating, 

 currents flow mainly through R, and accordingly that the re- 

 sistance and self-induction of the combination approximate to 

 R and L respectively. Rapidly alternating currents, on the 

 other hand, flow mainly through S, so that the resistance 

 of the combination approximates to S, and the self-induction 

 to zero. These common-sense conclusions are of course 

 embodied in the formulae. 



The conductors combined in parallel were (1) the coil of 

 stout copper (p. 483) with its two wires permanently con- 

 nected in parallel so as to give maximum self-induction (L), 

 and (2) a moderate length of somewhat fine brass wire. 

 With steady currents the resistances were 



R=-45, S = 229, Ro^-35. 



It had been expected that the resistances R, S, of the sepa- 

 rate conductors would have been sensibly the same whether 

 tested by steady or by periodic currents ; but the resistances 

 in the latter case tended always to appear higher. Thus with 

 the same reed as interrupter, 



R=-52, S=2-33, L=43°*7, N='3°; 



and for the combination, 



R' = 2-04, I/ = 3°'0. 



These results of observation illustrate satisfactorily the general 

 behaviour of the combination to periodic currents of high 

 frequency, and they agree fairly well with the formulae. 

 According to these, if we take the values of R and S as ob- 

 served with periodic currents, we have 



R' = 2*16, L' = 2°-61. 



The altered distribution of current under the influence of 

 in iuction, and consequent increase of resistance, exemplified 



2L2 



