501 Transactions — Miscellaneous. 



The resistance E' for high frequencies = v/^//. £>/R. 



R' oc 



rVL, I 



d VG VOL i- 



oc — =, where I is constant. 

 Vrcd 



The resistance of iron wires in these fields varies inversely 

 as the root of the radius, inversely as the root of the capacity, 

 and inversely as the root of the spark-length, and is inde- 

 pendent of the inductance of the circuit. 



The increase of resistance of iron wires for rapidly-alter- 

 nating currents has been ascribed to the concentration of the 

 current on the surface of the conductor. There is also, of 

 course, loss of energy by hysteresis on account of the mag- 

 netization and demagnetization of the iron wire. Although 

 much more energy is absorbed in steel than in soft iron, due 

 to hysteresis, the steel wire did not show any greater increase 

 of resistance than the soft-iron wire. It seems, therefore, that 

 the effect of hysteresis may be neglected as a factor in deter- 

 mining the increase of resistance of wires. 



It is possible that the absorption of energy due to hysteresis 

 may be much greater for a frequency of several millions than 

 for frequencies of 1,000; but it is a very difficult matter to 

 separate the effects of induced currents from those of hysteresis 

 in causing absorption of energy in an iron cylinder. 



VII. On the Division of Rapidly- alternating Currents 

 in Multiple Circuits, and the Effect of Metal 

 Cores on the Distribution of the Current. 



Plate XLIX., Fig. 15. 



Consider the distribution of an alternating current between 

 two conductors A C B, A D B, in parallel. 



Let R and L be resistance and self-inductance respectively 

 in branch A C B. 



Let S and N be resistance and self-inductance respectively 

 in branch A D B. 



If y be current in branch A C B, and x — y be current in 

 branch A D B, then it is shown (" Recent Researches," p. 513) 

 that for rapid alternations the distribution is such that 



y=\ S2 + N2P2 '"cos. (pt + e), 



