Self-induction of Wires. 20 i 



whereas Lord Rayleigh's high-speed formulae, which are 



n / 2 = L' 2 n=B J2 (izf 

 make 



B's = 2-234 R 2 , I/ 2 =i/i x -447. 



This particular speed makes the amplitude of the magnetic 

 force in the core case, and of the electric current in the other 

 case, fourteen times as great at the boundary as at the axis of 

 the wire or core (see Part I.). As, however, we do not ordi- 

 narily have very thick wires for use with the current longi- 

 tudinal, the high-speed formulae are not so generally applicable 

 as in the case of cores, which may be as thick as we please, 

 whilst by also increasing the number of windings the core heat- 

 ing per unit coil-current amplitude may be greatly increased. 

 If the core is hollow, of inner radius C , else the same, the 

 equation of the coil-current is, if e be the impressed force 

 and C the current in the coil-circuit whose complete steady 

 resistance and inductance are R and L, whilst L : is the part 

 of L due to the core and contained hollow (dielectric current 

 in it ignored), 



«=BC+(L-LJO+^ • T'ii'ffii LA • ( 53 <) 



v sc o (sc)—qrL (sv) ' 



when q depends upon the inner radius, being given by 



isc J {sc )— Ji(Mq) _ _ /££ x 



i sc o K o( sc o)-K!(sc ) 



(whose value is zero when the core is solid), and 



s 2 =-4:7rfjLk{d/dt). 



There may be a tubular space between the core and coil, and 

 R, L include the whole circuit. In reference to this (53c) 

 equation, however, it is to be remarked that there is consider- 

 able labour involved in working it out to obtain what may be 

 termed practical formulae, admitting of immediate numerical 

 calculations. The same applies to a considerable number of 

 unpublished investigations concerning coils and cores that I 

 made, including the effects of dielectric displacement ; the 

 analysis is all very well, and is interesting enough for educa- 

 tional purposes, but the interpretations are so difficult in 

 general that it is questionable whether it is worth while either 

 publishing the investigations or even making them. 



Professor Hughes * has also devoted some attention to 

 induction in cores, and has arrived at the remarkable conclu- 



* Pi-oc. Eoy. Soc. 1886. 

 Phil. Mag. S. 5. Vol. 23. No. 141. Feb. 1887, P 



