382 Lord Rayleigh on the Self-induction 



pushed further. The present paper may thus be regarded 

 partly as a review, and partly as a development of Maxwell's 

 chapter. 



The problems divide themselves into two classes. In the 

 first class the distribution of the currents is supposed to be 

 the same as it would be if determined solely by resistance, 

 undisturbed by induction ; in particular the density of cur- 

 rent in a cylindrical conductor is assumed to be uniform over 

 the section. The self-induction calculated on this basis can 

 be applied to alternating currents, only under the restriction 

 that the period of the alternation be not too small in relation 

 to the other circumstances of the case. If this condition be 

 not satisfied, the investigation must be modified so as to 

 include a determination of the distribution of current. A 

 problem of this class considered by Maxwell (§ 689) relates 

 to the " Electromotive Force required to produce a Current 

 of Varying Intensity along a Cylindrical Conductor/' * In 

 connection therewith another problem of the same class will 

 here be treated, in which the mathematical conditions are 

 simpler, and the results more readily apprehended. 



In § 685 Maxwell takes the problem of two cylindrical 

 conductors, the first of which conveys the outgoing and the 

 second the (numerically equal) return current. The external 

 radii are a Y , a{ ; the internal radii a 2 , a 2 ; o the distance 

 between the centres. A possible difference in the magnetic 

 quality is contemplated, the permeabilities for the material 

 composing the cylinders being denoted by //,, /j/ } and that of 

 the intervening space by /uu . 



The first correction 1 have to note relates merely to a slip 

 of the pen. The result (22) should run 



L , b 2 [ ai 2 -W W i (hi 



+ 2^ l a n_ a n + (< _ O 2'0g^J. 



As printed in Maxwell's book the square brackets are omitted. 

 This error does not affect the following formula (23), in which 

 the cylinders are supposed to be solid. By putting a 2 , a 2 

 equal to zero, we get 



* That some of the results arrived at experimentally by Hughes might 

 "be attributed to unequal distribution of current in the conductors was 

 pointed out by Prof. Forbes in the course of a discussion which followed 

 the delivery of Prof. Hughes's address. 



