118 



Lord Rayleigh and Dr. A. Schuster. 



[May 5, 



this approximation) by a simple application of (10). For twice this 

 quantity Mr. Niven found 301,802, and I found 301,920 metres. For 

 twice the mutual induction of the two parts I found, by Maxwell's 

 method, 145,820 metres. Adding 301,920 and 145,820, we get 447,740 

 metres as the value of the whole self-induction, on the supposition 

 that the curvature may be neglected. This corresponds to the value 

 437,440 given in the paper. 



As to the origin of the discrepancy I am not able to offer any satis- 

 factory explanation. It should be noticed, however, that owing to his 

 peculiar use of the words " depth " and " breadth " as applied to coils, 

 Maxwell has interchanged what, to avoid any possible ambiguity, I 

 have called the axial and radial dimensions of the section. Thus the 

 depth, i.e., in his use of the word, the axial dimension, is given as 

 '01608, but this is really the radial dimension, as appears clearly 

 enough from the Report of the Committee, as well as from our recent 

 measurements. The real value of the axial dimension is '01841 metre. 

 But I do not think that this interchange will explain the difference in 

 the results of the calculation. 



When we proceed to apply corrections for the finite size of the 

 section, further discrepancies develope themselves. The second term 

 in the expression for L given in the paper (p. 508) does not appear to 

 be correct, and the final numerical correction for curvature ( — 7,345 

 metres) differs in sign from that which we obtain, Mr. Niven has 

 attacked the problem of determining the correction for curvature in 

 the general case of a single coil of rectangular section, and (subject 

 to a certain difficulty of interpretation) has obtained a solution. The 

 application of the result to the actual case of a double coil would, 

 however, be a very troublesome matter. For the two particular cases 

 in which only one of the two dimensions of the section of a simple 

 coil is considered to be finite, Mr. Niven and myself have indepen- 

 dently obtained tolerably simple results. Thus, if the axial dimension 

 be zero (6 = 0), 



L= 



and if the radial dimension be zero 



Again, for a circular section of radius p, 



(12). 



(13). 



p oa" \ p 



In all these cases we see that the correction increases the value of 

 L, and there can be no doubt that the same is true for the double coil. 



