Mutual Induction of a Circle and a Coaxial Helix, 8fc. 197 



Mr. Rhodes under the direction of Prof. Ayrton in the Physical 

 Laboratory of the Central Institution, in which the Lorenz apparatus 

 of the McGill University was tested by Prof. Ayrton and myself 

 (Appendix to the Report of the Electrical Standards Committee 

 of the British Association, 1897). The calculation was made by the 

 somewhat laborious method indicated in my paper " On the Deter- 

 mination of the Specific Resistance of Mercury in Absolute 

 Measure." * It was checked by Mr. Mather, and subsequently I 

 calculated M afresh by the method given here. 



7. It is important in practice to determine the change in M con- 

 sequent on small changes in A, a, and a?, both for the calculation of 

 the effect on M@ of small errors of measurement, and because from 

 time to time the disc of any Lorenz apparatus needs to be re-ground 

 in place, and possibly the coil, owing to a breakdown in insulation, 

 may sometimes need to be re-wound. 



Let 



then 



A 



M 



a dM.& 



r = 



M da 



x 

 M dx 



dM. 



"AT~ 

 M 



dA. 



-ir 

 A 



da 





 a 



dx 



~ 

 x 



It may be shown by direct differentiation using relation (iii) 

 between the P functions and their differential coefficients that 



s = 2T/W 



1 



where 



2 deW )> 



r - l ~ S T+2Y 



2 " deW J 



W=2(-i)K fB , 



(5), 



2m 1 



and d, e have their former significations. W has already been found 

 in calculating M; and T and V are easily calculable from the known 

 values of K , K l9 K 2 , K 3 , &c. 



Since M is a homogeneous function of the first degree in 

 A, a, x it follows that q + r + s = 1, as is obvious in the formulae 

 above given. 



* 'Phil. Trans.,' A (1891), p. 21. 



P 2 



