344 Lord Rayleigh's Comparison of Methods for the 



Preparatory to the design of the apparatus for my experi- 

 ments, I made some calculations of the values of the induction- 

 coefficient and of its rates of variation for various ratios of the 

 radius of the coil (A) to that of the disk (a). The angle 7 

 (see method L) is here (& = 0) determined by tan 2 ^Y=a/A. 

 If we write 



SM , SA 8a 

 W = X A +V -a-' 



the sum of \ and v will be unity. The following are the 

 values found. Those under M are proportional only, and 

 relate to the case in which A is constant. 



a/A. 



X. 



V. 



M. 



•5 



-1-2 



+ 2-2 



4-37 



•6 



-1-36 



+ 2-36 



6-65 



•7 



-1-5 



+ 2-5 



9-80 



•8 



-2-0 



+ 3-0 



14-4 



In Lorentz's apparatus the value of a/A was even larger than 

 the last in the table, and the radial dimension of the coil was 

 no small fraction of (A — a). On this account, as has already 

 been pointed out by Rowland, no very accurate result could 

 be expected. 



In my experiments two similar coils were used whose radius 

 (A) = about 26 centirn., and in two distinct arrangements. 

 In the first arrangement the two cells were placed close 

 together; so that the case corresponded pretty closely with that 

 just spoken of. The radius of the disk is about 16 centim.; 

 and thus the proportions are nearly those of the second ex- 

 ample in the table. It will be seen that the circumstances are 

 not unfavourable to accuracy, the error of mean radius of the 

 coil entering into the result to a less extent than in any of the 

 methods hitherto described, except III. and IV. The disk is 

 so much more easily measured, that the larger coefficient 2*36, 

 applicable to it, should not lead to much error in the result. 



This arrangement was worked at two speeds of rotation in 

 the proportion of 10 : 16, and gave with close accordance 



1 B.A. unit =-9867 x 10 9 C.G.S. 



In the other arrangement the two coils were separated to a 

 considerable distance, and the induction-coefficient depended 

 not only upon the mean radii of the coils (and of the disk), 

 but also upon the distance of their mean planes. The pecu- 

 liarity of this arrangement, to which I wish to draw special 



