332 Lord Rayleigh's Comparison of Methods for the 



showing that as b diminishes [a approaches zero, and accord- 

 ingly \ approaches unity, as is indeed otherwise evident. But 

 when b is small, it is the absolute error db which we must 

 regard as given rather than the relative error db/b; and thus 

 we are directed to stop at a moderate value of b, even if the in- 

 creased correction necessary for the size of the section were not 

 an argument in the same direction. 



The following intermediate cases, calculated by the tables, 

 will give an idea of the actual conditions suitable for a deter- 

 mination by this method: — 



y- 



6/2A . 



X. 



fM. 



M. 



o 



60 



•577 



2-61 



-1-61 



•316 



70 



•364 



2-18 



-1-18 



•597 



75 



•268 



1-98 



- -98 



•829 



80 



•176 



1-76 



- -76 



1-186 



We may say that the error in the distance of mean planes will 

 reproduce itself something like proportionally in the final result, 

 and that the error of mean radius will be doubled. 



Any uncertainty in the actual position of the mean planes 

 relatively to the rings on which the wire is wound may be 

 eliminated, as Glazebrook has shown, by reversing the rings 

 relatively to the distance-pieces. 



This method is subject to whatever uncertainty attaches to 

 the use of a ballistic galvanometer*. In its favour it may be 

 said that the apparatus and adjustments are simple, and that 

 no measurements of distances between mirrors and scales is 

 necessary for the principal elements. It should be noticed 

 also that the error due to faulty determination of the distance 

 of mean planes can be eliminated in great measure by varying 

 this quantity, which can be done over a considerable range 

 without much difficulty or expense. 



With reference to the capabilities of the method for giving 

 results of the highest accuracy when carried out in the most 

 ambitious manner, it is important to consider the effect of in- 

 creasing the size of the coils. The coils used by Glazebrook 

 have a mean radius of about 26 centim.; the axial and radial 

 breadths of the section are each about 2 centim. If we sup- 

 pose the mean radius and the sides of the section to be doubled, 

 the number of turns (about 800) remaining unaltered, the 

 sensitiveness would be increased both by the doubling of M 

 and by the diminished resistances of the coils, while at the 

 * See Phil. Trans. 1882, p. 669. 



