338 Lord Rayleigh's Comparison of Methods for the 



where U is a numerical quantity dependent upon L, so that 

 the influence of self-induction is approximately proportional 

 to the square of the speed of rotation. The same law applies 

 also to any disturbances depending upon mutual induction 

 between the wire circuit and subordinate circuits in the ring. 



It will be seen that, if the law of squares may be depended 

 upon, the influence of self-induction (and mutual induction) 

 can be satisfactorily eliminated by combining observations 

 taken at different speeds. In my experiments four speeds 

 were used, of which the greatest and the least were in the ratio 

 of 2 : 1. The effect of self-induction was therefore four times 

 as great at the high speed as at the low speed. In other words, 

 the quantity (about 1 per cent.) by which the low-speed result 

 is to be corrected in order to eliminate the influence of self- 

 induction is only one third of the discrepancy between the 

 uncorrected results of the extreme speeds. If, therefore, the 

 observations are good for any thing at all, they are good 

 enough to determine this correction with all desirable preci- 

 sion. If a check be considered necessary, it is supplied by 

 the results of the intermediate speeds. 



The above reasoning proceeds upon the supposition that we 

 have no independent knowledge of the magnitude of the coeffi- 

 cient U. In point of fact, this coefficient can be calculated 

 with considerable accuracy from the data of construction, so 

 that the empirical correction is applied only to a small outstand- 

 ing residue. 



In considering the disadvantageous influence of self-induc- 

 tion as an argument in favour of II. as against III., we must 

 remember that the magnitude of the influence can be greatly 

 attenuated by simply diminishing the speed of rotation. At 

 half the lowest speed above spoken of, for which the correction 

 for self-induction would be reduced to £ per cent., the deflec- 

 tion (over 100 millim. at a distance of 2670 millim.) would 

 probably correspond to a much greater sensitiveness than it is 

 possible to obtain under II. If we prefer the higher speed, 

 it is because we estimate the advantage of doubled sensitive- 

 ness as outweighing the disadvantage of a fourfold correction 

 for self-induction. 



The fourth objection which may be taken to this method, 

 and it is one from which II. is free, lies in the necessary crea- 

 tion of mechanical disturbance in the neighbourhood of the 

 suspended magnet. 



How far these complications may be supposed to prejudice 

 the result of carefully conducted experiments must be left to 

 the estimation of the reader of my paper, in which very full 

 data for a judgment are given. My own opinion is, that while 



