﻿100 Lord liayleigh on- the Experimental 



parts of infinitely prolonged wholes. That is, if I be the 

 length, b the larger and a the smaller radius, the increase of 

 capacity is i^-f-log (bfa). 



The circumstance that in this method the smaller capacity 

 is much greater than that of the leads alone is scarcely an 

 objection. In the approximate formula the electromagnetic 

 capacity is proportional to the resistance of the opposite 

 member of the Wheatstone quadrilateral, so that it is merely 

 with the difference of resistances needed in this branch that 

 we are mainly concerned. The resistance that must be added 

 as we pass from one condenser to the other can be determined 

 with full accuracy. 



The length I and the smaller diameter 2a are readily 

 measured. The inner diameter 2b of the outer cylinder is less 

 easily dealt with ; and even if the error were no greater than 

 for 2a, it would be seriously multiplied in log (b/d), which is 

 approximately proportional to (b— a). In the Cambridge 

 apparatus the interval between the cylinders was intended to 

 be found by gauging the space with water, and the process is 

 described by Thomson and Searle (p. 600). If this plan be 

 adopted, there is no need to measure b otherwise. If v be the 

 included volume, 



v = irl(b 2 -a 2 ), 



and 



c= 



u 



& V via*) 

 or approximately 



n _ vPa 2 * 



v 



It is to be remarked that by this method we determine 

 what we really require, L e. the mean value of b— a. 



In carrying out the necessary measurements there should 

 be no difficulty over I or a. The evaluation of v is more 

 troublesome, and the principal uncertainty would seem to 

 arise out of the possible presence of air-bubbles. Thomson 

 and Searle used a vacuum towards the later stages of the 

 filling. Perhaps it would be an improvement to have a 

 vacuum (?from carbonic acid) from the first, and to intro- 

 duce the previously boiled water from below. It would be 



* In the Cambridge condenser 7=61 cm., 2« = 23| cm., and 

 2b— 2a=ricm. I do not know that these dimensions are susceptible 

 of much improvement. 



