﻿104 Lord Bayleigh on the Experimental 



Thus if a be the radius of the inner cylinder and b of the 

 outer, the force with which the former is drawn into B is 



iB 2 



~ log (pi a) ' 



It appears that F depends only on the ratio of the diameters 

 of the cylinders B, C. Suppose for example that 2a=2, 

 26 = 4 (perhaps in inches), then log (b/a)=log 2 = *69. If 

 the potential B correspond to 2000 volts, 



_ 2xl0 11 _ 2xl0 11 _20 

 v ~3xl0 10 ~ 3 ' 



and F = 16 dynes, or mgs. weight. This is rather small; 

 but since F oc B 2 , we get 64 mgs. for 4000 volts, and 144 mgs. 

 for 6000 volts. 



As regards the effect of errors in the fundamental measure- 

 ments b 3 a, we have if y = log (b/a), 



dy _db da t 



y ~h <*y' 



or with the above proportions 



dy _ d(2b) d(2a) 

 y --7(2b) -7(2a)" 



The outer cylinder is the more difficult to measure, but a 

 given absolute error in it is less important. If we suppose 

 25 = 4 inches, and d(2b) = joVo ^ ncD ' 

 d(2b) 1 , ■ 



T(26) = aooo aW ' 



and the proportional error in y is halved when we pass to 

 that of B. 



It should be borne in mind that what we have to do 

 with here is not the mean diameters of the cylinders, if such 

 diameters vary. 



This form of absolute electrometer was employed in the 

 researches of Hurmuzescu *, who mounted the cylinders on 

 a torsion balance, so that the motion w T as horizontal and not 

 strictly axial. Some advantages are attained in this arrange- 

 ment, especially perhaps that of being able to reverse the 

 force and so to double the rather inadequate value of the 

 subject of measurement ; but upon the whole it appears to 



* Ann. d. Chim. x. p. 433, 1897. This author erroneously attributes 

 Maxwell's reasoning above, by which the unknown parts of the electrical 

 distribution are eliminated, to Bichat & Blondlot (1866). 



