﻿Determination of the Ratio of the Electrical Units. 105 



me preferable to suspend the moving cylinder C vertically 

 in an ordinary balance, C and the upper fixed cylinder A 

 being in connexion with earth by wires which may be very 

 fine*. The force is then evaluated in gravitation measure ; 

 and it may of course in effect be doubled by duplicating the 

 cylinders on the other side of the balance. 



When w T e come to actual design the question at once 

 obtrudes itself as to how long the cylinders really need to be. 

 In theory it is easy to treat them as infinite, but in practice 

 some concession must be made. In particular the weight of 

 C must not be increased unnecessarily. 



The penetration of potential arising at the gap between B 

 and A into the annulus between C and A is easily investigated. 

 For practical purposes it suffices to treat the problem as in 

 two dimensions. If r be the radius and z (the axial co- 

 ordinate) be measured from the end of A, the potential V in 

 the annulus may be taken to be 



V=2H*-»«/(&-«) sin— r ; , 



b — a 



where m is an integer and H an arbitrary constant variable 

 with m. At the surfaces of the cylinders where r = a or 

 r = b, V vanishes. The term whose influence extends furthest 

 is that for w r hich m = l. Limiting ourselves to this, we take, 

 since e~* =23*2, 



V=H 1 (23-2)-*-a) s iri 7r ^T^, 



b — a 



showing that when z=b— a the value of Vis already reduced 

 to one twenty-third part of that at 2 = 0. When z = I (b — a), 

 that is at a distance from the end equal to four times the 

 thickness of the annulus, this term is attenuated 290,000 

 times, and it is safe to conclude that the whole disturbance 

 of potential may be neglected. A similar argument applies 

 to the annulus between B and C ; so that a total length of 

 8 or 9 times the thickness of the annulus — 8 or 9 inches in 

 the example spoken of above — should amply suffice. 



There is less objection to increasing unnecessarily the 

 length of the fixed cylinders, but even here there must be 

 some limit. It is easy to see that the prolongation of the 

 upper cylinder A at zero potential above C, also at zero 

 potential, is of little importance. But the case of the charged 

 cylinder B requires further consideration. 



* Further screens in connexion with earth may be introduced to protect 

 the moving parts of the balance more effectually from the influence of the 

 electricity upon B. 



