70 Barus — Displacement Interferometer. 



and hence the force acting in the direction x if W = W 1S + 

 W„ is after reduction 



x=ij£r r ( v ~ v ) ( 2 F -( F »+ F 3 )) 



On the other hand, the restoring force is for small displace- 

 ments 



X= Mgdx/l 



where M is the mass of the cylinder, I the length of the pendu- 

 lum suspension ; whence if dx = AN, in electrostatic units, 



which is the required equation. Since, if t is the thickness, L 

 the length, and p the density of the movable cylinder, 



\y, y* j \ y , 2 ;- i(\+B/r) AiV 



the appurtenances, like mirror, etc., being disregarded. A 

 given deflection AN will therefore correspond to smaller 

 V 3 — V 2 as M— r, Z, t, are smaller and I and T^are larger. 

 If the instrument is used idiostatically (electrostatic units), 



\ 8 Mq (R — r) 

 V. Y = — r^ —^ AN 



(f.-f,) 



l(R + r) 



If one pole of the cell V z — F 2 is earthed, T\, = 0, and the 

 deflections on commutation are AN and — AJV', 



4 Mq (R-r) AN+AN' 8 it Lt p (R-r) 



V = 300 XT , /„ , / = 300' 



^(soo) 2 



VJ{R + r) 2 ~"" v F^(l + ^/r) 

 volts. 



If the cylinder Y x is made of paper, the following dimensions 

 seem to be reasonably convenient limits, so that for AN — "0001 

 centimeter, L = 5 cm., t='2 cm., /? = 1 ; / = 100 cm., 1^ = 300 

 volts, whence 



V 2 = 3-8 X 10- 4 volts, 



or about 10~ 4 volts per ring. 



One should thus be able to measure voltages even within 

 4 X 10~ 4 ; but on trial the actual limits fall much within this. 

 The use of wide apparatus has the advantage only of dimin- 

 ishing the effect of appurtenances like the mirror, etc. In the 

 practical work below, however, these limits could not be 

 reached for reasons which will appear. 



