Barus — Displacement Interferometer. 71 



The idiostatic method under the same circumstances, AJV = 

 "0001 centimeter, should just measure 



V 3 = -5 volt, 



so that alternating currents much within 1 volt will apparently 

 be measurable. This method is naturally much less sensitive 

 than the other, but its absolute character and its adaptation to 

 alternating currents are of interest. The sensitiveness of the 

 idiostatic electrometer as here designed, and in the above case 

 of the absolute electrometer, would thus appear to have the 

 same practical limit. In the way of absolute measurement, 

 nothing has been gained. 



5. The Same. Disk electrometer. In this case a charged 

 disk with a guard ring (the apparatus to be described hereafter, 

 figs. 5 and 6) at potential V l is suspended bifilarly, as above, 

 between the two concentric parallel disks of the condenser, at 

 potentials Y 3 and V t . The adjustment may be regarded as 

 the extreme case of the cylinder electrometer with closed ends 

 and the equations will be, necessarily, nearly the same. Let d 

 be the distance apart of the plates of potential V 3 and V lf D 

 the distance between the plates of potential V 3 and V„ r the 

 radius of the movable disk. The total energy W of the vari- 

 able system is then, after reduction 



8tt ( d T D-d 



and the corresponding mechanical force 



r*/V-V V t -V \ (V-K V- VA 

 JL ~ 8 V D-d ■*" d J \ D-d ~ d J 



which depends essentially on d as well as on D. 



Let the disk be in the middle, or *2d = D, and put 

 X = MgAJV/l as above, where M is now the mass of the disk 

 and appurtenances, AiV the interferometer displacement, I the 

 length of the bifilar pendulum, and g the acceleration of grav- 

 ity. Then 



(^)(^^)=^- 



Let F 2 = and M — 7rr 2 tp, t being the thickness and p the 

 density of the disk, the latter being sufficiently large so that 

 the appurtenances may be ignored. Then on commutation 

 and in electrostatic units, AJV being-the mean displacement, 



which (for a sufficiently large disk) is independent of its area. 

 To estimate the limiting sensitiveness the following appar- 

 ently reasonable values may be inserted 



