72 Barns — Displacement Interferometer. 



Y x -=\ els., ^ = -05 cm., p=l, D=-l cm., A 2V~=10 -4 cm., Z=10 2 cm. 



Whence 



V 3 = 1-4 X 10- 3 volts. 



The limiting sensitiveness is thus of the same order as in the 

 cylindrical case for the same V r , as might have been antici- 

 pated. It is probable, however, that the present conditions 

 may be more nearly realized in practice, as the apparatus is 

 essentially simpler. 



If V i = Y x = 0, the idiostatic case is identical with the 

 absolute electrometer. 



6. The closed field electrometer (disk and cylinder com- 

 bined). If the two cases of the preceding paragraphs be com- 

 bined, with the symbols of potential and distance the same as 

 before, the energy of the system is, in electrostatic units, 



and hence the forces become 



If F 2 = 0, 



4 Mq A N 

 V = 



V i {r t /d'- + (B.+ r)/(JR—r)) I 



after commutation, where I is the length of the cylinder. The 

 sensitiveness of this apparatus depends very largely on d, that 

 is upon the disk, in any practical case; but it should be more 

 nearly absolute. Experiments were not made. 



1. Corrections. The most important consideration to be 

 made here is the effect attributable to the want of symmetry 

 in the orientation of the disk or movable charge, supposing the 

 latter and the plates are quite parallel. Let k be the axial dis- 

 tance of the uncharged disk from the plane midway between 

 the condenser plates (guard ring). In such a case, if the elec- 

 tric displacement is AN, the quantity A = k + AN must be 

 added on one side and subtracted on the other, so that 

 d = D/2 + A, d l = D/2 - A Thus the displacing force is, 

 after reduction, 



r*( V-V y-y \ / F _ F F _ F \ 

 ^~2 \Z>-2 A + l> + 2 A/ \L>-2 A D + 2 Aj 



which may be further reduced. 



If nothing is neglected, and under the assumption of a uni- 

 form "field, for a positive charge, Y s corresponding to a dis- 

 placement AiV 71 with F 2 = ; and for a negative charge, — V 3 



