82 Bar us — Displacement Interferometer. 



cylindric tube on the opposite side, where the tube must pass 

 through the circular perforation in the guard ring. The result 

 is an empiric instrument in which the deflections are propor- 

 tional to the voltages to be measured, of increased sensitiveness, 

 even 2 X 10 -3 centimeter per volt, but not yet sensitive enough 

 to be immediately valuable for refined practical purposes. 

 The idiostatic instrument, for voltages above 20 volts (after 

 the disk has been adjusted for k = by comparing the posi- 

 tions of the charged and uncharged disk) may in some cases 

 be useful. 



15. Case of the- unsymmetric disk. The cause of the 

 departure from linearity in the preceding experiments is to be 

 referred to a slight asymmetry in the disk, whereby an effect 

 varying as the square of voltage of the disk is superimposed 

 on an effect varying as its first power. To eliminate the non- 

 linear term, it should be sufficient to obtain no deflection in the 

 case of earthed plates, when the needle is successively charged 

 and uncharged. In fact, the charged non-symmetrical needle 

 between earthed plates introduces an interesting method of 

 electrometry as follows : 



Let k be the amount of non-symmetry for a disk whose 

 mean distance from the plates D centimeters apart would be 

 d = D/2. Hence for any displacement AN the distance of 

 the disk from one condenser plate will be d — D/2 + (k + AN) 

 and from the other plate, D — d — D/2 — (k + AN). Hence 

 the displacement force is (after reduction) 



„ V* r* k + AN 1 MgAN 



X ~~2~ D/2 Dyi-{/c + ANy~ T~ 



As (k -t- AN) 2 may usually be neglected in comparison with 

 D*/4:, the equation becomes 



MgD* A N 



v*=- 



41 r' k + A JST 



If k is large as compared with AN, which will usually be the 

 case, V* will vary linearly with AN. 



To use this method, k must, therefore, be known, and it may 

 be determined with the aid of a given voltage preliminarily. 

 Many experiments were made in this way, an example of 

 results being given in fig. 7 c. The asymmetry of the disk 

 was.about - 5 millimeter, and the plates were over 6 millimeters 

 apart. The equation employed answers the requirements as 

 closely as the observations could be made. At high voltages 

 (100 volts) there is liable to be divergence, while at low volt- 

 ages the displacement AN is too small for accurate work, see- 

 ing that the underlying equation is quadratic. 



An apparatus like the present, intended for actual measure- 

 ments, should be provided with a micrometer suspension for 



