566 BELL SYSTEM TECHNICAL JOURNAL 



when one electrode is grounded the effect is not symmetrical. Cover- 

 ing both sides of the sample should, therefore, cause an increase of 

 4.2 mmf. or 8.6% of the capacitance of the sample. Adding this to 

 the 9.3% fringe effect already determined makes a total of 17.9% as 

 compared with 13.9% by Kirchhoff's formula. At least part of this 

 difference is also due to the non-uniformity referred to above which is 

 very marked in this sample. 



A similar test was made on the Vs" phenol fibre sample. However, 

 this sample was somewhat warped so that there was an appreciable 

 air-gap between the electrode and the cover plate. The total effect 

 computed as above was 2.6%, which added to the 2.8% already 

 determined makes a total of 5.4% or slightly under the value com- 

 puted by Kirchhoff's formula. This, no doubt, is accounted for by 

 the air-gap. 



The agreement with Kirchhoff's formula is reasonably good, there- 

 fore, for disc electrodes completely surrounded by dielectric, but 

 it is evident that the formula does not apply to the case of disc elec- 

 trodes applied to sheet materials. 



The fringe effect for the 4^" upper circle and 6" lower square 

 electrodes is shown in Fig. 4. It is found to be about 2^ times as 

 large as for the equal 4^" electrodes. It also varies somewhat with 

 the dielectric constant of the sample, being greater for the lower 

 dielectric constant. The anomalous behavior of the phenol fibre 

 samples is show^i in this figure also. 



From Item 8 of Table II, it is seen that when a shallow metal 

 ring is placed on the upper disk to simulate the conditions of a mer- 

 cury electrode, a further increase of from 2 to 4% of the true capacit- 

 ance of the sample takes place. This likewise is greater the thicker the 

 sample and the lower its dielectric constant. A similar test for the 

 increase in capacitance due to vertical height of the metal ring was 

 made for the more exaggerated case of a 4" disk and a ring ^" high ; 

 the lower electrode being 6" square. In this case the increase varies 

 from 2}4% for Vs" phenol fibre to 8% for Yg" hard rubber. This 

 shows the importance of keeping the vertical dimension of the metal 

 ring as small as possible. 



Insulating Ring 



In order to determine the corresponding effect when an insulating 

 ring is used for confining mercury, a somewhat similar test was made. 

 Several different rings were used as follows: ring No. 1 is M" high 

 cut from hard rubber tubing having a %" wall with the edges cut 

 square. Ring No. 2 was the same as above except that the edge was 



