ELECTRODE EFFECTS 559 



constituting the lower electrode, C is the confining ring and D the 

 mercury of the upper electrode, ("onsider first the ideal case where 

 the ring is of finite height but infinitely thin. This corresponds to 

 the condition illustrated in Fig. 1 except that the fringing is increased 

 due to the size of the lower electrode. .Suppose now that the ring 

 is made of insulating material and of appreciable thickness. Some 

 of the lines of force then pass through the material of the ring and the 

 results become dependent on the nature and amount of this material. 

 On the other hand, suppose the ring is made of metal and of appreci- 

 able thickness. This, of course, increa.ses the effective area of the 

 electrode but this is easily remedied by making the outside diameter 

 of the ring equal to the size of electrode desired. However, that part 

 of the surface which is actually covered by the ring is subject to the 

 same error as in the case of plain metal electrodes, namely, that if 

 the surface of the sample is not a true plane there will be a gap between 

 the ring and the sample. One remedy for this is to make the ring 

 thin enough so that the area afTected is negligible compared with the 

 total. This may not seem to be consistent with suitable rigidity. 

 However, if a ring of at least 43^ inches diameter is used it can be as 

 much as 1 /16 inch thick and therefore quite rigid without serious 

 error. In this case the area of the ring is about 5.6% of the total 

 area and assuming a 10% error due to the air-gap as in the case of the 

 plain electrodes the result would be a net error of .56% in the dielectric 

 constant and a correspondingly slight error in the power factor. 



Another means of reducing this error without sacrificing the rigidity 

 of the ring is to bevel the edge of the ring either on the outside or 

 inside as shown in Figs. 2-A and 2-B, respectively. In this way the 

 area covered by the ring can be reduced to less than 1% of the total 

 area and the air-gap error to less than 0.1%. However, if the ring 

 is beveled on the outside the outer surface of the ring is no longer 

 perpendicular to the surface of the sample and a slight increase in the 

 stray field from this surface is produced. On the other hand, when 

 the ring is beveled on the inside, the angle between the inner surface 

 of the ring and the sample is less than a right angle and any tendency 

 of the mercury not to fill this angle will be increased. However, 

 both of these factors are probably but little afifected by the slight 

 bevel which is sufficient to reduce the thickness of the edge to a small 

 value. 



Another form of mercury electrode designed especialK- to eliminate 

 all errors due to air bubbles has been used by Dye and Hartshorn 

 for measuring the dielectric constant of mica in very thin sheets.;! 



^ Proceedings of the Physical Society of London, December 15, 1924. 



