Capacity of Solids under Varying Fields. 85 



Case II. — Where tivo equal Slabs of Dielectric are used. 



In this case plate A (fig. 4) is placed exactly midway be- 

 tween the plates B and C. Two equal slabs of dielectric are 

 used, one being placed upon C, the other upon A. The 

 thickness of the blocks of dielectric and the distances between 

 BA and CA are determined by considerations respecting the 

 approximate value of K for the dielectric. If these distances 

 are correctly taken, positions may be found for plates N and 

 M where they are always at the same potential, and where 

 they are approximately in the centre of the spaces between 

 the plates and the dielectric. 



The plate N is supported on three small ebonite posts upon 

 the slab D. Or, in the case of any other substance than 

 glass, a hole may be bored through the dielectric, through 

 which the ebonite rod which carries N may pass. The 

 capacities of the two sides of the apparatus will now always 

 remain equal, for if the field alternates at different rates, both 

 dielectrics will change their specific inductive capacities 

 equally. The formula giving the value of K is then obtained 

 as follows : — 



For the side AB, 



f v ' 4tt<7 C di C di+dA 



— \ dY=—j^\ dx + ^irax da; 



whence 



Y-V 1 =^"^ 1 + 47TC7^ (15) 



For the side AC, 



y-y 1 =47ro-^ (16) 



Equate (15) and (16), and we obtain 



K =A 4 ^ 



Use of Apparatus according to First Method. 



According to the theory given under Case I., the value of 

 K may be obtained when the capacities of the two sides of the 

 apparatus are unlike and unknown. It was found, however, 

 unless the apparatus is so disposed that the capacities of the 

 two sides are nearly equal, that the value of K obtained is 

 not quite exact in the case of slowly varying fields, and that 

 with oscillating fields no result whatever can be obtained. 

 The formula is based upon the assumption that static condi- 

 tions hold. Now the formula assumes that, when the centre 

 plate has a given potential, the surface-density of each side of 



