PRESSURE COEFFICIENTS OF CAPACITANCE 487 



in general and the result applied to each of the special cases to follow. 

 A relation between dielectric constant and density is required and 

 usually, when dealing with non-polar dielectrics, one assumes that the 

 Clausius-Mosotti relation gives the proper dependence. That is 



= (constant) p (1) 



£-^ 2 

 This formula may be differentiated to give 



i ^ = (g - l)(g + 2) 1 ap_ . . 



£ dP 3e p dP ^ ^ 



In the theory presented herein, (1) will be used though it is at best an 

 approximation. Corrections to the Clausius-Mosotti formula which 

 have been given do not seem applicable to polymer dielectrics and in- 

 troduce parameters which must be fitted. 



B. The effect of a One- Dimensional Pressure Acting on a Disc 



Consider a one-dimensional pressure, —P, acting along the axis of a 

 circular disc of dielectric material with electrodes affixed to opposite 

 faces. Assume the disc is constrained such that no lateral displacement 

 can occur. Let t be the thickness and A the area of the disc. 



The capacitance of such a capacitor is given by the equation 



C — £€q — 



so the desired pressure coefficient is 



CdP ~ E dP T dP ^ ^ 



where use has been made of the condition that the area is constant (i.e., 

 no lateral displacement). Hooke's law states 



k 



^^i = ;T71 ?rT [txx — (^{Tyy + Tz^] (4) 



^yy 



Wvy — air XX + r«)] (5) 



ezz = o(i _ 2 ) ^^" ~~ *^^'^" "^ "^"^^-^ ^^^ 



* C. J. F. Bottcher, Theorj^ of Electric Polarisation, Elsevier Publishing Co., 

 Amsterdam, 1952, p. 199 et. seq. 



