494 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



The integrand is approximately constant so 



In 



C{P) ^[{e- Die + 2) 



C(0) 



-[ 



3£ 



+ 1 



1 + cr 

 1 - a 



and 



C{P) = C(0) exp 



I 



(g - l)(c + 2) 

 Se 



+ lh^ 



l/cf l + g " 



kp 



10 " for the highest pressures used in the present experiments and 



^(£ - Die + 2) 



Se 



+ 1^ 



]i[^: 



is of the order of unity so the exponential may be expanded as 



CiP) ^C(O) h + 



[ 



iE - !)(£+ 2) 



3f 



+ 1 



1 + <r 



1 - (T 



P 



This treatment applies only to dielectrics for which c, k, and a are in- 

 sensitive to pressure. Equations (13) and (25) may be treated similarly, 

 ^^alues obtained experimentally and theoretically for polyethylene- 

 5% butyl rubber are compared in Table I. The experimental values 

 represent averages of many measurements. Agreement is considered 

 adequate but more careful experiments are needed. The necessary param- 

 eters assumed in making these comparisons are : 



£ = 2.28 



A; = 2.14 X 10"Vpsi 

 a- = 0.50 



Table I — Experimental and Theoretical Values for Poly- 



ETHYLENE-5 PeR CeNT BuTYL RuBBER 



Sample 



Sheet 



Cable /^/" = ^■^'^■ 

 ^^°^^ ^b/a = 4.68. 



Pressure 



one-dimensional 



radial 



radial 



C dP 



( /106 psi) 



Experimental Theoretical 



3.3* 



2.4 



2.2 



3.74 

 2.27 

 2.22 



* This value has not been corrected for stray capacitance. Such a correction 

 would tend to make the agreement between experimental and theoretical results 

 better. 



