48G THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



capacitance, L the inductance, and R the conductor resistance per unit 

 length. The second term contributes about 99% of the attenuation. 

 Considering only this term we deduce 



{\/ot){da/dP) ^ (l/R)(dR/dP) + (l/2C){dC/dP) - (l/2L)(dL/dP) 



Accurate knowledge of the coefficient (l/C)(dC/dP) is thus essential 

 in designing very long cables which are to be exposed to high pressures. 



In evaluating dielectric materials for use in cables it is often desirable 

 to make measurements on sheet specimens rather than cable. It thus be- 

 comes necessary to be able to translate sheet data into cable data. It 

 is the purpose of this paper to analyze the problem of calculating pres- 

 sure coefficients of capacitance for certain simple geometries and to 

 consider the methods of measurement which have been used. It will be 

 shown that results of theory and experiment are in as good agreement 

 as can be expected but more accurate measurements of electric and 

 elastic properties are needed. 



The equations which will be derived are also necessary if one wishes 

 to determine the dependence of dielectric constant on pressure using 

 any of the geometries described herein. 



The problems treated in this paper are particularly simple and amen- 

 able to mathematical treatment but many problems encountered in sub- 

 marine cable design are at present subject to solution only by empirical 

 means. Fundamental investigations of the effects of pressure on dielectric 

 materials are needed. 



II. THEORETICAL TREATMENT 



In the following treatment we consider that the dielectric substance 

 is an elastic solid which obeys Hooke's law. We denote the relative per- 

 mittivity or dielectric constant by e, the permittivity of free space by 

 £o ,* the principal stresses and strains by th and en , the density by p, 

 the compressibility by k, and Poisson's ratio by a. 



1 d£ 



A. Calculation of ^ 



•^ £ dP 



One of the quantities which will be needed in the evaluation of 



i^ac . 1 a£^ 



CdP ^^ E dP 



As £ is not dependent on the geometric configuration it can be calculated 



€0 = 8.86 X 10-12 farads/meter. 



