660 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



Table II shows the results of application of the ideal pair formulas to 1000 

 cps inductance and capacitance measurements on the experimental cable 

 both before and after injection ctf DXL-1 compound. The dielectric constant 

 so obtained for the cable pairs after injection of DXL-1 is 2.20. This figure is 

 within the limits set forth previously, and it seems probable that it is ac- 

 curate to =bl%, although there is evidently no way to make an independent 

 check. If we accept 2.20 for the dielectric constant of the cable after filling 

 with DXL-1, the dielectric constant for the unfilled or normal condition can 

 be evaluated. Since only the dielectric was altered in filling the cable, the 

 dielectric constant before filling is given by: 



. - 2 20 y 00881 _ ... 

 €.ut - 2.20 X ^j^ - 1.81, 



Where: 0.0881 /zf/mi. = Cmut before filling. 



0.1070 Mf/mi. = Cmut after filling. 



Table II shows, however, that apphcation of the ideal pair formulas gives 

 1.88 for the normal dielectric constant. This figure is 4% higher than the 

 correct 1.81 value. Examining the changes in mutual capacitance and 

 capacitance to ground which occurred when the cable was filled with 

 DXL-1, it is seen that Cg increased by 27.9% whereas Cmut increased by 

 only 21.4%. The direct capacitance between wires of a pair, Cu, increased 

 by only 12.5%. Since Cn is a component of Cmut but not of Cg, this ac- 

 counts for the lower increase in Cmut as compared with Cg. The amount 

 of air in the cable after filling is so small that it can be assumed that the 

 dielectric is substantially homogeneous. Had the dielectric been homo- 

 geneous before fiUing, the percentage changes in Cg, Cmut, and Cu would 

 all have been equal. Thus it is evident that in the normal condition there 

 is a dielectric constant (eg) applicable for Cg which is different from €mut. 

 We find that Cj, is: 



e =220X^:5??^ = 172 



Where 0.0983 juf/mi. = Cg before filling. 



0.1256 /xf/mi. = Cg after filling. 



For a given set of capacitance and inductance data, there is, of course, 

 only one value of dielectric constant which will satisfy the ideal pair for- 

 mulas. This value will not be truly representative of actual cable condi- 

 tions if non-homogeneity exists. Non-homogeneity, as evidenced by the 

 experimentally determined inequality in tg and €mut, accounts for the 4% 



