662 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



error in the 1.88 figure. This follows from the fact that if the Cg/C mut ratio 

 obtained in the filled or homogeneous condition is used in the determination 

 of the normal dielectric constant, then the correct 1.81 figure is obtained. 

 Of course, these statements regarding the accuracy of the normal dielectric 

 constant are predicated on the absolute accuracy of the 2.20 figure for 

 the dielectric constant of the filled cable. However, as pointed out previ- 

 ously, there is but little room for uncertainty in this connection. 



To summarize, it appears that the principal error involved in the use of 

 ideal pair formulas to determine the dielectric constant of cable pairs is due 

 to non-homogeneity of the dielectric. For polyethylene insulated 19-gauge 

 pairs the error is about 4-4%. The magnitude of error expected for paper and 

 pulp insulated pairs is less, as is explained below. 



a. Effective Diameter of Shield 



It has been shown that solution of equation (1) provides a value for S 

 which does in fact equal the average interaxial spacing between wires of a 

 cable pair. In the process of finding € using the ideal pair formulas, a value 

 for S/D is found from which a value for D can be determined. The relation 

 between the D value and the physical configuration of the cable pair struc- 

 ture is not precise. It is necessary to consider that D represents an effective 

 diameter of shield; it is the diameter of the cylindrical shield of an ideal 

 pair structure having the same d/2S and Q/Cmut ratios and the same d as 

 the cable pair. 



The value of effective D is larger if the dielectric is non-homogeneous, as 

 shown by comparing the figures for D in Table II obtained before and after 

 filling with DXL-1. The D value obtained under homogeneous conditions is 

 more representative of the average physical placement of conductors com- 

 prising the shield. 



b. Paper Ribbon and Paper Pulp Insulated Cable 



The distribution of solid insulating material in paper ribbon or pulp in- 

 sulated cable is different from that in polyethylene insulated cable. Whereas 

 in the latter there is a solid sheath of insulation around the conductor with 

 air occupying interstitial space only, the paper ribbon or pulp insulated cable 

 has some air dispersed among the insulating material in all portions of the 

 dielectric space. "Interstitial space" is not well defined since the paper 

 insulation tends to deform during cabling operations. This sort of dielectric 

 would seem to be more homogeneous than that of the polyethylene insulated 

 cable. 



A method for approximating the ep/e,„ut ratio in terms of power factor 

 measurements on the balanced and grounded circuits is discussed in Ap- 



