568 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



Fig. 8 also shows that the greatest percentage of points are ^\'ithin a 

 thickness range of approximately 0.010 inch. In moving downward from 

 maximum thickness the concentration of measured thicknesses increases 

 rapidly over approximately 0.003 inch and then becomes progressively 

 less covering an additional 0.010 inch. The calibration curve was placed 

 at about the location of maximum point concentration. By averaging the 

 thickness indications along a short length of the cable, a measurement 

 adjusted for the occasional extremes in flooding and surface variations 

 is obtained. The accuracy for practical use is therefore within limits of 

 d= 0.005 inch from the mean. 



Investigation was also made of flat samples of Pol^^ethylene placed 

 upon a flat metal plate. Flat samples eliminate the ^'ariables introduced 

 by the cable surface curvature, the corrugated metal undersheath and 

 the flooding material. A plot of capacitance against thickness for fiat 

 samples is shown in Fig. 9. Each point represents an individual molded 

 flat sample. The majorit}- of points are within ±0.003 inch of the curve. 



The measurement of sufficient points to obtain cur\'es for the many 

 cable diameters would invoh'e an impractical amount of work. 



The calibration curves for the three cable sizes and the curve for flat 

 samples drawn to the same capacitance versus thickness scale ha^-e simi- 

 lar form, but are displaced one from the other. The displacement of the 

 calibration curves for cables of core diameters of 1.39 to 2.38 inches is 

 shoAAii by Fig. 10. The displacement is approximately 1 meter division 

 for a diameter change of 0.1 inch. 



Calibration curves for other cable diameters than the three measured 

 were obtained by an approximation formula based on measurmg a few 

 points from each sheath diameter to determine the displacements and 

 slopes and multipljang the flat sample curve values by the displacement 

 and slope correction factors. 



The curve for flat samples and the curve for 2.38 inch diameter cable 

 plotted to the same scales is sho^^^l in Fig. 11. The two curves are suffi- 

 ciently alike so that by multiplying the flat sample curve thickness values 

 by a constant (Ki) obtamed from the ratio of the cable sheath thickness 

 to the flat sample thickness at zero recorder scale, the amount of curva- 

 ture of the resultant curve and the measured sheath curve are essentially 

 the same, and they have the same thickness and capacitance values at 

 zero recorder reading. A multiplier (Ko) can then be added to adjust the 

 slope of the percentage curve to make it practicall}^ coincide with the 

 sheath thickness curve. Actually, there is a slight difference between the 

 cur^'ature of the flat sample curve and those of cable sheath. The amount 

 of curvature increases as the cable diameter decreases. 



