Potential gradient: In cables discussion of the logarithmic formula, its modification and effect of internal heat

If the dielectric of a single-conductor concentric cable is homogeneous, the voltage gradient at any diameter x is given by
${d\ v \over d\ x} = {0.868 \ V \over x \log_{10} {D \over d}}$
where
${d\ v \over d\ x}$
is the voltage gradient or dielectric stress, V the voltage between conductor and sheath, D the diameter over the dielectric and d the diameter over the conductor. A complete discussion of the above formula is followed by considerable experimental data and curves accumulated from many breakdown tests. Results of tests on cables with large ratios of dielectric diameter to conductor diameter are included and a modification of the above theoretical formula is discussed. The modified formula is checked by tests on a special cable which was constructed for this purpose. A new relation between the rupturing gradient at the surface of the conductor and the ratio D/d is suggested and curves of experimental data given. Breakdown tests on three-conductor cables are included and the calculated rupturing stresses compared with those for single-conductor cables. Special cables were constructed so that measurements could be made of voltages between layers of insulation. From data obtained from these tests, curves are given showing the change in potential gradient as the internal heat of the cable is increased. Curves are given showing the effect of a change of temperature on the dielectric strength, the stresses and the factor of safety of cables. A complete description is given of the low-capacitance electrostatic voltmeter used in the temperature-potential-gradient tests.