Measurements of permittivity, power factor, and power loss, in alternating fields, and also of direct-current conductance, have been made with voltage gradients covering the range between 2 kV per mm and the region in which instability sets in (10 to 15 kV per mm).The law previously given, namely, that for low voltage-gradients, including the usual working range, the permittivity and power factor of the material are independent of the voltage, and the power loss is strictly proportional to the square of the voltage, was found no longer to hold when the voltage gradient exceeded a certain critical value. This value was about 2 or 3 kV per mm in all the tests made, including measurements on black and yellow material, at temperatures of 20° to 50° C. with varying moisture contents, and at frequencies of 50, 100, and 800, cycles per sec. As the voltage gradient was increased beyond the critical value, both the permittivity and the power factor of the material began to increase, slowly at first and afterwards more rapidly. The increase was smaller the drier the material, but the percentage increase was of the same order in all cases. The maximum increase of power factor observed was of the order of 10 per cent, and of permittivity 1 per cent.It was found that in all cases the power lossPin the material could be expressed as a function of the applied voltageV, by means of the formulaP=G0V2+G1V2+γP=G0V2(1 +pVγ)This formula holds for all voltage gradients, low and high, but the second term is negligible for low voltage-gradients.Gois therefore the low-voltage a.c. conductance. The values obtained for γ varied between 2.5 and 6.The increase in permittivity and power factor with increasing voltage is taken as an indication that the absorption currents in the material increase more rapidly than the voltage, and it is considered that this rules out the possibility of such currents being of the nature of the rotation of electrical doublets. An increase in the conductivity of one or more of the components of the material with voltage would seem to be the most probable explanation, and the evidence suggests that this conductance is ionic.The d.c. conductance (constant final value) of the material was also found to increase with increasing voltage gradient, but in a manner quite different from that of the a.c. conductance. Over the whole range covered by the measurements (2 to 15 kV per mm) the d.c. conductance was found to be a linear function of the voltage. This current is also probably carried by ions, and we conclude that we are concerned with at least two laws governing an increase of ionic conductance with voltage.The process of ionization by collision will account for the outstanding features of the a.c. results, namely the critical voltage-gradient corresponding to the critical ionic velocity at which a collision with a neutral molecule results in its ionization, and the more and more rapid increase of conductance as the voltage is further increased. It is, however, difficult to account for the d.c. results by this process, since these features are not apparent in them. The ions carrying the direct current are probably different from those carrying the absorption current of the a.c. measurements, and subject to a different law of motion.