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Paschen's similarity law, which expresses a certain relationship between the breakdown voltage of a gas, the gas pressure, and the distance between electrodes, is known to fail at high pressures. This is owing, at least in part, to a change in the way in which electrons dissipate energy to the gas molecules. At high enough pressure, the electron transfers energy principally to molecular vibrations. In condensed phases this vibrational barrier is dominant, and one should expect a new kind of similarity law to hold under certain controlled conditions. The liquid aliphatic hydrocarbons provide an illustration of such a law. The electric strengths of nine hydrocarbons of various densities were measured and found to depend linearly upon density. It has also been found that the temperature dependence of the electric strength of a liquid aliphatic hydrocarbon can be accounted for by the change in density of the liquid due to thermal expansion.