Most of the procedures employed so far in the literature for obtaining the amorphous volume of a polymer below its melting point have been based upon some kind of ad hoc assumptions. In this paper the principle of corresponding states, whose validity has been established for a number of polymers, is applied for obtaining the amorphous volume of polyethylene in the experimentally inaccessible region. The degree of crystallinity as a function of temperature is then calculated in a typical case using the actual sample volume data of Quinn and Mandelkern and the ideal crystal volume values obtained from X-ray measurements. Our results indicate the onset of a prominent relaxational transition at T1= 152°K. A careful analysis of the volume-temperature relationship indicates a much weaker transition at T2= 233°K. By making use of the isoprene volume concept, it is shown that the Simha-Boyer relation is valid in a more general form.