During recent years, considerable progress has been made in connection with theories of rubber elasticity. Two general types of theories have been advanced, one from a macroscopic point of view and the other from a molecular point of view. An example of the former is the theory of Mooney, who arrived at an equation which agrees well with observation. For molecular theories, the reader is referred to the work of Guth and Mark, Kuhn, and Pelzer, who carried through calculations of a statistical nature. More recently, the author extended the statistical theory along lines which avoided some of the earlier difficulties. In the present paper, the calculations will be carried still further, and the molecular theory will be related to the macroscopic theory of Mooney. It will also be shown theoretically that, although rubber does not obey Hooke's law for ordinary elongation, it should obey Hooke's law for shear. It will be supposed that individual rubber molecules are long chain hydrocarbons capable of assuming various lengths and shapes as a result of free rotation about carbon-to-carbon valence bonds. When a piece of rubber is under no stress, the rubber molecules have a certain distribution of shapes. When the rubber is subjected to a stress, however, the molecules assume another distribution of lower probability. The theory here advanced relates this probability to the entropy of strain, thus providing a means of arriving at the mechanical properties of rubber. Two postulates are made. (1) When a macroscopic piece of rubber is strained, the components of the lengths of the individual molecules (along some set of axes) change in the same ratio as does the corresponding dimension of the piece of rubber. (2) When a piece of rubber is elongated, no change in total volume takes place. The first assumption was made in the earlier paper of this series, whereas the second was not. Experimental support for the second postulate has been given by Holt and McPherson. Our first problem is to investigate the effect of this second assumption on the equation of state for rubber.