* By statistical weight we mean the factor that a segment contributes to the partition function, including, if appropriate, a Boltzmann factor; it is not just the number of quantum states, in contrast to one popular usage.

Formulas for the mean square radii of various branched and ringed polymer molecules are developed under the usual assumptions regarding the statistics of chain configuration. For branched molecules, the mean square radii vary less rapidly with molecular weight than for strictly linear molecules, while for systems containing only rings and unbranched chains the variation is more rapid than for the linear case. These results show that in principle the quantity of branches or of rings can be determined from light-scattering measurements.

Some alternatives to the Flory-Huggins-Guggenheim treatment of sorption of liquids by polymers are examined, using data on three systems, water-collagen, benzene-rubber and toluene-polystyrene. It is found that a simple rigid site type of sorption theory is illuminating for the hydrocarbon systems but breaks down badly when applied to water-collagen mixtures. However, an exact "clustering" theory may be applied to all three of these systems. This theory, which is based on the statistical mechanics of fluctuations, does not compete with the Flory-Huggins-Guggenheim treatment in that it does not predict isotherms, but it does serve to interpret them in molecular terms.

The problem of the motions of a chain molecule diffusing in a viscous fluid under the influence of external forces or currents is considered for a particular model. This model is a chain of beads connected by ideal springs. Hydrodynamic interaction between the beads is introduced in the approximate form due to Kirkwood and Riseman. It is possible to solve this problem exactly with the use of a transformation to a set of normal coordinates. The viscosity, birefringence of flow, and dielectric and tensile relaxation behavior are calculated explicitly. The intrinsic viscosity in steady flow is somewhat different from the Kirkwood-Riseman result, and there is no change of viscosity with shear rate. The spectrum of relaxation times is similar to that found by Rouse and by F. Bueche, but has its maximum at a lower frequency than those obtained by Kuhn and Kuhn and by Kirkwood and Fuoss in other ways.

A radial distribution function of polymer segments in a solution of a high polymer may be defined as a quantity proportional to the density of segments at a given distance from some given segment. An approximate expression is derived for this function for dilute solutions of chain molecules of moderate degrees of polymerization. By Fourier inversion a simple expression for the intensity of light scattering, as a function of angle and concentration, may be obtained.