The distribution of spaces in a random network of straight fibres is considered, such as might be occupied by a spherical object pIaced within the network or might allow free rotation to an elongated one. The approximate treatment of a network of flexible fibres is discussed briefly.

The problem is discussed of providing a theoretical explanation for the empirical equation of Laurent, Bjork, Pietruszkiewicz & Persson (1963) which relates the relative retardation of the sedimentation of compact particles in solutions of hyaluronic acid to the radius of the particle and the concentration of hyaluronic acid. From published and original data, the same relation is shown to apply also to sedimentation and diffusion in solutions of a number of linear and branched chain-polymers. Of several approaches to the problem, only one, based on the stochastic model of diffusional migration, yields the empirical relationship, and predicts a value of the numerical constant close to that observed. This treatment is shown to apply to other forms of migration, including the case where the chain-polymer is itself migrating. The theory is tested by calculation, from migration data, of the effective radii of the polymer chains. The results are consistent and comparable with values deduced from equilibrium experiments.

1. Simple thermodynamic expressions are used to describe the properties of uncharged binary and ternary polymer solutions, in particular the sedimentation equilibrium of binary systems and the osmotic pressures and ;incompatible' phase separations of ternary systems. 2. Sedimentation-equilibrium experiments were performed on four samples of dextran and two of polyethylene glycol. The critical points of the phase diagrams were determined for the mixed solutions of polyethylene glycol-dextran-water and of polyethylene glycol-bovine serum albumin-0.2m-sodium chloride solution. Osmotic pressures were measured on a single-phase mixed solution of a polyethylene glycol and a dextran. By use of the simple thermodynamic expressions consistent values of second virial and interaction coefficients for the materials used were obtained from these experiments. 3. The interpretation of the values of the second virial and interaction coefficients, on the basis of three models of molecular interaction, is discussed.

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1. Materials containing hyaluronic acid have been prepared by filtration (Ogston & Stanier, 1950) from ox synovial fluid and from a protein-rich human mesothelioma fluid. The ox material has been deproteinized by treatment with chloroform and pentanol and by gradient elution on DEAE-Sephadex; several fractions were obtained by the latter method. These materials can be stored in solution at -20 degrees without change of properties. The ox material contained 21% of protein; all other preparations contained less than 6% of protein. 2. The two materials have been compared by sedimentation and viscosity and shown to be closely similar. Treatment of the ox material with neuraminidase caused no change in its viscosity behaviour. 3. Information about the molecular configuration of the ox material has been obtained from measurements of light-scattering and viscosity. The results, though consistent with a highly extended configuration, are not consistent with a linear random-coil configuration. It is tentatively suggested that the structure may have some degree of branching and of cross-linking, which give it a rigidity with respect to expansion of the molecular domain that would not be possessed by a random coil. 4. The deproteinized material recovered from DEAE-Sephadex, though polydisperse, showed unchanged average molecular weight; however, the average radius of gyration was greater than before this treatment. 5. Acidification to approx. pH3 resulted in a contraction of the structure, with only a slight degree of expansion when the pH was restored to 6.8-7.0. 6. Measurements of optical rotatory dispersion qualitatively support a structure less simple than a linear random coil. 7. Colloid osmotic pressures of mixed solutions of bovine serum albumin and of hyaluronic acid prepared by filtration from ox synovial fluid have been measured. The results agree approximately with those of Laurent & Ogston (1963) but are in quantitative disagreement with the partition measurements of Ogston & Phelps (1960). The relationships between thermodynamic quantities in a quaternary system of electrolytes are discussed in Appendix 2. 8. Refractometric measurements have been made in connexion with light-scattering measurements, as the basis for a convenient method of determining the concentrations of solutions of hyaluronic acids, and to measure the partition of sodium chloride in dialysis experiments. The theory of the last use is discussed in Appendix 1. 9. Sedimentation measurements on the ox preparation have been made up to a concentration of 1.4x10(-2)g./ml. The form of the sedimentation coefficient-concentration relationship is discussed. The value of the sedimentation coefficient at higher concentration is the basis of an illustration of the likely effect of hyaluronic acid on the flow of water through narrow channels in connective tissue. 10. Available colorimetric methods have been shown to give low estimates for glucuronic acid when applied to highly polymerized materials, as compared with estimates by decarboxylation. A spectrop...

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