In the theories of the conductivity and viscosity of electrolyte solutions originally developed by Debye & Huckel, and Falkenhagen and his co-workers, the ions were regarded as dimensionless point charges. In the theory of activity and osmotic coefficients developed by Gronwall, La Mer & Sandved the ions were assumed to be of finite size, having a distance of closest approach, a. Making use of the Gronwall et al. results, the concept of closest approach has been introduced into the theories of conductivity and viscosity. These quantities are obtained in the form of infinite series, of which only the first few terms have been calculated, owing to the great complexity of the work. In the case of conductivity, for 1-1 salts in water the approximate range of validity of the results is for concentrations less than N/10. Complete quantitative agreement with experiment is found. Under other experimental conditions the calculated conductivity shows the correct qualitative behaviour. The new theory of viscosity should possess a similar range of validity, but comparison with experiment shows that the treatment gives no improvement on the Falkenhagen results. In their paper, Gronwall et al. gave only a very limited comparison between their theory and experiment. It has been necessary to extend this comparison, and values of a found thereby are compared in table 2 with those obtained from the new theory of conductivity. The significance of these values is discussed in the last section of the paper, together with reasons for the success of the conductivity theory and the absence of any improvement in the viscosity theory.