This paper describes the theoretical investigations which have been made in an effort to clarify several well-established but unexplained observations by previous workers who have carried out experiments by the unusual osmotic-pressure technique known as isothermal distillation. The treatment is essentially thermodynamic, and leads to the derivation of equations which agree with the accumulated experimental evidence while showing how substantial improvements in performance can be achieved by designing the apparatus in accordance with the guidance given by the theoretical study. One of the derived equations stresses the importance of good thermal conduction between the solvent and solution inside the stillhead, while another gives a quantitative relationship between thermostat temperature fluctuations and osmoticpressure errors. A description is then given of the essential features of the experimental apparatus which has been built for the application of these theoretical advances to the measurement of the molecular weights of high polymers.