We examine some theoretical and experimental aspects of the measurement of interfacial tension, stress relaxation in elongational flow, and yield stresses in organic liquids, blends of polymer melts, and liquid crystal polymers. This study is based on an instrument which is an improved version of the spinning drop apparatus that is commonly used to measure interfacial tension between melted polymers. Problems of vibrations at high speed, heating of the bearings, high temperatures required to melt the polymers, outgassing at the reduced pressures generated by rotation, and other problems have been eliminated in the improved apparatus. This same instrument can be used to generate curves of volume expansion versus temperature for blended systems and to detect and interpret yield stresses which occur in some polymers and strongly influence the properties of blends. The instrument has been enhanced for accurate measurements of drop diameter, length and shape as a function of time and initial conditions. A theory of upper and lower bounds for interfacial tension and a theoretically based method of exponential fitting has been developed to help to overcome the problems of slow approach to equilibrium between highly viscous melts. We have developed and propose to develop further a theory of relaxation in which transient measurements of drop diameter can be used to obtain rheological properties like elongational and yield stresses and interfacial tension and more generally to interpret the curves of relaxation generated in the experiments.