In this Bureau of Mines report, appropriate equations correlating the activity of water with the activities of electrolytes in binary and multicomponent solutions have been derived for computer calculation. It was found that the half-integer power series are far superior to the integer power series, for both types of series having the same number of terms. The proposed method of calculation is capable of accurately yielding the activities of all components from the measurements of the activity of a single component at various concentrations. This method replaces the cumbersome and objectionable method of graphical integration of the Gibbs-Duhem equation. Two novel methods are proposed for determination of activities of electrolyte solutions important in hydrometallurgy: (1) water vapor pressure measurement by differential pressure transducers having an accuracy of 0.001 pct, and (2) transpiration method with an inert gas bubbled through concentrated solutions followed by the analysis of the evaporated and redissolved electrolytes with specific ion electrodes having a sensitivity of +/- 10-10 molal. The first method is suitable for nonvolatile electrolytes, and the second, for volatile electrolytes such as hydrogen halides, hno3, h2so3, etc. The existing methods of estimation of ionic activities have been surveyed, and the best method has been selected, discussed, and summarized.