This theoretical study of the alpha star populations in loaded emulsions was undertaken in an effort to find a quantitative method for the analysis of less than microgram amounts of thorium in the presence of larger amounts of uranium. Analytical expressions for each type of star from each of the significantly contributing members of the uranium and thorium series as well as summation formulas for the whole series have been computed. The analysis for thorium may be made by determining the abundance of five-branched stars in a loaded nuclear emulsion and comparing of observed and predicted star populations. The comparison may also be used to check the half-lives of several members of the uranium and thorium series. ?? 1954.