The method of moments, as originally developed by statisticians, must be applied within some definite mathematical framework. Outside of such a framework the measures lose much of their effectiveness. Used properly, the method provides perhaps the most concise way to describe distributions and to quantify the differences among them. The method offers an alternative means for judging the value of the conventional graphical cumulative curve techniques. By its use the "line segments" seen on such cumulative curves can be understood as mathematical artifacts and be seen to have no necessary relation to possible grain subpopulations.