In an earlier paper by the former of the present authors (BOCHER, 1935), a modification of Raunkier's method of frequency determination was described. This modification made it possible to evaluate the density of shoots or individuals in plant communities. However, the experience subsequently gained has indicated the desirability of further modification of the method, and of subjecting it to a critical examination by a statistician. Accordingly, a team-work was organized, the results of which are published in the present paper. The authors chose to write one part each, and the two parts may thus be studied separately by botanically and mathematically interested readers. Ecologists will possibly take an interest in both parts.