Lengths and Diameters of Plant Roots in Non-Random Populations by Analysis of Plane Surfaces

Abstract

SUMMARY This paper conisiders the theory associated with an experimental procedure for estiimiating the length of plant roots in soil by calculation from the frequency at which roots intersect planes cut through the soil. To generalize the treatment, roots are assumed to comprise segments each of which is a straight rod. The theory is extended from random distributions of rods to two types of non-randomness: (1) the probability of rods going in a particular direction is represented by the length of a radius of an ellipsoid; (2) the directional probability does not vary from one spot to another, but the total length of rods per unit volume is linear with distance. In both cases it is shown how the length of rods per unit volume may be calculated from the density of intersections in three mutually perpendicular faces which intersect one another symmetrically.