Chord intercepts in the two-dimensional cell model

The two-dimensional cell model is defined by the following conditions of its formation: athermal nuclei may be randomly (Poisson) distributed in a thin amorphous film. From these nuclei spherulites may start to grow instantaneously, circularly, and at the same rate. Where two spherulites touch growth stops, and all points of contact form a straight intersection between neighboring spherulites. Finally, if the film contains spherulites only, each spherulite (cell) is completely limited by straight intersections, forming an irregular polygon. All irregular polygons of the film together form a planar irregular net of straight intersections. In quantitative microscopy this net is characterized by a “lineal analysis.” A straight line (Rosiwal's line) is arbitrarily put into the plane of the net. The net divides Rosiwal's line into chord intercepts of different lengths. The distribution of these lengths is analytically derived in the present paper by use of the theory of probability.