The Shapes of Birds' Eggs: Mathematical Aspects

In the Handbook of North American birds the description of egg sizes, and more particularly of egg shapes, proceeds on somewhat different lines from those of previous works. The present paper explains the methods of measuring and methods of "reducing" the observations. The elements actually measured are the conventional average length and breadth, plus the (unconventional) radii of the blunt and pointed ends. The standard deviations of each of these are estimated from the sample. From these measurements, all of which in effect are measurements of size, certain dimensionless quantities are derived hereinafter referred to as asymmetry, bicone, and elongation. These are specifications of shape independent of size. This paper sets forth the theory, modifies the theory to achieve maximum practical utility, and gives reasons for believing the results valid and adequate. In addition methods of sampling are discussed, and a new procedure of sampling is given for getting somewhat more representative results than heretofore.