The Avian Egg: Surface Area, Volume, and Density

The surface area of the avian egg through which the developing embryo must exchange heat, metabolic gases, and water vapor is a variable of prime importance for quantitation of the permeability of the egg shell to these substances. Surface-area measurements are necessary if one is to compare the permeability properties of shells ranging in size from less than 0.5 g in hummingbirds, to 1.5 kg in the Ostrich (Struthio camelus), and to more than 10 kg in the extinct Aepyornis. In the course of experiments designed to measure and compare the water vapor permeability of eggs of many species (Ar et al. 1974), we found it necessary to develop a method of measuring surface area that was both convenient and accurate. The problem of surface-area measurement in eggs is complicated by the fact that eggs come in a variety of shapes, few of which can be described by simple, analytic functions. Shapes vary from the nearly spherical eggs of owls to the sharply pointed eggs of murres and gulls. In their classic text, Romanoff and Romanoff (1949) reviewed many of the empirical and theoretical formulas for calculating surface area and volume of eggs. Although a mathematical description of surface area and volume was developed by Carter (1968) for the hen’ s egg, we required a method which would be applicable to eggs of any shape, as long as there was circular symmetry about an axis of rotation. Once such a method was developed, it was used to establish allometric relations between surface area and egg weight and volume. Correlative data provided by Schijnwetter (1960-71) enabled us to define additional relations between egg weight (as the independent variable), and shell weight, shell density, and egg density ( as dependent variables).