Introduction

The egg of a bird can be envisaged as a naturally occuring organ culture which, given sufficient heat and oxygen, allows the original single cell to transform the acellular substrate into a complex multicellular animal. The feature of the system which concerns us in this chapter is the calcareous shell which imparts a fixed shape to this system. A typical avian egg presents to the eye a regular profile, symmetrical about its long axis with one end more pointed than the other yet this shape has been strangely difficult to characterise mathematically. An equation describing egg curvature is useful as a shape descriptor and for understanding the forces which give rise to the ovoid form. Also, since an egg is axisymmetric, an equation that can be solved from simple linear measurements allows the volume and surface area of the solid of revolution generated by its profile to be calculated by integration (Paganelli, Olszowka & Ar, 1974).

Egg volume and surface area are rather special parameters as they are constants of the system. It is remarkable that a given volume of organic molecules, constituting a new-laid egg, is constrained within an envelope of constant area through which all respiratory exchanges must be conducted. This predetermined surface area, established when only one diploid nucleus is present, must eventually be compatible with mediating the gaseous transfer required by the many millions of aerobically respiring cells of the embryo (Paganelli, Chapter 16).