The Volume of an Egg

RECENTLY I have received several inquiries as to how one calculates the volume of an egg from its dimensions, and by dimensions is meant the length and the maximum breadth. The answer is that it cannot be done with any real accuracy on the basis of only two measurements. I have shown (Preston 1969) that the shape, i.e. the longitudinal contour, of an egg and its size can be described with a high order of accuracy by means of four parameters, length, breadth, asymmetry, and bicone, and that it cannot usually be described with less. The contour determines the volume, and hence volume cannot be estimated from two measurements only. In cross section an egg is remarkably circular. It is therefore legitimate to consider an egg as a of revolution, and this assumption is always made. An egg lies between two simple geometrical figures, a cylinder and a true bicone. In Figure IA, we show a cylinder of length L (= 2b) and diameter B (= 2a). Its volume is (7r/4) * LB2 or 2rba2. An ellipsoidal egg of length L and diameter B would lie entirely inside the cylinder, touching the centers of both ends and making contact with the cylindrical surface on a circle. In Figure 1B, we show a bicone. Its volume is (7r/12) * LB2. Our egg would lie entirely outside the surfaces of the bicone, and, if symmetrical, it would pass through the apices of the two cones and would touch the bases of the cones all the way round. If our egg is asymmetrical, it would touch the same points and places of the bicone in Figure 1C, whose volume is still (7X/12) LB2. We may surmise therefore that in real eggs, which lie between Figures lA and 1C, asymmetry (the extent to which one end is bigger or blunter than the other) makes little difference to volume, but bicone makes a great deal, the coefficient of LB2 varying somewhat but lying between (Ir/4) and (7r/12). The preliminary assumption of the early writers is that the egg is, to a first approximation, an ellipsoid of revolution. If so, its volume would be (7r/6) * LB2. The approximation is sometimes quite good, and taking r = (22/7), the formula becomes