The hen's egg: Estimation of shell superficial area and egg volume from four shell measurements

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Abstract
In research on egg shell strength it is often necessary to estimate the shell's superficial area or the egg's volume without recourse to water displacement. Accurate methods are available but they entail making numerous measurements of the shell. Approximate methods that require only three measurements are available but suffer from two disadvantages; they entail measuring the distance from the plane of maximum breadth to a pole, which is difficult to do accurately, and they make no provision for variation in the degree of plumpness (marilynia) of the egg at levels between the plane of maximum breadth and the poles. A simple method is described that is free of these disadvantages. Four measurements are made: the length, L, and maximum breadth, B, of the egg and the distances, X 1 and L − X 2, by which the poles project into an annulus of radius R. Each of these is divided by L to give quotients 1, b, x 1, x 2 and r. A skewness parameter p is estimated by solving the equation and its value is inserted in the equation which is then solved for the marilynia parameter n. These values of p and n are inserted in the equations which together describe the profile of a figure with a shape approximating closely to that of the egg. The superficial area, s, and volume, v, of the corresponding solid of revolution are found by integration. Estimates of the superficial area, S, and volume, V, of the egg are given by The method was tested by comparing the computed volumes of 64 eggs from hens of four strains with those measured by water displacement. It showed a nonsignificant systematic error of +0.06% and a random error standard deviation of 0.18% of mean egg volume.