Describing the range of avian egg shapes quantitatively has long been recognized as difficult. A variety of approaches has been adopted, some of which aim to capture the shape accurately and some to provide intelligible indices of shape. The objectives here are to show that a (four‐parameter) method proposed by Preston (1953, The Auk, 70, 160) is the best option for quantifying egg shape, to provide and document an R program for applying this method to suitable photographs of eggs, to illustrate that intelligible shape indices can be derived from the summary this method provides, to review shape indices that have been proposed, and to report on the errors introduced using photographs of eggs at rest rather than horizontal.

The adaptive significance of avian egg shape in birds is poorly understood. The pyriform (pear‐like) shape of the Common Guillemot's Uria aalge egg has long been considered to be an adaptation to prevent eggs rolling off the bare cliff ledges on which this species breeds. Rolling was thought to be prevented either by the egg spinning like a top, which is not the case, or by rolling in an arc, which it does but with little influence on whether the egg will fall from a ledge. We therefore sought alternative explanations for the pyriform shape of the Common Guillemot's egg. This species breeds in extremely dense colonies, which makes their eggs vulnerable to mechanical damage from conspecifics, and to contamination by debris such as faeces and soil. We present evidence consistent with both these possible explanations. First, the pyriform shape of Common Guillemot eggs means that a higher proportion of the eggshell lies in contact with the substrate and this may minimize the effect of impacts. Resistance to impacts may be further enhanced because their eggshells are especially thick where they are in contact with the substrate. Secondly, Common Guillemot eggs are often heavily contaminated with faecal material and other debris during incubation. Most contamination is on the pointed end of the egg where it is in contact with the substrate; the pyriform shape thus keeps the blunt end of the egg, which has the highest porosity, relatively free of contamination, which in turn may facilitate both gas exchange during incubation and the hatching process, because the chick emerges from the blunt end of the egg.

A recent broad comparative study suggested that factors during egg formationin particular 'flight efficiency', which explained only 4% of the interspecific variationare the main forces of selection on the evolution of egg shape in birds. As an alternative, we tested whether selection during the incubation period might also influence egg shape in two taxa with a wide range of egg shapes, the alcids (Alcidae) and the penguins (Spheniscidae). To do this, we analysed data from 30 species of these two distantly related but ecologically similar bird families with egg shapes ranging from nearly spherical to the most pyriform eggs found in birds. The shape of pyriform eggs, in particular, has previously proven difficult to quantify. Using three egg-shape indicespointedness, polar-asymmetry and elongationthat accurately describe the shapes of all birds' eggs, we examined the effects of egg size, chick developmental mode, clutch size and incubation site on egg shape. Linear models that include only these factors explained 70-85% of the variation in these egg-shape indices, with incubation site consistently explaining > 60% of the variation in shape. The five species of alcids and penguins that produce the most pyriform eggs all incubate in an upright posture on flat or sloping substrates, whereas species that incubate in a cup nest have more spherical eggs. We suggest that breeding sites and incubation posture influence the ability of parents to manipulate egg position, and thus selection acting during incubation may influence egg-shape variation across birds as a whole.

A modified form of the magnetic balance previously designed by one of us, is described. In this apparatus the gradient is made independent of the magnetizing field. With such an apparatus measurements have been made on the variation of the intensity of magnetization with magnetic field for single-crystal specimens cut along appropriate crystal axes, both for the hexagonal close-packed and face-centred cubic cobalt. Such measurements enable the magnetic anisotropy constants to be determined. The nature of the phase change from close-packed hexagonal to face-centred cubic occurring at about 400° C is such that single crystals can be cut at room temperature, which will transform to give single crystals of known orientation in the face-centred cubic phase. The values of the magnetic anistropy constants for the hexagonal phase for various temperatures are compared with those of earlier determinations and fair agreement is found. Measurements on the face-centred cubic phase were made every 50° C in the temperature range 500 to 1000° C; at the latter temperature the material became magnetically isotropic. For face-centred cubic cobalt it was found that the crystal directions in order of increasing difficulty of magnetization are [111], [110] and [100], as is the case for nickel. Moreover, the value of the anisotropy constant k 1 obeys the same empirical law, giving the variation with temperature, as nickel. The similarity in the magnetic behaviour of these two ferromagnetics having the same crystal structure is thus evident.

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