Chapter XV on the Shapes of Eggs, and of Certain Other Hollow Structures

The eggs of birds and all other hard-shelled eggs, such as those of the tortoise and the crocodile, are simple solids of revolution; but they differ greatly in form, according to the configuration of the plane curve by the revolution of which the egg is, in a math­e­mat­i­cal sense, generated. Some few eggs, such as those of the owl, the penguin, or the tortoise, are spherical or very nearly so; a few more, such as the grebe’s, the cormorant’s or the pelican’s, are ap­prox­i­mate­ly ellipsoidal, with symmetrical or nearly symmetrical ends, and somewhat similar are the so-called “cylindrical” eggs of the megapodes and the sand-grouse; the great majority, like the hen’s egg, are ovoid, a little blunter at one end than the other; and some, by an exaggeration of this lack of antero-posterior symmetry, are blunt at one end but char­ac­teris­ti­cally pointed at the other, as is the case with the eggs of the guillemot and puffin, the sandpiper, plover and curlew. It is an obvious but by no means negligible fact that the egg, while often pointed, is never flattened or discoidal; it is a prolate, but never an oblate, spheroid.

The careful study and collection of birds’ eggs would seem to have begun with the Count de Marsigli, the same celebrated naturalist who first studied the “flowers” of the coral, and who wrote the Histoire physique de la mer; and the specific form, as well as the colour and other attributes of the egg have been again and again discussed, and not least by the many dilettanti naturalists of the eighteenth century who soon followed in Marsigli’s footsteps. {653}

We need do no more than mention Aristotle’s belief, doubtless old in his time, that the more pointed egg produces the male chicken, and the blunter egg the hen; though this theory survived into modern times and perhaps still lingers on. Several naturalists, such as Günther (1772) and Bühle (1818), have taken the trouble to disprove it by experiment. A more modern and more generally accepted explanation has been that the form of the egg is in direct relation to that of the bird which has to be hatched within—a view that would seem to have been first set forth by Naumann and Bühle, in their great treatise on eggs, and adopted by Des Murs and many other well-known writers.

In a treatise by de Lafresnaye, an elaborate comparison is made between the skeleton and the egg of the various birds, to shew, for instance, how those birds with a deep-keeled sternum laid rounded eggs, which alone could accommodate the form of the young. According to this view, that “Nature had foreseen” the form adapted to and necessary for the growing embryo, it was easy to correlate the owl with its spherical egg, the diver with its elliptical one, and in like manner the round egg of the tortoise and the elongated one of the crocodile with the shape of the creatures which had afterwards to be hatched therein. A few writers, such as Thienemann, looked at the same facts the other way, and asserted that the form of the egg was determined by that of the bird by which it was laid, and in whose body it had been conformed.

In more recent times, other theories, based upon the principles of Natural Selection, have been current and very generally accepted, to account for these diversities of form. The pointed, conical egg of the guillemot is generally supposed to be an adaptation, {654} advantageous to the species in the circumstances under which the egg is laid; the pointed egg is less apt than a spherical one to roll off the narrow ledge of rock on which this bird is said to lay its solitary egg, and the more pointed the egg, so much the fitter and likelier is it to survive. The fact that the plover or the sandpiper, breeding in very different situations, lay eggs that are also conical, elicits another explanation, to the effect that here the conical form permits the many large eggs to be packed closely under the mother bird. Whatever truth there be in these apparent adaptations to existing circumstances, it is only by a very hasty logic that we can accept them as a vera causa, or adequate explanation of the facts; and it is obvious that, in the bird’s egg, we have an admirable case for the direct in­ves­ti­ga­tion of the mechanical or physical significance of its form.

Of all the many naturalists of the eighteenth and nineteenth centuries who wrote on the subject of eggs, one alone (so far as I am aware) ascribed the form of the egg to direct mechanical causes. Günther, in 1772, declared that the more or less rounded or pointed form of the egg is a mechanical consequence of the pressure of the oviduct at a time when the shell is yet unformed or unsolidified; and that accordingly, to explain the round egg of the owl or the kingfisher, we have only to admit that the oviduct of these birds is somewhat larger than that of most others, or less subject to violent contractions. This statement contains, in essence, the whole story of the mechanical conformation of the egg.

Let us consider, very briefly, the conditions to which the egg is subject in its passage down the oviduct.

• (1) The “egg,” as it enters the oviduct, consists of the yolk only, enclosed in its vitelline membrane. As it passes down the first portion of the oviduct, the white is gradually superadded, {655} and becomes in turn surrounded by the “shell-membrane.” About this latter the shell is secreted, rapidly and at a late period; the egg having meanwhile passed on into a wider portion of the oviducal tube, called (by loose analogy, as Owen says) the “uterus.” Here the egg assumes its permanent form, here it becomes rigid, and it is to this portion of the “oviduct” that our argument principally refers.
• (2) Both the yolk and the entire egg tend to fill completely their respective membranes, and, whether this be due to growth or imbibition on the part of the contents or to contraction on the part of the surrounding membranes, the resulting tendency is for both yolk and egg to be, in the first instance, spherical, unless otherwise distorted by external pressure.
• (3) The egg is subject to pressure within the oviduct, which is an elastic, muscular tube, along the walls of which pass peristaltic waves of contraction. These muscular contractions may be described as the contraction of successive annuli of muscle, giving annular (or radial) pressure to successive portions of the egg; they drive the egg forward against the frictional resistance of the tube, while tending at the same time to distort its form. While nothing is known, so far as I am aware, of the muscular physiology of the oviduct, it is well known in the case of the intestine that the presence of an obstruction leads to the development of violent contractions in its rear, which waves of contraction die away, and are scarcely if at all propagated in advance of the obstruction.
• (4) It is known by observation that a hen’s egg is always laid blunt end foremost.
• (5) It can be shown, at least as a very common rule, that those eggs which are most unsymmetrical, or most tapered off posteriorly, are also eggs of a large size relatively to the parent bird. The guillemot is a notable case in point, and so also are the curlews, sandpipers, phaleropes and terns. We may accordingly presume that the more pointed eggs are those that are large relatively to the tube or oviduct through which they have to pass, or, in other words, are those which are subject to the greatest pressure while being forced along. So general is this relation that we may go still further, and presume with great plausibility {656} in the few exceptional cases (of which the apteryx is the most conspicuous) where the egg is relatively large though not markedly unsymmetrical, that in these cases the oviduct itself is in all probability large (as Günther had suggested) in proportion to the size of the bird. In the case of the common fowl we can trace a direct relation between the size and shape of the egg, for the first eggs laid by a young pullet are usually smaller, and at the same time are much more nearly spherical than the later ones; and, moreover, some breeds of fowls lay proportionately smaller eggs than others, and on the whole the former eggs tend to be rounder than the latter598.

We may now proceed to inquire more particularly how the form of the egg is controlled by the pressures to which it is subjected.

The egg, just prior to the formation of the shell, is, as we have seen, a fluid body, tending to a spherical shape and enclosed within a membrane.

Our problem, then, is: Given a practically incompressible fluid, contained in a deformable capsule, which is either (a) entirely inextensible, or (b) slightly extensible, and which is placed in a long elastic tube the walls of which are radially contractile, to determine the shape under pressure.

If the capsule be spherical, inextensible, and completely filled with the fluid, absolutely no deformation can take place. The few eggs that are actually or ap­prox­i­mate­ly spherical, such as those of the tortoise or the owl, may thus be alternatively explained as cases where little or no deforming pressure has been applied prior to the solidification of the shell, or else as cases where the capsule was so little capable of extension and so completely filled as to preclude the possibility of deformation.

If the capsule be not spherical, but be inextensible, then deformation can take place under the external radial compression, {657} only provided that the pressure tends to make the shape more nearly spherical, and then only on the further supposition that the capsule is also not entirely filled as the deformation proceeds. In other words, an incompressible fluid contained in an inextensible envelope cannot be deformed without puckering of the envelope taking place.

Let us next assume, as the conditions by which this result may be avoided, (a) that the envelope is to some extent extensible, or (b) that the whole structure grows under relatively fixed conditions. The two suppositions are practically identical with one another in effect. It is obvious that, on the presumption that the envelope is only moderately extensible, the whole structure can only be distorted to a moderate degree away from the spherical or spheroidal form.

At all points the shape is determined by the law of the distribution of radial pressure within the given region of the tube, surface friction helping to maintain the egg in position. If the egg be under pressure from the oviduct, but without any marked component either in a forward or backward direction, the egg will be compressed in the middle, and will tend more or less to the form of a cylinder with spherical ends. The eggs of the grebe, cormorant, or crocodile may be supposed to receive their shape in such circumstances.

When the egg is subject to the peristaltic contraction of the oviduct during its formation, then from the nature and direction of motion of the peristaltic wave the pressure will be greatest somewhere behind the middle of the egg; in other words, the tube is converted for the time being into a more conical form, and the simple result follows that the anterior end of the egg becomes the broader and the posterior end the narrower.

With a given shape and size of body, equi­lib­rium in the tube may be maintained under greater radial pressure towards one end than towards the other. For example, a cylinder having conical ends, of semi-angles θ and θ ′ respectively, remains in equi­lib­rium, apart from friction, if p cos θ = p ′ cos θ ′, so that at the more tapered end where θ is small p is small. Therefore the whole structure might assume such a configuration, or grow under such conditions, finally becoming rigid by solidification of the envelope. {658} According to the preceding paragraph, we must assume some initial distribution of pressure, some squeeze applied to the posterior part of the egg, in order to give it its tapering form. But, that form once acquired, the egg may remain in equi­lib­rium both as regards form and position within the tube, even after that excess of pressure on the posterior part is relieved. Moreover, the above equation shews that a normal pressure no greater and (within certain limits) actually less acting upon the posterior part than on the anterior part of the egg after the shell is formed will be sufficient to communicate to it a forward motion. This is an important consideration, for it shews that the ordinary form of an egg, and even the conical form of an extreme case such as the guillemot’s, is directly favourable to the movement of the egg within the oviduct, blunt end foremost.

The math­e­mat­i­cal statement of the whole case is as follows: In our egg, consisting of an extensible membrane filled with an incompressible fluid and under external pressure, the equation of the envelope is p n + T(1 ⁄ r + 1 ⁄ r ′) = P, where p n is the normal component of external pressure at a point where r and r ′ are the radii of curvature, T is the tension of the envelope, and P the internal fluid pressure. This is simply the equation of an elastic surface where T represents the coefficient of elasticity; in other words, a flexible elastic shell has the same math­e­mat­i­cal properties as our fluid, membrane-covered egg. And this is the identical equation which we have already had so frequent occasion to employ in our discussion of the forms of cells; save only that in these latter we had chiefly to study the tension T (i.e. the surface-tension of the semi-fluid cell) and had little or nothing to do with the factor of external pressure (p n), which in the case of the egg becomes of chief importance.

The above equation is the equation of equi­lib­rium, so that it must be assumed either that the whole body is at rest or that its motion while under pressure is not such as to affect the result. Tangential forces, which have been neglected, could modify the form by alteration of T. In our case we must, and may very reasonably, assume that any movement of the egg down the oviduct during the period when its form is being impressed upon it is very slow, being possibly balanced by the advance of the {659} peristaltic wave which causes the movement, as well as by friction.

The quantity T is the tension of the enclosing capsule—the surrounding membrane. If T be constant or symmetrical about the axis of the body, the body is symmetrical. But the abnormal eggs that a hen sometimes lays, cylindrical, annulated, or quite irregular, are due to local weakening of the membrane, in other words, to asymmetry of T. Not only asymmetry of T, but also asymmetry of p n, will render the body subject to deformation, and this factor, the unknown but regularly varying, largely radial, pressure applied by successive annuli of the oviduct, is the essential cause of the form, and variations of form, of the egg. In fact, in so far as the postulates correspond near enough to actualities, the above equation is the equation of all eggs in the universe. At least this is so if we generalise it in the form p n + T ⁄ r + T ′ ⁄ r ′ = P in recognition of a possible difference between the principal tensions.

In the case of the spherical egg it is obvious that p n is everywhere equal. The simplest case is where p n = 0, in other words, where the egg is so small as practically to escape deforming pressure from the tube. But we may also conceive the tube to be so thin-walled and extensible as to press with practically equal force upon all parts of the contained sphere. If while our egg be in process of conformation the envelope be free at any part from external pressure (that is to say, if p n = 0), then it is obvious that that part (if of circular section) will be a portion of a sphere. This is not unlikely to be the case actually or ap­prox­i­mate­ly at one or both poles of the egg, and is evidently the case over a considerable portion of the anterior end of the plover’s egg.

In the case of the conical egg with spherical ends, as is more or less the case in the plover’s and the guillemot’s, then at either end of the egg r and r ′ are identical, and they are greater at the blunt anterior end than at the other. If we may assume that p n vanishes at the poles of the egg, then it is plain that T varies in the neighbourhood of these poles, and, further, that the tension T is greatest at and near the small end of the egg. It is here, in short, that the egg is most likely to be irregularly distorted or {660} even to burst, and it is here that we most commonly find irregularities of shape in abnormal eggs.

If one portion of the envelope were to become practically stiff before p ceases to vary, that would be tantamount to a sudden variation of T, and would introduce asymmetry by the imposition of a boundary condition in addition to the above equation.

Within the egg lies the yolk, and the yolk is invariably spherical or very nearly so, whatever be the form of the entire egg. The reason is simple, and lies in the fact that the yolk is itself enclosed in another membrane, between which and the outer membrane lies a fluid the presence of which makes p n for the inner membrane practically constant. The smallness of friction is indicated by the well-known fact that the “germinal spot” on the surface of the yolk is always found uppermost, however we may place and wherever we may open the egg; that is to say, the yolk easily rotates within the egg, bringing its lighter pole uppermost. So, owing to this lack of friction in the outer fluid, or white, whatever shear is produced within the egg will not be easily transmitted to the yolk, and, moreover, owing to the same fluidity, the yolk will easily recover its normal sphericity after the egg-shell is formed and the unequal pressure relieved.

These, then, are the general principles involved in, and illustrated by, the configuration of an egg; and they take us as far as we can safely go without actual quantitative determinations, in each particular case, of the forces concerned.

In certain cases among the invertebrates, we again find instances of hard-shelled eggs which have obviously been moulded by the oviduct, or so-called “ootype,” in which they have lain: and not merely in such a way as to shew the effects of peristaltic pressure upon a uniform elastic envelope, but so as to impress upon the egg the more or less irregular form of the cavity, within which it had been for a time contained and compressed. After this fashion Dr Looss of Cairo has {661} explained the curious form of the egg in Bilharzia (Schistosoma) haematobium, a formidable parasitic worm to which is due a disease wide-spread in Africa and Arabia, and an especial scourge of the Mecca pilgrims. The egg in this worm is provided at one end with a little spine, which now and then is found to be placed not terminally but laterally or ventrally, and which when so placed has been looked upon as the mark of a supposed new species, S. Mansoni. As Looss has now shewn, the little spine must be explained as having been moulded within a little funnel-shaped expansion of the uterus, just where it communicates with the common duct leading from the ovary and yolk-gland; by the accumulation of eggs in the ootype, the one last formed is crowded into a sideways position, and then, where the side-wall of the egg bulges in the funnel-shaped orifice of the duct, a little lateral “spine” is formed. In another species, S. japonicum, the egg is described as bulging into a so-called “calotte,” or bubble-like convexity at the end opposite to the spine. This, I think, may, with very little doubt, be ascribed to hardening of the egg-shell having taken place just at the period when partial relief from pressure was being experienced by the egg in the neighbourhood of the dilated orifice of the oviduct.

This case of Bilharzia is not, from our present point of view, a very important one, but nevertheless it is interesting. It ascribes to a mechanical cause a curious peculiarity of form; it shews, by reference to this mechanical principle, that two conditions which were very different to the systematic naturalist’s eye, were really only two simple mechanical modifications of the same thing; and it destroys the chief evidence for the existence of a supposed new species of worm, a continued belief in which, among worms of such great pathogenic importance, might lead to gravely erroneous pathological deductions.