1 12 



NA TURE 



[June 4, 1908 



actinij from within and the forces of tension and pressure 

 that niay have acted from without. 



Certain elementary points in regard to the formation of 

 the egg; must be borne in mind : — • 



(i) The " egg," as it enters the oviduct, consists of the 

 volk onlv, enclosed in its vitelline membrane. As it passes 

 down the first portion of the oviduct, the white is gradually 

 superadded, and becomes in turn surrounded by the 

 '■ shell-membrane." .-^bout this latter the shell is secreted, 

 rapidiv and at a late period. 



"(2) Both the yolk and the entire egg tend to fill com- 

 pletely their respective membranes, and, w^hether this be 

 due to growth or imbibition on the part of the contents 

 or to contraction on the part of the surrounding mem- 

 branes, the resulting tendency is for both yolk and egg 

 to be, in the first instance, spherical, unless otherwise 

 distorted by external pressure. 



(j) 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 con- 

 tractions 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 for- 

 ward 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. We may accordingly presume 

 that the more pointed eggs are those that are large re- 

 latively 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 formed or shaped. 

 So general is this relation that we may go still further, 

 and presume with great plausibility in the few exceptional 

 cases (of which the aptery.x 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 (or perhaps weak) 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 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 latter. 



We may now" proceed to inquire more particularlv 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 with a membrane. 



Our problem, then, is ; Given a practically incompressible 

 lluid, contained in a deformable capsule, which is either 

 (a) entirely inextensible, or (6) slightly extensible, and 

 placed in a long elastic tube the walls of which are radially 

 contractile, to determine the shape under pressure. 



(i) If the capsule be spherical, inextensible, and com- 

 pletely filled with the fluid, absolutely no deformation can 

 take place. The few eggs that are actually or approxi- 

 mately 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 cap- 

 sule was so little capable of extension and so completely 

 filled as to preclude the possibility of deformation. 



(2) If the capsule be not spherical, but be inextensible, 

 then deformation can take place under the external radia. 

 compression, 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 



NO. 2014, VOL. 78] 



inextensible envelope cannot be deformed without pucker- 

 ing of the envelope taking place. 



Let us ne.xt 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 fi.xed conditions. The two suppositions are 

 practically identical with one another in effect. 



(3) 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. 



(4) 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. 



(5) 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. 



(6) 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. 



(7) With a given shape and size of body, equilibriuin 

 in the tube may be maintained under greater radial pres- 

 sure towards one end than towards the other. For 

 example, a cylinder having conical ends, of semi-angles 

 S and S' respectively, remains in equilibrium, apart from 

 friction, if p cos-6 = p' cos'B', so that at the more tapered 

 end where 9 is small p is large. Therefore the whole 

 structure might assume such a configuration, or grow 

 under such conditions, finally becoming rigid by solidifi- 

 cation of the envelope. According to the preceding para- 

 graph, we must assume some initial distribution of pres- 

 sure, some squeeze applied to the posterior part of the egg, 

 in order to give it its tapering from. 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. More- 

 over, the above equation shows 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 com- 

 municate to it a forward motion. This is an important 

 consideration, for it shows 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. 



(,S) ' The mathematical statement of the whole case is 

 as follows : — In our egg, consisting of an extensible mem- 

 brane filled with an incompressible fluid and under external 



pressure, the equation of the envelope is /„ + T( -4-— J = P. 



where /)„ 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. 



The above equation is the equation of eijuilibrium, 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 peri- 

 -tiltic wave which causes the movement, as well as by 

 friction. 



The quantity T is the tension of the enclosing capsule — 



1 The mathematical <t.itement is not my own ; I am indebted for it and 

 for ether help in the editing of this paper to my colleague, Prof. W. Peddle. 



