658 ON THE SHAPES OF EGGS [ch. 



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 reheved. Moreover, 

 the above equation shews that a normal pressure no greater and 

 (within certain hmits) 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^-^ T {Ijr -rljr') ^ P, where 'p^^ 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 httle or nothing to do with the 

 factor of external pressure (p„), 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 



