XV] AND OTHER HOLLOW STRUCTURES 941 



and without momentum; and the question, common in dynamical 

 problems, of the relation between the period of the appHcation of 

 the force and the free period of response or adjustment to it need 

 not concern us at all. 



Again, the case of the egg is somewhat akin to a hydrodynamical 

 problem ; for as it lies in the oviduct we may look on it as a stationary 

 body round which waves are flowing, with the same result as when 

 a body moves through a fluid at rest. Thus we may treat it as a 

 hydrodynamical problem, but a very simple one — simphfied by the 

 absence of all eddies and every form of turbulence; and we come 

 to look on the egg as a streamlined structure, though its streamlines 

 are of a very simple kind. 



The mathematical statement of the case begins 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 (1/r + \jr') = 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 senii-fluid cell) and had little or nothing to do with the factor 

 of external pressure (^„), which in the case of the egg becomes of 

 chief importance. 



To enquire how an elastic sphere or spheroid will be deformed 

 in passing down a peristaltic tube is an ill-defined and indeterminate 

 problem ; but we can study the effect produced in the shape of any 

 particular egg, and so far infer the forces which have been in action. 

 We need only study a single meridian of the egg, inasmuch as we 

 have found it to be a solid of revolution. At successive points 

 along this meridian, let us determine the amount of curvature, that 

 is to say the principal radii of curvature, in latitude and longitude, 

 in the Gaussian formula P = pn + T (1/r 4- l/r') : or, as we may write 

 it if we have any reason to doubt the uniformity or isotropy of the 



