XI] 



OF SEPTA 



579 



elastic membrane. They must then follow the general law, 

 applicable to all elastic membranes under uniform pressure, that 

 the tension varies inversely as the radius of curvature; and we 

 come back once more to our old equation of Laplace, that 



'1 



P = T 



r'J' 



Moreover, since the cavity below the septum is practically 

 closed, and is filled either with air or with 

 water, P will be constant over the whole 

 area of the septum. And further, we must 

 assume, at least to begin with, that the 

 membrane constituting the incipient septum 

 is homogeneous or isotropic. 



Let us take first the case of a straight 

 cone, of circular section, more or less like an 

 Orthoceras ; and let us suppose that the 

 septum is attached to the shell in a plane 

 perpendicular to its axis. The septum itself 

 must then obviously be spherical. Moreover 

 the extent of the spherical surface is constant, 

 and easily determined. For obviously, in 

 Fig. 302, the angle LCL' equals the sup- 

 plement of the angle [LOL') of the cone; that is to say, the 

 circle of contact subtends an angle at the 

 centre of the spherical surface, which is con- 

 stant, and which is equal to tt — 26. The 

 case is not excluded where, owing to an asym- 

 metry of tensions, the septum meets the side 

 walls of the cone at other than a right angle, as 

 in Fig. 303 ; and here, while the septa still 

 remain portions of spheres, the geometrical 

 construction for the position of their centres is 

 equally easy. 



If, on the other hand, the attachment of the 

 septum to the inner walls of the cone be in a 

 plane oblique to the axis, then it is evident that 

 the outline of the septum will be an ellipse, and its surface an 



37—2 



Fig. 303. 



