842 THE l^QUIANGULAR SPIRAL [ch. 



side walls of the cone at other than a right angle, as in Fig. 416; 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 the outhne of 

 the septum will be an elhpse, but its surface will still be spheroidal. If 



Fig. 41fi. 



the attachment of the septum be not in one plane, but forms a sinuous 

 line of contact with the cone, then the septum will be a saddle-shaped 

 surface, of great complexity and beauty. In all cases, provided only 

 that the membrane be isotropic, the form assumed will be precisely 

 that of a soap-bubble under similar conditions of attachment : that 

 is to say, it will be (with the usual limitations or conditions) a surface 

 of minimal area, and of constant mean curvature. 



If our cone be no longer straight, but curved, then the septa will 

 by symmetrically deformed in consequence. A beautiful and in- 

 teresting case is afforded us by Nautilus itself. Here the outline 

 of the septum, referred to a plane, is approximately bounded by 

 two elliptic curves, similar and similarly situated, whose areas are 

 to one another in a definite ratio, namely as 



A_^l^'l_ 4^C0ta 

 ^a ^2^ 2 



and a similar ratio exists in Ammonites and all other close-whorled 

 spirals, in whi^h however we cannot always make the simple 



