592 THE SPIRAL SHELLS [ch. 



chambered Foraminifera, are convex outwards (Fig. 308), whereas 

 they are concave outwards in Nautilus (Fig. 304) and in the rest 

 of the chambered molluscan shells. The reason is perfectly 

 simple. In both cases the curvature of the septum was deter- 

 mined before it became rigid, and at a time when it had the 

 properties either of a fluid film or an elastic membrane. In both 

 cases the actual curvature is determined by the tensions of the 

 membrane and the pressures to which it was exposed. Now it 

 is obvious that the extrinsic pressure which the tension of the 

 membrane has to withstand is on opposite sides in the two cases. 

 In Nautilus, the pressure to be resisted is that produced by the 

 growing body of the animal, lying to the outer side of the septum, 

 in the outer, wider portion of the tubular shell. In the Foraminifer 

 the septum at the time of its formation was no septum at all; 

 it was but a portion of the convex surface of a drop — that portion 

 namely which afterwards became overlapped and enclosed by the 

 succeeding drop; and the curvature of the septum is concave 

 towards the pressure to be resisted, which latter is inside the 

 septum, being simply the hydrostatic pressure of the fluid contents 

 of the drop. The one septum is, speaking generally, the reverse 

 of the other; the organism, so to speak, is outside the one and 

 inside the other; and in both cases ahke, the septum tends to 

 assume the form of a surface of minimal area, as permitted, or as 

 defined, by all the circumstances of the case. 



The logarithmic spiral is easily recognisable in typical cases* 

 (and especially where the spire makes more than one visible 

 revolution about the pole), by its fundamental property of con- 

 tinued similarity : that is to say, by reason of the fact that the 

 big many-chambered shell is of just the same shape as the smaller 

 and younger shell — which phenomenon is apparent and even 

 obvious in the nautiloid Foraminifera, as in Nautilus itself: but 

 nevertheless the nature of the curve must be verified by careful 

 measurement, just as Moseley determined or verified it in his 



* Tt is obvious that the actual outline of a foraminiferal, just as of a molluscan 

 shell, may depart \videl3'^ from a logarithmic spiral. When we say here, for short, 

 that the shell is a logarithmic spiral, we merely mean that it is essentially related 

 to one: that it can be inscribed in such a spiral, or that corresponding points 

 (such, for instance, as the centres of gravity of successive chambers, or the 

 extremities of successive septa) will always be found to lie upon such a spiral. 



