XII] OF THE FORAMINIFERA 855 



In both cases the curvature of the septum was determined before 

 it became rigid, and at a time when it had the properties 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 with- 

 stand 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 



Fig. 423. Nummulina antiquior R. and V. After V. von Moller. 



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 alike, 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 



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

 shell, may depart widely 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 be found to lie upon such a sj)iral. 



