578 THE LOGARITHMIC SPIRAL [ch. 



to that which it occupied before: just, indeed, as a httle ball 

 drops far down into the cone, but a big one must stay farther up. 

 Then, when the animal after a period of growth has moved farther 

 up in the shell, the mantle- surface continues its normal secretory 

 activity, and that portion which had been in contact with the 

 former septum secretes a septum anew. In short, at any given 

 epoch, the creature is not secreting a tube and a septum by 

 separate operations, but is secreting a shelly case about its rounded 

 body, of which case one part appears to us as the continuation 

 of the tube, and the other part, merging with it by indistinguishable 

 boundaries, appears to us as the septum*. 



The various forms assumed by the septa in spiral shells'}" 

 present us with a number of problems of great beauty, simple in 

 their essence, but whose full investigation would soon lead us 

 into mathematics of a very high order. 



We do not know in great detail how these septa are laid down ; 

 but the essential facts are clear J. The septum begins as a very 

 thin cuticular membrane (composed apparently of a substance 

 called conchyolin), which is secreted by the skin, or mantle- 

 surface, of the animal ; and upon this membrane nacreous matter 

 is gradually laid down on the mantle-side (that is to say between 

 the animal's body and the cuticular membrane which has been 

 thrown off from it), so that the membrane remains as a thin pellicle 

 over the hinder surface of the septum, and so that, to begin with, 

 the membranous septum is moulded on the flexible and elastic 

 surface of the animal, within which the fluids of the body must 

 exercise a uniform, or nearly uniform pressure. 



Let us think, then, of the septa as they would appear in their 

 uncalcified condition, formed of, or at least superposed upon, an 



* "It has been suggested, and I think in some quarters adopted as a dogma, 

 that the formation of successive septa [in Nautilus] is correlated with the recurrence 

 of reproductive periods. This is not the case, since, according to my observations, 

 propagation only takes place after the last septum is formed;" WiUey, Zoological 

 Results, p. 746, 1902. 



f Cf. Woodward, Henry, On the Structure of Camerated Shells, Pop. Set. Rev. 

 XI, pp. 113-120, 1872. 



X See WiUey, Contributions to the Natural History of the Pearly Nautilus, 

 Zoological Results, etc. p. 749, 1902. Cf. also Bather, Shell-growth in Cephalopoda, 

 A7m. Mag. N. H. (6), i, pp 298-310^ 1888; ibid. pp. 421-427, and other papers by 

 Blake, Riefstahl, etc. quoted therein. 



