854 THE SPIRAL SHELLS [ch. 



The analogy is plain between this experiment and those diffusion 

 experiments by which Leduc produces his beautiful hexagonal 

 systems of artificial cells, with which we have dealt in a previous 

 chapter. 



But let us come back to the shell itself, and consider particularly 

 its spiral form. That the shell in the Foraminifera should tend 

 towards a spiral form need not surprise us ; for we have learned that 

 one of the fundamental conditions of the production of a concrete 

 spiral is just precisely what we have here, namely the develop- 

 ment of a structure by means of successive graded increments 

 superadded to its exterior, which then form part, successively, of 

 a permanent and rigid structure. This condition is obviously forth- 

 coming in the foraminiferal, but not at all in the radiolarian, shell. 

 Our second fundamental condition of the production of a logarithmic 

 spiral is that each successive increment shall be so posited and so 

 conformed that its addition to the system leaves the form of the 

 whole system unchanged. We have now to enquire into this latter 

 condition; and to determine whether the successive increments, or 

 successive chambers, of the foraminiferal shell actually constitute 

 gnomons to the entire structure. 



It is obvious enough that the spiral shells of the Foraminifera 

 closely resemble true logarithmic spirals. Indeed so precisely do 

 the minute shells of many Foraminifera repeat or simulate the spiral 

 shells of Nautilus and its allies that to the naturalists of the early 

 nineteenth century they were known as the Cephalopodes micro- 

 scopiques*, until Dujardin shewed that their little bodies comprised 

 no complex anatomy of organs, but consisted merely of that sUme-like 

 organic matter which he taught us to call "sarcode," and which 

 we learned afterwards from Schwann to speak of as "protoplasm." 



One striking -difference, however, is apparent between the shell 

 of Nautilus and the little nautiloid or rotaline shells of the Fora- 

 minifera: namely that the septa in these latter, and in all other 

 chambered Foraminifera, are convex outwards (Fig. 423), whereas 

 they are concave outwards in Nautilus (Fig. 347) and in the rest 

 of the chambered molluscan shells. The reason is perfectly simple. 



* Cf. Ale. d'Orbigny, Tableau methodique de la classe des Cephalopodes, Ann. 

 des Sci. Nat. (1), vii, pp. 245-315, 1826; Felix Dujardin, Observations nouvelles 

 sur les pretendus Cephalopodes microscopiques, ibid. (2), iii, pp. 108, 109, 312-315, 

 1835, Recherches sur les organismes inferieurs, ibid, iv, pp. 343-377, 1835; etc. 



