XIl] 



OF THE FORAMINIFEKA 



591 



is obviously forthcoming in the foraminiferal, but not at all in 

 the i;adiolarian, 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 

 7nicroscopiques* , until Dujardin shewed that their httle bodies 

 comprised no complex anatomy of organs, but consisted merely 

 of that slime-like organic matter which he taught us to call, 

 "sarcode," and which we learned afterwards from Schwann to 

 speak of as "protoplasm." 



Fig. 309. Nummulina antiquior, R. and V. (After V. von Moller.) 



One striking difierence, however, is apparent between the shell 

 of Nautilus and the httle nautiloid or rotaUne shells of the Fora- 

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



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

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

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

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



