750 THE EQUIANGULAR SPIRAL [ch. 



speaking fundamentally different ; and not only are they biologically 

 remote, but they are also physically different, in regard to the causes 

 to which they are severally due. For in the first place, the spiral 

 coil of the elephant's trunk or of the chameleon's tail is, as we have 

 said, but a transitory configuration, and is plainly the result of 

 certain muscular forces acting upon a structure of a definite, and 

 normally an essentially different, form. It is rather a position, or 

 an attitude, than a form., in the sense in which we have been using 

 this latter term; and, unhke most of the forms which we have been 

 studying, it has little or no direct relation to the phenomenon of 

 growth. 



Fig. 348. A foraminiferal shell {Pulvinnlina). 



Again, there is a difference between such' a spiral conformation 

 as is built up by the separate and successive florets in. the sunflower, 

 and that which, in the snail or Nautilus shell, is apparently a single 

 and indivisible unit. And a similar if not identical difference is 

 apparent between the Nautilus shell and the minute shells of the 

 Foraminifera which so closely simulate it: inasmuch as the spiral 

 shells of these latter are composite structures, combined out of 

 successive and separate chambers, while the molluscan shell, though 

 it may (as in Nautilus) become secondarily subdivided, has grown 

 as one continuous tube. It follows from all this that there cannot 

 be a physical or dynamical, though there may well be a mathematical 

 law of growth, which is common to, and which defines, the spiral 

 form in Nautilus, in Globigerina, in the ram's horn, and in the 

 inflorescence of the sunflower. Nature at least exhibits in them all 

 ^'un reflet des formes rigoureuses qu'etudie la geometrie"^ .'' 



* Haton de la Goupilliere, in the introduction to his important study of the 

 Surfaces Nautiloides, Annaes sci. da Acad. Polytechnica do Porto, Coimbra, ni, 1908. 



