xiij OF THE FORAMINIFERA 605 



In Textularia and its allies (Fig. 317), we have a precise 

 parallel to the hehcoid cj-me of the botanists (cf. p. 502): that 

 is to say we have a screw translation, perpendicular to the plane 

 of the underlying logarithmic spiral. In other words, in tracing 

 a genetic spiral through the whole succession of chambers, we do 

 so by a continuous vector rotation, through successive angles of 

 180° (or 120° in some cases), while the pole moves along an axis 

 perpendicular to the original plane of the spiral. 



Another type is furnished by the "cyclic" shells of the 

 Orbitolitidae, where small and numerous chambers tend to be 

 added on round and round the system, so building up a circular 

 flattened disc. This again we perceive to be, mathematically, a 

 limiting case of the logarithmic spiral, where the spiral has become 

 a circle and the constant angle is now an angle of 90°. 



Lastly there are a certain number of Foraminifera in which, 

 without more ado, we may simply say that the arrangement of 

 the chambers is irregular, neither the law of constant ratio of 

 magnitude nor that of constant form being obeyed. The chambers 

 are heaped pell-mell upon one another, and such forms are known 

 to naturaUsts as the Acervularidae. 



While in these last w^e have an extreme lack of regularity, we 

 must not exaggerate the regularity or constancy which the more 

 ordinary forms display. We may think it hard to beheve that 

 the simple causes, or simple laws, which we have described should 

 operate, and operate again and again, in millions of individuals to 

 produce the same delicate and complex conformations. But we 

 are taking a good deal for granted if we assert that they do so, 

 and in particular we are assuming, with very httle proof, the 

 "constancy of species" in this group of animals. Just as Verworn 

 has shewn that the typical Amoeba proteus, when a trace of alkah 

 is added to the water in which it lives, tends, by alteration of 

 surface tensions, to protrude the more dehcate pseudopodia 

 characteristic of A. radiosa, — and again when the water is rendered 

 a httle more alkahne, to turn apparently into the so-called A. 

 Umax, — so it is evident that a very slight modification in ,the 

 surface-energies concerned, might tend to turn one so-called 

 species into another among the Foraminifera. To what extent 

 this process actually occurs, we do not know. 



