746 A PARENTHETIC NOTE [ch. 



of locomotion*. A certain physiologist observed that an Amoeba, 

 crawling within a narrow tube, wound its slow way in a spiral course 

 instead of going straight along the tube. The creature was going 

 nowhere in particular, but merely following the direction in which 

 it had begun : in curious illustration of a familiar statement in the 

 "dynamics of a particle," that a particle moving on a surface 

 without constraint will describe geodesic lines. 



But it is after a different fashion, and without any constraint to 

 a surface, that the smaller ciliated organisms, such as the ciliate 

 and flagellate infusoria, the rotifers, the swarm-spores of various 

 Protista, and so forth, shew a tendency to pursue a spiral path in 

 their ordinary locomotion. The means of locomotion which they 

 possess in their cilia are at best somewhat primitive and inefficient; 

 they have no apparent means of steering, or modifying their 

 direction; and, if their course tended to swerve ever so little to 

 one side, the result would be to bring them round and round again 

 in an approximately circular path (such as a man astray on the 

 prairie is said to follow), with little or no progress in a definite 

 longitudinal direction. But as a matter of fact, by reason of a 

 more or less unsymmetrical form of the body, all these creatures 

 tend more or less to rotate about their long axis while they swim. 

 And this axial rotation, just as in the case of a rifle-bullet, causes 

 their natural swerve, which is always in the same direction as 

 regards their own bodies, to be in a continually changing direction 

 as regards space: in short, to make a spiral course around, and more 

 or less near to, a straight axial line|. 



In this short chapter we have touched on phenomena where form 

 repeats itself, and mathematical analogies recur, in very different 

 things and very different orders of magnitude. The spiral muscles 

 of heart or stomach are the mechanical outcome of twists which 

 these tubular organs have undergone in the course of their develop- 

 ment, and come, accordingly, under the general category of organic 



* Cf. Butschli, "Protozoa," in Bronn's Thierreich, ii, p. 848, in, p. 1785, etc., 

 1883-87; Jennings, Amer. Nat. xxxv, p. 369, 1901; Putter, Thigmotaxie bei 

 Protisten, Arch. f. Anat. u. Phys. {Phys. Abth. Swppl.), pp. 243-302, 1900. 



t Cf. W. Ludwig, Ueber die Schraubenbahnen niederer Organismen, Arch. f. 

 vergl. Physiologic, ix, 1919. 



