492 A PARENTHETIC NOTE ON GEODETICS [ch. x 



As a parenthetic corollary to the case of the spiral pattern 

 upon the wall of a cylindrical cell, we may consider for a 

 moment the spiral line which many small organisms tend to 

 follow in their path of locomotion*. The helicoid spiral, traced 

 around the wall of our cylinder, may be explained as a composition 

 of two velocities, one a uniform velocity in the direction of the 

 axis of the cylinder, the other a uniform velocity in a circle 

 perpendicular to the axis. In a somewhat analogous fashion, the 

 smaller cihated organisms, such as the ciliate and flagellate 

 Infusoria, the Rotifers, the swarm-spores of various Protists, and 

 so forth, have a tendency to combine a direct with a revolving 

 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 httle or no progress 

 in a definite longitudinal direction. But as a matter of fact, 

 either through the direct action of their cilia or 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 approximate to, a straight axial line. 



pp. 4()-148), and by Pettigrew [Phil. Trans. 1864), and of late by J. B. Macallum 

 {Johm Hopkins Hospital Report, ix, 1900) and by Franklin P. Mall {Amer. J. of 

 Anat. XI, 1911). 



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

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

 Protisten, Arch. f. Anat. v. Phys. {Phys. Abth. SuppL), pp. 243-302, 1900. 



