434 THE FORMS OF CELLS [ch. 



a figure of equilibrium under certain special conditions of restraint. 

 The cylindrical coil of the Spirillum, on the other hand, is a surface 

 of constant mean curvature, and therefore of equilibrium, as truly, 

 and in the same sense, as the cylinder itself. 



A very beautiful " saddle-shaped " surface, of constant mean 

 curvature, is to be found in the little diatom Cmnpylodiscus, and 

 others, a httle more complicated, in the allied genus Surirella*. 



These undulating and helicoid surfaces are exactly reproduced 

 among certain forms of spermatozoa. The tail of a spermatozoon 

 consists normally of an axis surrounded by clearer and more fluid 

 protoplasm, and the axis sometimes splits up into two or more 

 slender filaments. To surface-tension operating between these and 

 the surface of the fluid protoplasm (just as in the case of the flagellum 

 of the Trypanosome), I ascribe the formation of the undulating 

 membrane which we find, for instance, in the spermatozoa of the 

 newt or salamander; and of the helicoid membrane, wrapped in a 

 far closer and more beautiful spiral than that which we saw in 

 Spirochaeta, which is characteristic of the spermatozoa of many 

 birds. The undulatory membrane which certain ciliate infusoria 

 exhibit is, seemingly, a difl'erent thing. It is not based on a single 

 marginal flagellum, but consists of a row of fine ciha fused together. 

 The membrane can be broken up by certain reagents into fibrillae, 

 and — what is more remarkable — a touch of the micro-dissection 

 needle may split it into a multitude of cilia, all active but beating 

 out of time; a moment more and they unite again, all but dis- 

 appearing from view as they fuse into the optically homogeneous 

 membrane. They unite as quickly and as intimately as though 

 they were so many liquid jets, and they manifestly "partake of 

 fluidity." Neither they, nor cilia in general, have received, nor 

 seem hkely to receive, a simple explanation f. Nevertheless, we 

 may see a httle hght in the darkness after all. 



It would be overbold to seek for every form of living cell a parallel 

 configuration due to simple capillary forces, as manifested in drop 

 or bubble or jet. And yet, if the simple cases of sphere or cyhnder 

 be the beginning of the story, they assuredly are not the end. The 



* Van Heurck, Synopsis des Diatomees de Belgique, pis. Ixxiv, 6; Ixxvii, 4. 



t H. N. Maier, Der feinere Bau der Wimperapparate der Infusorien, Arch. f. 

 Protistenk. ii, p. 73, 1903; R. Chambers and J. A. Dawson, Structure of the 

 undulating membrane in the ciliate Blepharisma, Biol. Bull, xlviii, p. 240, 1925. 



