432 THE FORMS OF CELLS [ch. 



description of the mode of development which, from theoretical 

 considerations alone, we should conceive to be the natural if not 

 the only possible way in which the undulating membrane could 

 come into existence. 



There is a genus closely alhed to Trypanosoma, viz. Trypanoplasma, 

 which possesses one free flagellum, together with an undulating 

 membrane; and it resembles the neighbouring genus Bodo, save 

 that the latter has two flagella and no undulating membrane. In 

 lijce manner, Trypanosoma so closely resembles Herpetomonas that, 

 when individuals ascribed to the former genus exhibit a free 

 flagellum only, they are said to be in the "Herpetomonas stage." 

 In short, all through the order, we have pairs of genera which are 

 presumed to be separate and distinct, viz^ Trypanosoma-Herpeto- 

 monas, Trypanoplasma-Bodo, Trichomastix-Trichomonas, in which 

 one differs from the other mainly if not solely in the fact that a free 

 flagellum in the one is replaced by an undulating membrane in the 

 other. We can scarcely doubt that the two structures are essen- 

 tially one and the same. 



The undulating membrane of a Trypanosome, then, according 

 to our interpretation of it, is a hquid film and must obey the law 

 of constant mean curvature. It is under curious limitations of 

 freedom: for by one border it is attached to the comparatively, 

 motionless body, while its free border is constituted by a flagellum 

 which retains its activity and is being constantly thrown, like the 

 lash of a whip, into wavy curves. It follows that the membrane, 

 for every alteration of its longitudinal curvature, must at the same 

 instant become curved in a direction perpendicular thereto; it 

 bends, not as a tape bends, but with the accompaniment of beautiful 

 but tiny waves of double curvature, all tending towards the 

 estabhshment of an " equipotential surface", which indeed, as it is 

 under no pressure on either side, is really a surface of no curvature 

 at all; and its characteristic undulations are not originated by an 

 active mobihty of the melhbrane but are due to the molecular tensions 

 which produce the very same result in a soap-film under similar 

 circumstances. Some of the larger Spirochaetes possess a structure so 

 like to the undulating membrane of the Trypanosomes that it has led 

 some persons to include these peculiar allies of the bacteria among the 

 flagellate protozoa; but it would seem (according to the weight of 



