V] OF UNDULATING MEMBRANES 269 



difficult to believe one was not dealing with a small, blunt 

 trypanosome*.'' This in short is a precise 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 allied to Trypanosoma, viz. Trypano- 

 plasma, which possesses one free flagellum, together with an 

 undulating membrane ; and it resembles the neighbouring genus 

 Bodo, save that the latter has two fiagella and no undulating 

 membrane. In like 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 "Her- 

 petomonas stage." In short all through the order, we have pairs 

 of genera, which are presumed to be separate and distinct, viz. 

 Trypanosoma-Herpetomonas, 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 essentially one and the same. 



• The undulating membrane of a Trypanosome, then, according 

 to our interpretation of it, is a liquid 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 apd 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 

 establishment of an " equipotential surface " ; and its characteristic 

 undulations are not originated by an active mobility of the 

 membrane but are due to the molecular tensions which produce 

 the very same result in a soap-film under similar circumstances. 

 In certain Spirochaetes, S. anodontae (Fig. 90) and S. halhiani 



* D. L. Mackinnon, Herpetomonads from the Alimentary Tract of certain 

 Dungtlies, Parasitoloyy, ni, p. 268, 1910. 



