166 Regulation of Size in Unicellular Organisms 



The power required for locomotion was considered 

 as a function of body size by Angerer ('19a) and Lud- 

 wig ('28a), using rod bacteria and Paramecium as 

 types. They concluded that the expenditure for loco- 

 motion would be proportional to the square of the body 

 surface, which is a fairly close approximation to 

 Thompson's value. The possibility always remains 

 that types of cilia may differ so that in larger indi- 

 viduals more power is exerted by each cilium. When 

 sea-water is the natural medium, the density of the 

 body may equal that of the medium, thus avoiding this 

 consequence of size. 



Assimilation. In an analogous way it can be sup- 

 posed that a ciliary mechanism of ingestion which is 

 adequate for a small race would be inadequate for some 

 larger race. The power of the cilia will be proportional 

 to the body surface, instead of to the body volume 

 which is to be supplied with food. No one has con- 

 ceived a utility for measuring growth as a function of 

 body surface ; yet from the standpoint of most mechan- 

 isms of assimilation, increment of body substance 

 would be expected to be proportional to surface. The 

 tacit assumption seems to be that somehow an organis- 

 mal type will increase its surface in order to keep up 

 with the demands of its mass. 



4. Forces Peculiar to Surfaces 



The principle of similitude is the recognition of the 

 fact that of physical forces, a certain number act at the 

 surface or are proportional to the surface, while cer- 

 tain others act upon all the units of the mass and there- 

 fore are proportional to bulk. For instance, the den- 

 sity of a body is wholly the expression of the intensity 

 with which gravity acts upon its mass ; but the velocity 

 with which the body sinks through water or another 



