Size as Structure and Function 13 



are in the former highly important, convection of 

 molecules and gravity are probably never limiting cir- 

 cumstances (Thompson, '17). Thus, the surface-elec- 

 trical charge upon a bacterium may be of great con- 

 sequence for this individual, but can play no role of 

 life and death in a whale. Again, forces with which 

 aquatic organisms are concerned are far other from 

 those with which terrestrial organisms cope. Viscos- 

 ity of the medium and convection of its constituents 

 assume different roles. For two Paramecia of differ- 

 ent lengths to swim at the same velocity, the force ex- 

 pended in resistance to the medium is as the square 

 of the length, and the force required to accelerate by 

 the same amount is as the cube. But that any of these 

 is a limiting factor in controlling the size of Parame- 

 cium itself, has not been discovered. 



The consequences of subdividing ad infinitum a sphere 

 or a cube have frequently been pictured, as by Ryder 

 ('93a). The acceleration of the increase in surface- 

 mass ratio as subdivision proceeds serves to focus 

 attention upon certain classes of geometrical factors; 

 but no real progress has been made until some of these 

 possible factors have been tested to find whether they 

 are actually effective in modifying size. 



Lower limits to size. As is well known, there are 

 theoretical lower limits to the size of organized beings. 

 One of the obvious limits, as was pointed out by Max- 

 well (75) r is the size of one molecule itself. Errera 

 ('03) further developed this line of argument. All liv- 

 ing matter that is known contains proteins. A spheri- 

 cal micro-organism less than 0.01 micron in diameter, 

 and having 14 per cent of proteins, could contain only 

 about ten molecules of proteins. If it be assumed that 

 the proteins present contain sulfur in about the pro- 

 portion usual in living matter, such an organism would 

 contain not more than three atoms of sulfur. 



