Size in Relation to Body Surface 165 



number, and the number on an individual is propor- 

 tional to its surface. But the mass of the body, which 

 is, if of the same density, proportional to three-halves 

 power of the surface, has to be propelled against 

 gravity as well as horizontally. To keep from sinking 

 it is necessary to increase its velocity with its size; the 

 force expended to do so must be proportional to the 

 seven-fourth power of the surface (Thompson, '17). 



Power required. The force developed in locomotion 

 in Paramecium was estimated by Jensen ('93) from 

 the centrifugal force necessary to prevent its char- 

 acteristic progression away from gravity. From this 

 force he calculated the power expended in normal 

 movement, which depended also upon the difference 

 in density between body and water. Jensen estimated 

 the relative density as 1.25, a value higher than is now 

 tenable for almost any living tissue. Allison ('24) by 

 a more reliable method arrived at a mean value of 1.042 

 for a particular lot of ciliate bodies. From his erron- 

 eous estimate Jensen obtained a figure which was much 

 too high for the power exerted during locomotion by 

 cilia. 



It was shown by Bresslau ('13) that the power ex- 

 erted by the individual to lift its own body can be 

 calculated without knowing its specific gravity. He 

 found that the limiting length for a Paramecium would 

 be about 2 mm. ; which is far beyond the actual dimen- 

 sion of any living Paramecium, but barely beyond that 

 of a Spirostomum. Bresslau pointed out that among 

 rhabdocoele worms, all those species which are over 

 3 mm. long characteristically creep, and only those un- 

 der this length use their cilia in swimming. This ratio 

 of ciliary power to momentum may be a concrete limit- 

 ing factor for species in general, but it has not been 

 tested experimentally as a factor of size within a spe- 

 cies. 



