32 ON MAGNITUDE [ch. 



to study, alike in swimming, in flight and in walking, the general 

 result, attained under very different conditions and arrived at by 

 very different modes of reasoning, is in every case that the velocity 

 tends to vary as the square root of the linear dimensions of the 

 organism. 



From all the foregoing discussion we learn that, as Crookes 

 once upon a time remarked*, the form as .well as the actions of our 

 bodies are entirely conditioned (save for certain exceptions in the 

 case of aquatic animals, nicely balanced with the density of the 

 surrounding medium) by the strength of gravity upon this globe. 

 Were the force of gravity to be doubled, our bipedal form would 

 be a failure, and the majority of terrestrial animals would resemble 

 short-legged saurians, or else serpents. Birds and insects would 

 also suffer, though there would be some compensation for them 

 in the increased density of the air. While on the other hand if 

 gravity were halved, we should get a lighter, more graceful, more 

 active type, requiring less energy and less heat, less heart, less 

 lungs, less blood. 



Throughout the whole field of morphology we may find 

 examples of a tendency (referable doubtless in each case to some 

 definite physical cause) for surface to keep pace with volume, 

 through some alteration of its form. The development of "vilh" 

 on the inner surface of the stomach and intestine (which enlarge 

 its surface much as we enlarge the effective surface of a bath- 

 towel), the various valvular folds of the intestinal lining, including 

 the remarkable "spiral fold" of the shark's gut, the convolutions 

 of the brain, whose complexity is evidently correlated (in part 

 at least) with the magnitude of the animal, — all these and many 

 more are cases in which a more or less constant ratio tends to be 

 maintained between mass and surface, which ratio would have 

 been more and mOre departed from had it not been for the 

 alterations of surface-form f. 



* Proc. Psychical Soc. xn, pp. 338-355, 1897. 



f For various calculations of the increase of surface due to histological and 

 anatomical subdivision, see E. Babak, Ueber die Oberflachenentwickelung bei 

 Organismen, Biol. Centralbl. xxs, pp. 225-239, 257-267, 1910. In connection 

 with the physical theory of surface-energy, Wolfgang Ostwald has introduced the 

 conception of specific surface, that is to say the ratio of surface to volume, or SjV. 

 In a cube, V=P, and S = 61^; therefore SjV — Q/l. Therefore if the side I measure 



