CHAPTER VI. 



A CRITIQUE OF THE BODY-SURFACE LAW. 



The simple relation between the volume and the surface-area of 

 comparable solids has always appealed to biologists. Absorption, 

 secretion, or excretion, whether of water, of aqueous solutions, or of 

 gases, are surface phenomena. Gills, lungs, glands, or other organs 

 which are highly specialized for these functions in the higher organisms 

 are primarily characterized by great surface exposure. Thus the well- 

 being of the organism as a whole in many ways depends upon the 

 ratio of the surface-area to the mass of many of its tissues. 



Again, except when great changes in the proportion of parts are 

 concomitant with increase in size, it is evident that growth must 

 decrease the ratio of external surface-area to body-mass. Inphylogeny 

 the same relationship obtains as in ontogeny. In organisms of gen- 

 erally similar physical conformity, the larger species must expose a 

 relatively smaller surface. It is therefore natural that one should 

 find the two-thirds power relationship considered in various general 

 writings on body-size. A whale in the Arctic exposes relatively far 

 less surface to the surrounding water than a flying-fish in the tropics. 

 An auk in the Arctic exposes relatively far less surface for the 

 loss of heat than a humming-bird in the tropics. Biologists have not 

 failed to grasp the possible significance of such facts for geographical 

 distribution. 



Turning to an entirely different phase of the general discussion, 

 we may refer to the investigations of Dreyer, Ray, and Walker, 1 in 

 which they considered blood-volume, area of the cross-section of the 

 trachea, and area of the cross-section of the aorta in various animals 

 and birds in relation to this principle. 



Surface rather than volume has been suggested as an important 

 factor in muscular work. In the problem of the physiology of excretion 

 it has been stated that the volume of urine is not proportional to the 

 weight of the kidney but to the internal surface. Snell and Warnecke 

 have attempted to arrange vertebrates in series according to relative 

 brain-weight, brain-surface, and intelligence. Perhaps the most ex- 

 treme application of the principle in biological theory is that in Mtihl- 

 mann's theory of old age, which depends upon the change in the relation 

 of surface and volume with increasing size. 2 



1 Dreyer and Ray, Phil. Trans., 1909-1910, 201, ser. B, p. 133. Dreyer, Ray, and Walker, 

 Proc. Roy. Soc., 1912-1913, 86, ser. B, pp. 39 and 56. 



2 See bibliography and extensive discussions of Miihlmann's writings by Minot, The Problem 

 of Age, Growth, and Death, 1908, and by Child, Senescence and Rejuvenescence, 1916. 



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