A CRITIQUE OF THE BODY-SURFACE LAW. 149 



Here comparison is made of the coefficients of variation, 



100<r w 100(r g 



w s 



where a denotes the standard deviations and the bars indicate the 

 means, for body-weight and body-surface as measured by the two 

 methods. Without exception the measures of body-surface show a 

 lower percentage of variation than do the measures of body-weight. 



It is inevitable that the greater variability of body- weight a purely 

 mathematical phenomenon, not physiological should influence any 

 ratios into which body- weight enters. It is quite possible that the 

 difference in the variability of calories per kilogram and in calories 

 per square meter of body-surface due to this factor may be so great 

 as to invalidate any judgment concerning the physiological significance 

 of ratios to body-weight or body-surface based on inspection and per- 

 sonal judgment merely. 68 



Objections essentially similar to the above may be raised against 

 one of the earliest series of calorimetric experiments, those of Richet, 67 

 who, working with rabbits of weights ranging from about 200 to nearly 

 4,000 grams, concluded "La perte de chaleur est fonction de la sur- 

 face." Richet arranged his animals according to weight and calculated 

 the average heat-production per kilogram for the ascending weight 

 classes. The constants in this table lead to the "Resultat des plus 

 inte"ressants et des plus nets, puisqu'il nous montre combien, avec 

 1'augmentation de volume, diminue la production de chaleur par kilo- 

 gramme du poids de Fanimal." He also arranges the same animals 

 according to weight and determines the loss of heat per unit of surface 

 on the assumption that the areas of the animals bore to each other the 

 relationship of surfaces of spheres of comparable weights. From these 

 figures he concludes "On voit quelle ressemblance il y a entre ces 

 chiffres, tres proches les uns des autres." 



But close examination shows that the heat-production per unit of 

 body-surface decreases with the increasing weight of the animals, 

 though apparently at a far lower rate than in the case of that per 

 kilogram of weight. Without more detailed information and closer 

 analysis it is impossible to say to what extent the greater decrease (when 

 heat-production is expressed in calories per kilogram) is due to the 

 fact that the volume of a solid is necessarily more variable than its 

 surface. 



There is a statistical difficulty in classifying animals by weight 

 and computing the average heat per unit of weight for each weight 



66 The logical fallacy of deciding between weight and surface as a basis of reference has appar- 

 ently been overlooked by even so keen an analyst as Moulton (Journ. Biol. Chem., 1916, 24, p. 

 320), who says: "On this basis the smallest variations are shown in the heat-consumption per unit 

 of body-surface and the greatest variations in the heat-consumption per unit of body-weight." 



67 Richet, La chaleur animale, Paris, 1889; see pp. 219-221. 



