September 2, 1921] 



SCIENCE 



197 



Contrast with this the relationship between 

 individuals weighing 4 and 40 kilograms, or 

 still better, an infant weighing 3i kilograms 

 and a man weighing 70 kilograms. The 

 weights are to each other as .05 to 1, and the 

 surfaces as .135 to 1. In other words, the 

 weight of the larger individual is twenty times 

 that of the smaller, while the surface is a 

 little over seven times that of the smaller. In 

 this case the weight and surface can not pos- 

 sibly be of equal value as measures of the 

 metabolism. One is nearly three times as 

 good (or as bad) as the other. As a matter 

 of fact it is now well known that surface is 

 about two and one half times as good a meas- 

 ure as weight between two such individuals. 



In the judgment of the writer it is incorrect 

 to suppose that physiologists have believed the 

 metabolism to be absolutely proportional to 

 surface, regardless of circumstances. Rubner 

 for the German literature and Richet for the 

 French are responsible for the first demonstra- 

 tions of the applicability of the law. Rubner 

 worked with dogs of adult stature but widely 

 different size, estimating their metabolism by 

 the indirect method. Richet worked first 

 with rabbits ranging from 2,000 to 3,500 grams 

 in weight but he determined only the heat of 

 radiation and conduction, neglecting, as nearly 

 all subsequent French observers have done, the 

 heat given off by evaporation. Naturally his 

 quantities would be more nearly proportional 

 to surface than the total. However, in the es- 

 timation of surfaces he says, 



If one supposes tliat animals of different size 

 are like spheres of different volumes, then the 

 respective volumes are related among themselves 

 as the cubes of their radii; while the respective 

 surfaces are related among themselves as the 

 squares of their radii. These considerations apply 

 to living animals, and, since their form is so ir- 

 regular compared with that of a perfect sphere, 

 one can only apply the geometrical facts to them 

 approximately.2 



Further in summing up the factors which 

 determine heat production Richet notes that 



2 Eichet, Ch., "Eecherehes de Calorimetrie, " 

 Arch, de Physiol, norm, et path., 1885, 3d ser., 

 VI., 237. 



one of these is " the nature of the integument." 

 In two important respects, therefore, Richet 

 made saving clauses regarding the application 

 of the law of surface, one concerning the 

 measurement of surface and the other concern- 

 ing the nature of the skin, meaning, of course, 

 its conducting properties. Rubner in the be- 

 ginning considered that he had demonstrated 

 the law only for adult animals and later in 

 applying it to children made this very em- 

 phatic reservation: 



The law of surface area holds under all physio- 

 logical conditions of life, but for its proof it is a 

 reasonable presumption that only organisms of 

 similar physiological capacities, as regards'^nutri- 

 tion, climatic influences, temperament,3 and func- 

 tional power, should be compared.* 



Other students of metabolism have made 

 similar reservations. Thus Schlossman says. 



The presumption is on the one hand that the 

 environment is relatively normal, on the other 

 that the child has a relatively normal surface, that 

 is, a functioning and good conducting skin with 

 the normal amouat of subcutaneous fat." 



Otherwise, he thinks, the law could not be ex- 

 pected to apply. 



One other point of some importance may be 

 mentioned in this connection. There has been 

 much discussion regarding the formula which 

 should be used to express the body surface of 

 infants. Rubner and Huebner modified the 

 old formula of Meeh changing the constant 

 from 12.3 to 11.9. Later Lissauer, from the 

 measurements of a group of infants most 

 of whom were distinctly undernourished, found 

 the constant 10.3 to be more exact. Then came 

 the formula of Howland and Dana of the 

 y == mx + & form, and still more recently the 

 height-weight formula and the linear formula 

 of DuBois, the latter similar to one previously 

 devised by Roussy and first applied to infants 



3 Misquoted as "temperature" by Harris and 

 Benedict, loc. cit., p. 196. 



* Eubner, M., ' ' Ernahrungsvorgiinge beim Wach- 

 stum des Kindes," Arch. f. Eyg., 1908, LXVI., 

 89. 



6 Schlossmann, A., "Atrophie und respirator- 

 ischer Stoff wechsel, " Zeitsehr. f. KinderheilJc., 

 Orig., 1912-13, V., 227. 



