198 



SCIENCE 



[N. S. Vol. LIV. No. 1392 



by Variot and Lavialle. Benedict and Talbot 

 have recently shown that the linear formula of 

 DuBois gives results very nearly the same 

 as the formula of Lissauer with a somewhat 

 variable constant. Which of these formulae 

 is most nearly correct for body surface can 

 only be determined by a statistical study of 

 a large number of cases. However, if one of 

 them is clearly superior to the others as a 

 mieasure of heat production it should appear 

 in the coefficients of correlation between heat 

 production and surface as measured by the 

 several formula. Harris and Benedict include 

 in their statistical studies the basal metab- 

 olism of a series of 94 newborn infants, pre- 

 viously published by Benedict and Talbot. 

 They did not, however, carry the analyses so 

 far as to determine which formula gives the 

 closer correlation with heat production. I 

 have taken the trouble to work out the coeffi- 

 cients of variability and of correlation for the 

 Boston series of 94 newborns using four differ- 

 ent formulse. They are given below. 



TABLE 11 



Coeffleients for the Minimal Metabolism of New- 



born Infants (According to the data of 



Benedict and Talbot) 



CoefEcients of Variability Coefficients of Correlation 



Vh =15.37 ±0.79 



Yw = 14.68 ± 0.72 Vhw = 0.7530 ± 0.0205 

 Vsit= 9.92 ±0.48 p;is3/=0.7672± 0.0202 

 7si =10.08 ± 0.49 p/isi= 0.7762 ± 0.0195 

 rsB= 10.25 ± 0.50 7hsir= 0.7677 ± 0.0202 

 VsB = 8.84 ± 0.43 FhsD = 0.7682 ± 0.0202 

 Fa = Coefficient of variability of heat produc- 

 tion, F,o of -weight ; etc. s 3 ;= Su rface by Meeh- 

 Eubner formula (s = 11.9 f (w)-) ; 8^^^= Surface 

 by Lissauer 's formula, (s = 10.3 f (w)-) ; Sb = 

 Surface by Howland and Dana formula (y = mx 

 + b, where x is body weight, m represents a con- 

 stant 0.483 and b represents 730 sq. cm.); So = 

 Surface by weight-height formula of DuBois and 

 DuBois (s = wt.°-*^ X ht.''-"= X 71.84) . 



There are two surprises in this table: one, 

 that heat production as determined by Bene- 

 dict and Talbot is more variable than either 

 body weight or body surface, no matter by 

 which formula it is measured; and the other, 

 that it makes very little difference which for- 

 mula is used for body surface so far as cor- 



relation with heat production is concerned. 

 The formula of Howland and Dana gives the 

 most variable body surface; the height- weight 

 formula of DuBois, which has never been 

 confirmed for infants, gives the least variable. 

 But the formula of Lissauer gives a body sur- 

 face which parallels the metabolism slightly 

 better than the others, the difference, however, 

 being altogether negligible. Taking the entire 

 group of newborns in this series we may con- 

 clude that the sleeping metabolism, which is 

 practically the whole of metabolism in the 

 newborn, is as well measured by one formula 

 as another; also that surface by any formula 

 is but slightly better than body weight as a 

 measure. 



We must distinguish clearly the arguments 

 against the law of surface as of two classes: 

 (1) on the basis of fact and (2) on the basis 

 of explanation. The arguments against the 

 law, so far as they rest upon facts, seem, as 

 we have just seen, to have been misconceived. 

 It never was supposed by its chief proponents 

 that the law would apply to all physiological 

 and pathological conditions but only to similar 

 physiological (normal) conditions. Also, a 

 very superficial understanding of the neces- 

 sary mathematical relations shows that the 

 law has natural limitations which must be 

 recognized if one is to avoid compromising it 

 with impossible conditions. 



There is no doubt that Eubner, following 

 Bergmann, first conceived of the law as casu- 

 ally related to ISTewton's law of cooling. This 

 dependence as commonly accepted may be 

 phrased in this way. , Solid bodies .when 

 warmed lose heat in proportion to the differ- 

 ence between the temperature of the body 

 and the temperature of the surrounding me- 

 dium. Since this heat must all pass through 

 the surface it follows, other things equal, 

 that they will lose heat for any particular 

 gradient of temperature in proportion to sur- 

 face. As applied to the animal body it is ob- 

 served that the body temperature is nearly 

 constant. Hence, if heat is lost in proportion 

 to surface, it must also be produced in pro- 

 portion to surface. This implies a causal re- 

 lationship between surface loss and interior 



