A CRITIQUE OF THE BODY-SURFACE LAW. 183 



are forced to use his predicted metabolism in health as a basis of com- 

 parison with his measured metabolism in disease, in order to reach any 

 conclusion of value concerning the influence of disease on metabolism. 80 



We shall now consider the possibility of predicting the basal metab- 

 olism of an individual by the simultaneous use of two physical charac- 

 ters. Should the method of the use of two or more characters prove 

 more advantageous than the use of a single character, the selection of 

 the most suitable physical characters for use in the estimation of the 

 normal metabolism of the individual will present a problem of some 

 practical importance. At present, it is quite natural to take the two 

 measurements which are most easily and generally made, namely 

 stature and body-weight. 



Let s= stature, w= weight, ft = total heat-production. Then the 

 prediction of ft from both s and w will be carried out by the formula 81 



I, Tl^Au' r hs^sw ff h f \ | Tsh ^hw^wa &h / ~\ 



ii n~r - (w w) n ^ - - v.o 6y 



or in terms more convenient for purposes of calculation 

 ft =ft _ * 2 WS - - w ~~ ^ ^7^- ' ~ ^ 



_ 2 



o 



ws "w -^ 'ws "s 



Or following another notation 82 we may determine the prediction 

 equations as follows : 



The individual partial regression slopes are given by 



- r r 



h s' u-h wfsh w' sh 



where the three standard deviations of the second order, su ,a hj 3h a 

 wh <r s , are given by 



=<r h 



-r 2 =<r Vl-r 2 



=<r Vl- 



wfl - 



80 The emphasis which has been laid upon the variation in metabolism from individual to 

 individual throughout this volume should have convinced the reader that conclusions concerning 

 the influence of any disease on metabolism can never be safely drawn from the determinations 

 based on a single individual. It is only when a number of comparisons are made that conclusions 

 may be safely drawn. This point will be further considered in Chapter VIII. 



81 In this volume no attempt is made to discuss in detail the statistical theory employed, or 

 even to give full citations of the literature. Multiple prediction formulas are treated by Pearson, 

 Phil. Trans. Ser. A, 1896, 187, p. 253; loc. cit. 1898, 192, p. 169. Yule, An Introduction to the 

 Theory of Statistics, London, 1911, Chapter XII gives a general discussion of the subject with 

 bibliography. Some of the formulas have been given in the form used by Goring in The English 

 Convict, London, 1913. 



82 Yule, Introduction to the Theory of Statistics, 1911, p. 236. 



