A CRITIQUE OF THE BODY-SURFACE LAW. 189 



10. PREDICTION OF HE AT- PRODUCTION FROM TWO PHYSICAL 

 CHARACTERS (STATURE AND BODY- WEIGHT) AND AGE. 



In the foregoing section we demonstrated the efficiency of equations 

 involving stature and body-weight for the prediction of the heat- 

 production of the individual. From the analyses in the preceding 

 chapter it is clear that age is another factor which should be taken 

 into account in estimating the basal metabolism of the individual. 



Our problem in this section is therefore twofold: First, we must 

 determine some means of including an age factor in our prediction 

 equation. Second, we must, on the basis of the available observational 

 data, replace the symbols in these equations by numerical constants 

 and determine empirically whether equations involving age as well as 

 body-weight and stature show a superiority for the prediction of the 

 heat-production of the unknown subject. While Du Bois has given a 

 tentative correction for age we have not considered it worth while, in view 

 of the very approximate nature of his terms as given on page 123 to 

 apply his age correction in drawing a comparison between equations 

 based on body-surface and those based on stature, weight, and age. 



Working in terms of partial correlations and variabilities, the 

 multiple-prediction formulas for the estimation of total heat-production 

 from stature, body-weight, and age require: 



Partial correlation between weight and total heat-production for constant stature and 



age, tor-**. 

 Partial correlation between stature and total heat-production for constant weight and 



age, w .,n*. 

 Partial correlation between age and total heat-production for constant weight and stature, 



Partial correlation between age and stature for constant body-weight and daily heat-pro- 

 duction, h-iTas. 

 Partial correlation between stature and weight for constant age and daily heat-production, 



afiTfie- 



These are: 



'wA\-*- 'OS ) 'aw' ah ' sw' sh i ' as \' auv sh I" ' ah' sw) 



-r as 2 -r sw *-r aw 2 +2r as r aw r sw ) (l -r as 2 -r sh *-r af ?+2r as r ah r sh ) 



'sh\*- 'aw ) 'as' ah 'ws'wh\'aw\'as'wh\'ah'ws) 



tea 



u-s^ah 



hvi'as 



r as 2 +2r aw r as r ws } (l -r aw 2 -r wh 2 -r ah 2 +2r aw r ah r u , h ) 



'sw ) 'sa's'n ' tea' wh I ' sw\' sa' wh "I ' shTwa) 



-r sw 2 -r wa 2 -r sa 2 +2r sw r sa r wa ) (l -r sw 2 -r wh 2 -r sh z +2r sw r sh r wh ) 



^saV-*- ^hw ) ^hs^ha T ws i wa ~l~Thw V hs^ 



-r hv ?-r ws 2 -r h 2 +2r hw r hs r ws ) (l- r hw * - r wa 2 - r h< *+2r hw r ha r wa ) 



TSIO\*- T ah ) T as T aV! 'hs^'h 



-r ah * - r h 2 - r a *+2r ah r as r hs ) (l - r at ? - r hv ? - r aw *+2r ah r av ,r llW ) 



