190 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



The first three lead to the partial regressions which are required 

 for computing the variations in heat-productions associated with differ- 

 ences in weight, stature, and age. The last two are useful in checking 

 the partial variabilities. The partial regressions are: 



p wsa p _ wsa f> r 



sa u-h sa'wh wa fih wa ' sh ws ah we 1 ah 



sah^w watfls 



where the partial variabilities are given by 



= ffh Vl -r ah * Vl- a r sh * Vl- sa r wh * 



= & ' * - 'u' * *- 



sa'wh 



-r sa 2 - a 



= cr s Vl -r s!t , 2 Vl -,,r s , 2 Vl - 



a = ff a Vl-r ah z Vl 



ah - h r 



aw * 



= <r u Vl r 2 V 1 r 2 Vl r >, 2 



A '03 A ' aiv - 1 - tfs 1 a/i 



These give the characteristic equation 



Substituting constants and having h = total heat-production per 24 

 hours, w weight in kilograms, s = stature in centimeters, and a = age 

 in years, we have for the six series of adults dealt with: 



Gephart and Du Bois selection, N = 72, h = +175.4866+13.0642 w;+4.9520s-9.1252a 



Men other than Gephart and Du Bois selection, Af = 64, 



h=- 67.3458 + 13.6734 w+5.7310s -6.1234 a 



Grand total men, AT = 136, h = + 66.4730 + 13.7516 w +5.0033 s- 6.7550 a 



Original women, JV = 68, fe=* +657.4595+10.3698 w+1.3988s -3.5332 a 



Supplementary women, N=35, h = +491.3238+ 8.4793 w+3.2667 s -4.8748 a 



All women, ^ = 103, A = +655.0955+ 9.5634 to + 1.8498 -4.6756 a 



The testing of these formulas is carried out in precisely the same 

 manner as that employed in dealing with those in which total heat- 

 production was predicted from body-weight and stature in the preced- 

 ing section. Thus tables 73 to 75 are quite comparable with tables 

 70 to 72. The first column gives the results of predictions of total heat- 

 production from weight, stature, and age. The five following columns 

 show the differences between these results and those obtained by other 

 methods. The final column shows the difference between prediction 

 from weight and stature as given in the first column of tables 70 to 72 

 and that from weight, stature, and age as given in the first column of 

 tables 73 to 75. The subtractions are so made that a minus sign denotes 

 a smaller error of prediction when the equation involving weight, 

 stature, and age is used. In taking these differences in the case of 



