PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 93 



of the girl babies a reduction of 0.3144 or about 39 per cent, while if 

 sex be disregarded the reduction is 0.2520 or about 32 per cent. The 

 results indicate, however, that the correlation is primarily due to body- 

 mass rather than to body-length. 



The partial correlations for men and women are laid beside the gross 

 correlations in table 29. 



We note that without exception the correction for stature has 

 reduced the correlation between weight and total heat-production. 

 The amount of reduction is not, however, large. For the various series 

 it is as follows : 



Percentage 

 Men: Reduction. 



Original series, AT = S9 11.3 



Gephart and Du Bois selection, TV = 72 17.2 



First supplementary series, N = 2S 16.9 



Original and first supplementary series, N = 117 12.0 



Total men, N = 136 13.7 



Women : 



Original series, N = 68 1.4 



Supplementary series, N =35 21.6 



Total women, N = 103 4.7 



The results which are based upon moderately large series of men 

 are fairly regular. The smaller groups, of course, give much more 

 variable percentages. The two series of women differ very greatly. 

 The whole series of women seems to show a much smaller reduction 

 in the correlation between weight and heat as a result of the correction 

 for stature than do the total men. When more data are available, the 

 detailed investigation of this point will be well worth while. 



We now turn to the corrections for age in the adults. The results 

 due to the formula 



' wh 'ah' aw 



Vl -r a Vl - 



are laid beside the gross correlations in table 30. The results in this 

 table are very striking. The partial correlations are, with the insig- 

 nificant exception of the small series of athletes, larger than the original 

 correlations uncorrected for age. Thus age heterogeneity has a meas- 

 urable disturbing influence on the relationship between body-weight 

 and total heat-production. When this influence is removed the close- 

 ness of correlation is increased. 



Correcting for the influence of both age and stature, we have the 

 partial correlations between weight and heat-production given by the 

 formula 



_ 

 ae'u'h ~ 







V (1 -r as 2 -r sw *-r aw 2 +2r as r aw r sw ) V (1 -r as z -r sh *-r ah 2 +2r as r ah r sh ) 



