CHANGES IN METABOLISM WITH AGE. 113 



Turning now to the correlations between age and heat-production 

 per unit of body-weight and body-surface, we may compare the corre- 

 lations between age and total heat-production with those between age 

 and relative heat-production, i. e., heat-production per kilogram of 

 weight or per square meter of body-surface, in tables 38 and 39. 



From table 38, in which the correlations between age and total 

 heat-production are compared with those between age and heat per 

 kilogram of body-weight, we note that in all cases except the athletes 7 

 heat per kilogram of weight is negatively correlated with age that is 

 relative heat-production as well as total heat-production decreases with 

 age. In the larger series of men, with the exception of the Gephart and 

 Du Bois selection and the second supplementary series, the correlation 

 between age and relative heat-production is numerically larger than 

 that between age and gross heat-production. This is also true in 

 the supplementary series and in the grand total series of women. 

 Thus variations in the size of the individuals as measured by weight 

 tend to disturb to some extent the correlations between age and heat- 

 production. 



Turning now to the correction for differences in size resulting from 

 the expression of heat-production in calories per square meter of body- 

 surface we have the results set forth in table 39. Without exception 

 the 24 correlations are negative in sign. With three exceptions only 8 the 

 correlations between age and heat-production per square meter of body- 

 surface are of a more strongly negative order than the correlations 

 between age and total heat-production. 



In determining the relationship between age and total heat- 

 production, correction for the influence of both body-weight and 

 stature may be made by the use of the partial correlation formula for 

 two variables constant 



'ah\*- 'aw ) 'sa'sh 'wa'whi'sw\'sa'whi'sh'wa/ 



stir ah ~ 



* V.J- ^siu ~ T wa T sa ~\^r sw T sa r wa )\ \L r sw 1 w h 



Comparing the values of sw r ah with the gross correlations, r ah , and 

 the partial correlations for stature and weight, s r ah and w r ah , we have 

 the results in table 40. 



Correction for both stature and weight has not given constants 

 very different from those in which the correlation is corrected for weight 

 only. 



Correction for both stature and weight has rendered the correla- 

 tions between age and heat-production in the two sexes much more 



7 There are only 16 athletes. The age range is only 19-29 years, and the correlation is small 



in actual magnitude and only about one-fourth of its probable error. 

 8 A11 of these exceptions are trivial in magnitude and only a fraction of their probable errors. 



