148 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



body- weights w i} w 2 , w 3 , . . . . w n for each individual are available; 

 the following ratios are determined : 



Wi 



h* 

 w s } 



h r 



h, 



Si 



S3 



Clearly enough the variability of the ratios will be determined not 

 merely by the variability of the values of h but by the variability of 

 the values of w and s as well. If the relationship between w and a 

 be such that one of them is necessarily more variable than the other, 

 the ratio in which the more variable measure is employed must of 

 necessity be more variable also. 



Now this is precisely the condition which obtains in the relationship 

 between body-weight and body-surface. In computing body-surface 

 by the Meeh formula, the deviation of the surface-area of an individual 

 from its mean bears only the ratio of ^w' 2 to the deviation of the weight 

 from the average weight of the series. 



TABLE 50. Comparison of coefficients of variation for body-weight and two measures 



of body-surface. 



Thus a lower variability of surface-area as compared with body- 

 weight is an arithmetical necessity. Conversely, a higher variability 

 of the ratio of total heat to body-weight (i.e., of the measures of heat- 

 production in terms of calories per kilogram) is a statistical consequence 

 of the use of the Meeh formula or of direct measurement of body- 

 surface in individuals reasonably similar in physical configuration. 

 It is presumably a necessary consequence of the use of the body-surfaces 

 given by the Du Bois height-weight chart also. 



How great may be the differences in the variability of the physical 

 measurements themselves is readily seen by expressing the variabilities 

 of body-weght and surface-area in relative terms as in table 50. 



