A CRITIQUE OF THE BODY-SURFACE LAW. 151 



of the inert tissue, and since the increase in weight subsequent to 

 maturity is largely dependent upon the deposition of fat, it is quite 

 clear that in a series of individuals of the same species the metabolism 

 per kilogram of body-weight should decrease as the body-weight 

 increases. Metabolism as measured in units of body-weight decreases 

 as body- weight increases. That metabolism as measured in units 

 of body-surface decreases at a lower rate is perhaps attributable merely 

 to the fact that the values of x* increases less rapidly than x. 



This type of relationship has long been familiar to statisticians. 

 If we correlate between x and y/x we get a negative relationship which 

 has been designated as a spurious correlation between indices. 69 The 

 relationship may be easily demonstrated on our own data. In table 51 

 we have given the correlation between body-weight and heat-produc- 

 tion in calories per kilogram of body-weight for certain of our series. 

 The coefficients are negative and of a rather large size throughout. 



5. STATISTICAL TESTS OF RELATIVE VALUE OF THE MEEH FORMULA 

 AND OF THE DU BOIS HEIGHT- WEIGHT CHART. 



From table 50 the reader may have noted that without exception 

 the Du Bois height-weight chart gives a lower percentage variability 

 for body-surface than does the Meeh formula. This point brings up 

 the question of the relative value of these two measures of body-surface. 

 Quite incidentally to carrying out the calculations for this chapter, 

 we have been able to secure certain statistical tests of the relative value 

 of the Meeh formula and of the Du Bois height-weight chart; it there- 

 fore seems desirable to insert these data in this place, after which we 

 shall return to the discussion of our main problem of the validity of 

 the body-surface law as applied to human individuals. 



There are two distinct sources of error in the Meeh formula. First, 



Q t 



the validity of the use of V w 2 as a measure of the surface-area of differ- 

 ent bodies rests on the two assumptions (a) that the two bodies have 

 the same specific gravity, and (6) that they are comparable in form. 

 Neither of these assumptions can be considered strictly valid when 

 applied to men and women of different weights. The specific gravity 

 of a very fat individual is certainly sensibly different from that of a 

 lean one. The relative proportions of length of trunk and of leg differ 

 according to the stature of the individual. 70 Finally a study of profile 

 photographs of very fat and very lean individuals should suffice to 

 convince any one that as far as form is concerned the two extremes 

 can not be regarded as "comparable solids." Secondly, the constant 

 factor of the Meeh formula is determined empirically. It carries with 

 it, therefore, both the errors of measurement and the probable errors 

 of random sampling attaching to any direct measurements of variable 



69 Pearson, Proc. Roy. Soc. Lond., 1S97, 60, p. 492. 



70 Harris, unpublished constants. 



