A CRITIQUE OF THE BODY-SURFACE LAW. 181 



The constants in this table show : 



1. That in all four comparisons prediction from means gives a 

 higher error than prediction by use of equations. 



2. That prediction from body-surface gives lower average devia- 

 tions than prediction from body- weight. This is true whether predic- 

 tion is made by considering the production proportional to body- 

 weight or body-surface, or as given by a linear equation. 



3. That by all methods the error of prediction is larger in the 

 women than that due to comparable methods in the men. 



In prediction from body-weight the disadvantage of the method of 

 estimation from average heat per unit is particularly conspicuous. It 

 gives an average error of 24.9 calories in men and 67.3 calories per 

 24 hours in women greater than prediction from equations based on 

 body-weight. In the case of prediction from body-surface the differ- 

 ence between the error resulting from the use of means and the use of 

 equations is not so great, but amounts to 1.7 calories in men and 2.5 

 calories in women. 



Results secured by the use of equations are conspicuously more 

 consistent than those reached by prediction from means of heat- 

 production per unit of surface. For example, in the men the mean 

 error of the prediction of heat-production from the mean heat-produc- 

 tion per kilogram in the series as a whole is 28.8 calories per 24 hours 

 greater than prediction from the mean heat-production per square 

 meter of body-surface in the whole series. For the women the differ- 

 ence is 65.6 calories. But when equations are used the excess error of 

 28.8 calories in the men shrinks to 5.6 calories and the excess error of 

 65.6 calories in the women shrinks to 0.8 calorie. Again, in comparing 

 the men and the women we note differences of 42.8 and 6.0 calories 

 when prediction is made by considering heat-production proportional 

 to body-weight or body-surface, but these differences are only 0.4 

 and 5.2 calories per day when prediction is made by equations. 



Turn now to our third and final standard of comparison the square 

 root of mean-square error of prediction. 



Calculation from body-weight Men - Women. Difference. 



By means 160.99 225.74 +64.75 



By equations 123.88 123.03 - 0.85 



Difference + 37.11 +102.71 



Calculation from body-surface 



By means 119.44 126.81 + 7.37 



By equations 117.21 122.86 + 5.65 



Difference + 2.23 + 3.95 



The conclusions to be drawn from this table are in essential agree- 

 ment with those drawn from the preceding tests. Prediction from 

 body-surface gives a far lower error than prediction from body-weight 

 when heat-production is considered directly proportional to weight 



