A CRITIQUE OF THE BODY-SURFACE LAW. 163 



series of 35 from the original series of 68 women, and in turn to predict 

 the heat-production of the original series from constants or equations 

 based on the supplementary series. Thus a very comprehensive 

 test of the validity of the different methods of forming check series is 

 secured. 



Two methods of calculating the metabolism of an individual whose 

 actual heat-production is unknown suggest themselves. 



First, one may merely multiply the body-weight or body-surface 

 of the subject by the average heat-production per unit of weight or 

 per unit of surface in the standard series. This has been the method 

 hitherto employed in the calculation of the control values to be used 

 in clinical calorimetry. 



Second, one may use a mathematical prediction equation based on 

 the standard series. So far as we are aware, this method has not 

 hitherto been employed in studies on basal metabolism. 



While the second method seems the more logical of the two, we 

 shall give the results of both. 



When prediction of the heat-production of an individual is made 

 by either of the methods a value is obtained which may be identical 

 with the actually determined constant, but which in general deviates 

 somewhat from it. Deviation may, therefore, be either positive or 

 negative in sign. We shall, in consequence, have to consider whether 

 the predictions made by a given method are on the whole too large or 

 too small. Since we are in this case testing methods of prediction 

 against actual observation, we have taken the differences (calculated 

 heat-production) less (actually determined heat-production). Thus 

 when a given prediction method gives results which are on the average 

 too high, the mean deviation (with regard to sign) of the calculated 

 from the actual heat-production will have the positive sign. When it 

 is too low, it will have the negative sign. Dividing the sum of the 

 deviations with regard to sign by the total number of individuals in 

 the series in hand we have a measure of the average deviation in the 

 direction of too high or too low prediction. 



But the question as to whether a given prediction method gives on 

 the whole too high or too low values is not the only one to be answered. 

 One wishes to know the extent of deviations both above and below 

 the observed value in the case of each of the methods used. One 

 measure of such deviation is obtained by ignoring the signs and simply 

 regarding a difference between observed and predicted values as an 

 error of a given magnitude. Dividing the sum of these errors for the 

 whole series by the number of individuals in the series, we have, in 

 terms of average deviation without regard to sign, a measure of the rela- 

 tive precision of the different methods of prediction employed. This 

 method has two disadvantages. First, it does violence to sound mathe- 

 matical usage with regard to signs. Second, it gives the deviations 



