The Growth of the Body in Man. 



159 



correctly be expressed as a function of the body-weight, and conforms to the 

 formula 



I = &W» 



where / is the length of the body (stem-length) in millimetres, W the weight 

 (without clothes) in grammes, h a constant, and n a power of the approximate 

 value \. The evidence on which this conclusion is based will now be presented. 



Males. 



Table I (not printed, but preserved for reference in the archives of the 

 Eoyal Society) contains a full record of the data for boys, together with 

 the calculated value of the length constant /<• for each individual, deduced 

 from the formula k = W"//, where n has the value 0'33 as determined in 

 Table II. 



In Table II the boys are grouped according to weight in twenty groups. 

 The average body-weight and average body-length for each group is set out, 

 and the figures in the various columns are calculated for each group from the 

 average body- weight and body-length of the group. The body-weights of the 

 groups cover a range in weight from 8168 grin, to 51,480 grm. and show a more 

 than six-fold increase from the lightest group to the heaviest. 



In the first instance the " best n " for these groups in the formula 

 / = L~W n was ascertained graphically to lie in the neighbourhood of 0'3. 

 The precise values of n and k were then determined by trial from the 

 formula log k = log I — a log W. The " best n" was thus found to have the 

 value - 33 while the value - 32 for n is nearly as good. 



The values of k for the groups are shown in the columns for length 

 constant calculated and are seen to be free from periodicity. They give an 

 average value for /,- of 23'23 wlien n is 0'33, and a value of 25"73 when 

 n is 0-32. 



Substituting these values of n and Jc in the formula I = kW n the theoretical 

 value of I is calculated for each group in the appropriate column. The 

 observed values of I are in good agreement with these calculated values and 

 show an average deviation from them of only 1*32 per cent. 



If account be taken of the number of individuals in each group the average 

 deviation becomes T10 per cent, when nis 033, and 1*14 per cent, when n is 

 0'32. The mean deviation calculated by the method of least squares is, under 

 the same circumstances, 148 per cent, when the best n (0 - 33) is used, and 

 T50 per cent, when n is given the value 0*32. 



It follows, therefore, that the stem-length of boys conforms to the formula 



