170 



Dr. E. W. A. Walker. 



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

 percentage deviation becomes l - 28 when n is 0'32, and T43 when n is 033. 

 The mean deviation calculated by the method of least squares is, under the 

 same circumstances, l - 59 per cent, when the "best n" (0'32) is used, and 

 1'87 per cent, when n is given the value - 33. 



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

 I — k~W n , where n has the value of 0'32 and the value of h for the grouped 

 girls is 25 - 60. Moreover, since the grouped girls range in weight from 

 3834 to 76,000 grm. (12 stone 5 lb.), and in age from two weeks to over 

 17 years, it may probably be taken that the formula holds for females 

 generally throughout the period of growth from birth to adult age. 



For the individual girls the average value of k is 25 - 58. Its greatest value 

 in the series (28"68) exceeds the average value by 12 - 12 per cent., and its 

 least value (22 - 58) falls below the average value by 1T73 per cent. 



Using the average value of k (25*58) and the value 032 for n, the 

 theoretical body-length of each individual has been calculated from the 

 body-weight by means of the formula 



I = 25-58 W°- 32 . 



The figures thus obtained (which from consideration of space have not 

 been tabulated) showed an average percentage difference between the 

 calculated body-length and that actually observed for the individual girls 

 of only 3'02 per cent., and a mean deviation (calculated by the method of 

 least squares) of 4 - 149 per cent. 



The Difference between the Sexes. 

 The formula for the grouped males has been shown to be 



I = 23-23 W - 33 . 



That for the grouped females is I = 25-60W ' 32 . If we desire to work in 

 pounds avoirdupois and inches instead of grammes and millimetres, the 

 formula for males becomes I = 6-91W ' 33 , and that for females I = 7'14W ' 32 . 



Now, it has been noted in what has gone before that while the best n for 

 males is - 33 and the best n for females is - 32, in each case the values 

 0*32 and 0'33 are nearly equally good (values on either side of these 

 quantities being distinctly less good). 



This fact at once suggested that in taking the power 0'33 for males and 

 - 32 for females, the sex difference was to some extent exaggerated, the true 

 value of n lying in each case somewhere between - 32 and - 33, but nearer 

 - 32 for females and nearer - 33 for males. 



Accordingly, the " best n " was recalculated for each sex to three places of 



