166 



Dr. E. W. A. Walker. 



Accordingly the groups in Tables III and IV do not fit the formula for 

 grouped boys, I — 23 '23 W - 33 . They give a series of values for the length 

 constant as calculated from the expression k = W 0-33 //, which increases 

 regularly from a value of about 22 to a value of about 24 as the weight 

 diminishes. 



As a matter of fact the calculations summarised in Table III show that 

 the 1000 undergraduates of the first series as grouped give a value for 

 k of 98-22 with a " best n " of 0-20 and fit the formula I = 98"22 W ' 20 . 

 And the calculations summarised in Table IV for the 500 undergraduates of 

 the second series give the value 109 - 9 for k with a " best n " of 0-19. 



These facts, however, do not mean that the body-length and body-weight 

 of young men are differently related to each other from the same measure- 

 ments in boys, and that their bodies are built on a different plan. 



The discrepancy depends entirely on the fact that the individuals in 

 question are selected individuals — selected for age. It is well brought out 

 by comparing the figures for body-length as a percentage of body-weight in 

 the heavier boys (Table II) with the corresponding figures for the lighter 

 groups of undergraduates (Tables III and IV). 



That it is due entirely to the fact of age-selection follows from the 

 observation that precisely the same phenomenon appears if we select for age 

 among the boys whose measurements have just yielded the formula 

 j / = 23 , 23W 0,33 . This is seen to be the case in four instances in Table VI 

 where the boys already dealt with have been selected for age, the ages chosen 

 being 11 to 12, 10 to 11, 9 to 10, and 7 to 9 years respectively. In each case 

 the individuals are grouped according to weight, and the value of k is 

 calculated for each group from the average body-weight and average body- 

 length of the group by means of the formula k = W 0,33 /l. It is at once evident 

 that in every case by selecting for age and thus excluding from the lower 

 half of each series the heavy boys of ages below the selected age, and from 

 the upper half the lighter boys of ages more advanced, we produce a series 

 of groups which is exactly comparable to the groups exhibited in Tables III 

 and IV. 



But though these groups of undergraduates cannot be employed as groups 

 for the calculation of a growth formula, there remains a way in which their 

 measurements can be employed to test the. formula for males. This is by 

 averaging the whole material of each series of observations so as to obtain an 

 average individual. These averages are given in Table VII along with the 

 averages of my own 30 undergraduates, and for each series the length constant 

 is calculated from the expression k = W 0-33 //. It happens by a curious 

 chance that the three figures are identical. But the point of importance is 



