Where 3I^= the mean, 



and d = the probable deviation 



] 



Anthropological Measurements of Children. 27 



might inflict irreparable damage on the organism. Such 

 indefinite and fragmentary knowledge can never be the basis 

 of a practical reform. Any solution of this problem which 

 shall gain general acceptance must be easy to understand 

 and easy to apply, and must give the probable degree of 

 abnormality of any observed deviation. These conditions 

 are, I believe, fulfilled by the following method. 



According to the theory of probabilities the heights of a 

 thousand individuals of the same class will arrange them- 

 selves as follows : — 



-^71 d 3 



-|-4cZ 18 

 -\-^d 67 

 -\-2d 162 

 4- d 250 

 M 



— d 250 



— 2d 162 



— 'dd 67 



— ^d 18 



— n d 3 



Let these be divided into seven groups : — 



I. All individuals between -\- n d and 3 c? 21 



II. " " u _|_3^ .; 2rf 67 



III. " ■ " " J^2d ^' -\- d 162 



ly. " " •' M '' -\- d 500 



V. " " " ^ d '' —2d 162 



VI. " " " —2d''—^d 67 



VII. " '^ " —^d''—7id 21 



The mean height, weight, girth of chest, etc. of each of 

 these groups at any given age will be the typus of a certain 

 degree of deviation from the mean of the age, — that is to 

 say, the heights, weights, etc. of each group will be symmetri- 

 cally distributed above and below the mean height, weight, 

 etc. of the group in the manner already illustrated for the 

 entire undivided number of observations, i. e., the entire 



