The Growth of Children. 97 



the Boston boy is therefore by no means to be described as 

 tall and thin in comparison with his English cousin. Dr> 

 Baxter's conclusion, " that the mean weight of the white 

 native of the United States is not disproportionate to his 

 stature"* seems, therefore, as far as these boys are concerned, 

 as applicable to growing children as to adults. 



It will thus be seen that the theory of the gradual physical 

 degeneration of the Anglo-Saxon race in America derives no 

 support from this investigation.! 



Distribution of Observations. 



Tables Nos. 4 to 15, inclusive, sliow the distribution of the 

 observations on both height and weight. For instance, from 

 Table No. 4 it will be seen that of the 848 boys of five years 

 of age whose heights were measured four (or 0.47 per cent 

 of the whole number) were between 47 and 48 inches high, 

 190 (or 22.4 per cent of the whole number) were between 

 41 and 42 inches high, etc. The distribution of observations 

 on both sides of the average height or weight may be repre- 

 sented, according to Quetelet, by the binomial curve. That 

 is, if the individuals measured are sufficiently numerous, it 

 will be found that the number of observations at each succes- 

 sive inch (or pound) will first increase and then diminish in 

 the same way as the successive coefficients of (a-j-i)^, as 

 determined by Newton's binomial theorem. It will be noticed 

 that the figures in the above-mentioned tables do not increase 

 and diminish with the regularity which a conformity with 

 this law demands ; but it must be borne in mind that the 

 observations at each age are comparatively few in number, 

 and that more numerous measurements or a distribution of 

 the present observations in larger groups (e. (/., of two inches, 

 or of eight pounds each) would doubtless cause the appear- 

 ance of a closer agreement with the law. 



These tables (Nos. 4 to 15) show at a glance the range of 



* Op. cit., p. 55. 



t See an article on this subject by Rev. A. A. Livermore, in the February number of the 

 " Unitarian Review and Religious Magazine." 



