; 2 THE POPULAR SCIENCE MONTHLY. . 



fere with this special one) the " mean man " thus stands as a repre- 

 sentative of the whole population, individuals as they differ from him 

 being considered as forms varying from his specific type. 



To realize a conception which even among anthropologists has 

 scarcely yet become familiar, it is desirable to show by what actual 

 observations M. Quetelet was led to the discovery of his principle. 

 When a large number of men of a practically homogeneous population 

 are measured, and arranged in groups accordingly, it becomes evident 

 that the individuals are related to one another by a law of distribution 

 A central type is represented by the most numerous group, the adjoin- 

 ing groups becoming less and less numerous in both directions. Thus, 

 on classifying the measured heights of some 26,000 American soldiers 

 of the Northern army during the late war, the proportionate number 

 of men to each height was ascertained to be as follows (" Phys. Soc," 

 i., p. 131 ; " Anthropom.," p. 259) : 



Height, inches 60 61 62 63 64 65 66 67 68 



No. of men in 1,000.... 1 1 2 20 48 75 117 134 157 



Height, inches 69 70 71 72 73 74 75 76 



No. of men in 1,000.... 140 121 80 57 26 13 5 2 



Here it is seen that the mean man is a little under 5 ft. 8 in. in height, 

 the numbers of men shorter and taller diminishing with evident regu- 

 larity, down to the few representatives of the very short men of 5 ft. 

 and under, and the very tall men of 6 ft. 4 in. and over. The law of 

 relation of height to numerical strength is shown graphically by the 

 binomial curve figured above, where the abscissae (measured from an 

 origin on the left) represent the heights of the men, and the ordinates 

 the relative numbers of men corresponding to each height. The maxi- 

 mum ordinate, representing the number of mean men, is at m = about 

 5 ft. 8 in., the ordinates on both sides diminishing almost to nothing as 

 they reach the dwarfish and gigantic limits d and g, and vanishing 

 beyond. 



Again, measurement around the chest, applied to the soldiers of 

 the Potomac Army, shows a similar law of grouping ("Phys. Soc," 

 ii., 59 ; " Anthropom.," p. 289) : 



Kound chest, inches 28 29 30 31 32 33 34 35 



No. of men in 1,000 1 3 11 36 67 119 160 204 



Round chest, inches 36 37 38 39 40 41 42 



No. of men in 1,000 166 119 68 28 13 4 1 



Here the mean man measures about 35 in. round the chest, the numbers 

 diminishing both ways till we reach the few extremely narrow-chested 

 men of 28 in., and the few extremely broad-chested men of 42 in. 

 These two examples may represent the more symmetrical cases of dis- 

 tribution of individuals on both sides of a central type, as worked out 

 by M. Quetelet from various physical measurements applied to large 

 numbers of individuals. Here the tendency to vary is approximately 



