Page:Popular Science Monthly Volume 1.djvu/62

fere with this special one)—the "mean man" thus stands as a representative 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 adjoining 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 regularity, 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 abscissæ (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 maximum ordinate, representing the number of mean men, is at $\textstyle {m=}$ about 5 ft. 8 in., the ordinates on both sides diminishing almost to nothing as they reach the dwarfish and gigantic limits $\textstyle {d}$ and $\textstyle {g}$, 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):

Round 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 distribution 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