A STATISTICAL STUDY OF EMINENT MEN. 367 



say 5 ft. 8 in., and a great part of all the men would be of nearly this 

 height, one quarter being not more than 1% inches shorter and one 

 quarter not more than l 1 ^ inches taller. The line of the heads would 

 be nearly horizontal, but would gradually slope more and more, until 

 at one end we should have the comparatively few dwarfs and at the 

 other the few giants. These relations can be illustrated by the bell- 

 shaped curve, whose properties are well known. 



8 



Ogive and Bell-shaped Curves Showing the Distribution of Traits. 



Five feet eight inches is the average height of men, and the number 

 of men of that height (within say 1/10 in.) is proportional to the line 

 OY. The number of men say 1% inches (within 1/10 in.) larger than 

 the average by an amount equal to the probable error or V/2 in. is 

 proportional to the line PQ, and the number of men within these limits, 

 one quarter of all the men, is proportional to the area OYQP which 

 is one quarter the area of the curve. The number of men 6 ft. 2 in. 

 in height who depart from the mean by 6 in., or four times the 

 probable error would be OJJ , only 1/50 as many as are 5 ft. 9y 2 in. 

 in height, and but three in a thousand of all men would be taller than 

 6 ft. 2 in. 



Now applying this to the collective traits giving efficiency, we have 

 one half of all men coming within the limit OP which may be taken as 

 a unit of measure. The total number of men surpassing the average 

 by four times the amount of the average departure would be about 

 300,000. Most of us may hope to fall within this group. The thou- 

 sand preeminent men filling the extreme area of the curve would begin 

 at a point six times the average departure, and the relative excellence 

 of the greater men on the list can also be expressed numerically. 



Turning now to the distribution of these eminent men in time and 

 race we may review statistics not wholly devoid of interest. The num- 

 ber of great men born in each half century since the beginning of his- 

 tory is shown in the accompanying curve. In still more remote ages 

 there were leaders of men, gods, prophets and heroes, whose names are 

 forgotten or obscured, and at the beginning we have four names, rep- 

 resenting rather work than persons Zoroaster, Homer, Hesiod, 



