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large influences are not sufficiently subdivided into phases (refer 
back to 3), when it does not conform to this law. The law shows 
that the frequency of small deviations must be very much greater 
than that of large ones, and that the larger the deviation is, 
whether above or below the average, so the frequency of the 
occurrence diminishes in an accelerating degree. It also shows, 
owing to the suppositions introduced, that the deviations on 
either side of the average are symmetrical; this is rarely strictly 
the case in nature. The rate of diminution, according to the 
above-mentioned theory, is shown in the following diagram, 
in which I suppose 1000 men to be ranged in a long line in 
order of stature, beginning with the tallest at A and ending 
with the shortest at B. Then the middle man at C (500th in 
the scale) will be of the average height, and the 250th man at 
D will be as much taller than the one at C (owing to the sym¬ 
metry of the curve) as the 750th, at E, is shorter. Knowing 
these two facts, the height at C (call it c ) and the difference 
(call it r) between C and D (or O and E), we can tell the 
distribution of height all along the line until we come near 
the ends, where the run of the figures always becomes irre¬ 
gular. Thus it will be found that the height of the 90th man 
is c+2r • that of the 20th man is c-\-3r. Similarly the 910th 
man is c — 2r, and the 980th is c—3r. The curved line of the 
diagram remains unaltered whatever may be the number of 
equal parts into which the horizontal line A B is supposed to 
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