276 Trans. Acad. Sci. of St. Louis. 
mean. The accidental or varying influences, however, are 
much more numerous than the constant or unvarying, and 
thus compensation is in their case much more complete. 
Constant, unvarying influences are therefore more deceptive 
than varying, accidental influences. 
In practice, the influences determining the result of a single 
measurement elude all attempts at calculation, and the extent 
to which the result of a single observation approximates the 
truth cannot be told. But if many measurements are made 
of the same thing, for example the height of a man, the 
individual measurements arrange themselves on either side of 
the true height. If only accidental influences have been at 
- work in each individual measurement in the series, the dis- 
tribution of the observed heights on either side of the real 
height would, if the number of observations were infinite, be 
symmetrical. Thus the true height would at once appear, and 
the probability or degree of deviation of any single measure- 
ment would also be visible. Even with finite numbers a 
probability so great as to amount to a practical certainty can 
be secured. If 2,000 measurements of the same physical 
dimension, e. g. the height of an individual, are made care- 
fully, the total number of observations will be distributed 
nearly as follows : — 
