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statistical la w. The obvious effect of multifariousness is to 
make it an extremely rare event that all or nearly all the 
influences should be exerted in the same direction. Ex. It is 
a very rare event that all the cards in a hand at whist are 
found to be of the same colour. This is a simple result of the 
law of permutation : there are a vast and calculable number of 
different events each of which is equally likely to occur, and 
only one of these is the event in question. Proceeding on this 
principle and making certain rather forced suppositions to 
render calculation feasible, the law of deviation is mathema¬ 
tically deduced ; and comparing fact with theory, wherever 
comparison is possible, it is found that they agree very fairly 
and in many cases surprisingly well. Reasoning backwards, 
we may suspect that a group is not homogeneous, or that the 
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 accele¬ 
rating 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. 
Useful Data .-—When collecting data of strength, stature, 
keenness of eye-sight, or of hearing, accuracy of aim in 
shooting, or any other variable performance, a ready and 
efficacious process is to use two fixed tests in each particular, 
and to note the number of those who fail and of those who 
succeed in either test. We are able to make use of the law 
of deviation described in the last paragraph, and thereby to 
calculate with fair precision from these two data, the pro¬ 
portion of those who would fail at any other test of the kind. 
Similarly, we can calculate the value of the test that would 
be beyond the powers of just one half of those submitted to 
it; in other words, we know what would be the average 
performance. Example —Suppose strength is to be tested. 
Select two stones and weigh them. Then offer small prizes 
to those who can lift both of them in succession, beginning 
