144 
(as in par. 3) runs through all the observations, no increase in 
their number will eliminate it. Otherwise, the rule is that the 
precision varies as the square root of the number of observa¬ 
tions; thus, twice the precision necessitates four times the 
labour. It is the best plan to proceed tentatively; if the 
results fall into more harmonious sequence as you proceed, it is 
worth proceeding; and if after dividing your statistics into 2, 3, 
or 4 groups you find the groups agree pretty well and that their 
sums form a yet more regular curve than that obtained from 
any of the subdivisions, you may safely trust it. 
5. The law of deviation.—Mention is above made of 
u homogeneous ” groups: this epithet is applicable when in¬ 
dividual differences are entirely due to the aggregate effect of a 
great many small and independent variable influences. Ex. 
The stature of an English male adult is due to his being a 
man of English race, reared under the range of those conditions 
of food, temperature, clothing, disease, and the like which 
prevail in England. The large causes common to all are the 
English breed and the range of English conditions; the small 
causes are differences of varieties and families, and of food, 
temperature, clothing, and the rest, within the range. The 
law of deviation depends wholly on the fact of multifariousness 
of origin ; it has no more to do with the particular items of that 
multifariousness than the rules of arithmetic have to do with 
the quality of the things to be added or multiplied. Two and 
three make five, whether the objects be pence, or peas, or bills 
before Parliament; so the law of deviation holds for the 
stature of men and animals, and apparently, in a useful degree, 
for every homogeneous group of qualities or compound quali¬ 
ties, mental or bodily, that can be named. It is a very general 
statistical law. 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 
