atives. But
experience shows us that in six successive draws the same ball may
come out twice or even three or four times, although when thousands of
drawings are made each comes out nearly an equal number of times.
So in tossing a coin, heads may turn up ten or twelve times in
succession, though in thousands of tosses heads and tails are nearly
equal. Runs of luck are thus within the rational doctrine of chances:
it is only in the long run that luck is equalised supposing that the
events are pure matter of chance, that is, supposing the fundamental
alternatives to be equal.

If three out of six balls are of the same colour, we expect a ball of
that colour to come out three times as often as any other colour on
the average of a long succession of tries. This illustrates the second
clause of our principle. The third is illustrated by a loaded coin or
die.

By making regressive application of the principle thus ascertained by
experience, we often obtain a clue to special causal connexion. We are
at least enabled to isolate a problem for investigation. If we find
one of a number of alternatives recurring more frequently than the
others, we are entitled to presume that they are not equally possible,
that there is some inequality in their conditions.

The inequality may simply lie in the greater possible frequency of
one of the coinciding events, as when there are three black balls in
a bottle of six. We must therefore discount the positive frequency
before looking for any other cause. Suppose, for example, we find that
the ascendancy of Jupiter coincides more frequently with the birth of
men afterwards distinguished in business than with the birth of men
otherwise distinguished, say in war, or at the bar, or in scholarship.
We are not at liberty to conclude planetary influence till we have
compared the positive frequency of the different modes of distinction.
The explanation of the more frequently repeated coincidence may simply
be that more men altogether are successful in business than in war
or law or scholarship. If so, we say that chance accounts for the
coincidence, that is to say, that the coincidence is casual as far as
planetary influence is concerned.

So in epidemics of fever, if we find on taking a long average that
more cases occur in some streets of a town than in others, we are not
warranted in concluding that the cause lies in the sanitary conditions
of those streets or in any special liability to infec