34

64

This family of inductions has three different
kinds quite distinct logically. Beginning with
the lowest and least certain, we have cases in
which a class of individuals recur in endless succession
and we do not know in advance whether
the occurrences are entirely independent of one
another or not. But we have some reason to suppose
that they would be independent and perhaps that they have
some given ratio of frequency. Then what has
to be done is to apply all sorts of consequences
of independence and see whether the statistics
support the assumption. For instance, the
value of the ratio of the circumference of a
circle to its diameter, a number usually
called π has been calculated in the decimal