le of these has also a choice of 100,000 to pair with. The
probabilities are, therefore, that nine-tenths of them--that is,
81,000--would pair with their normal fellows, while 9000 would pair with
the opposite abnormal variety forming the above-mentioned sterile
unions.

Now, as the number of individuals forming a species remains constant,
generally speaking, from year to year, we shall have next year also
100,000 pairs, of which the two physiological varieties will be in the
proportion of eighty-one to one, or 98,780 pairs of the normal variety
to 1220[64] of the abnormal, that being the proportion of the fertile
unions of each. In this year we shall find, by the same rule of
probabilities, that only 15 males of the abnormal variety will pair with
their like and be fertile, the remaining 1205 forming sterile unions
with some of the normal variety. The following year the total 100,000
pairs will consist of 99,984 of the normal, and only 16 of the abnormal
variety; and the probabilities, of course, are, that the whole of these
latter will pair with some of the enormous preponderance of normal
individuals, and, their unions being sterile, the physiological variety
will become extinct in the third year.

If now in the second and each succeeding year a similar proportion as at
first (10 per cent) of the physiological variety is produced afresh from
the ranks of the normal variety, the same rate of diminution will go on,
and it will be found that, on the most favourable estimate, the
physiological variety can never exceed 12,000 to the 88,000 of the
normal form of the species, as shown by the following table:--

1st Year. 10,000 of physiological variety to 90,000 of normal variety.
2d " 1,220 + 10,000 again produced.
3d " 16 + 1,220 + 10,000 do. = 11,236
4th " O + 16 + 1,220 + 10,000 do. = 11,236
5th " O + 16 + 1,220 + 10,000 = 11,236
and so on for any number of generations.

In the preceding discussion we have given the theory the advantage of
the large proportion of 10 per cent of this very exceptional variety
arising in its midst year by year, and we have seen that, even under
these favourable conditions, it is unable to increase its numbers much
above its starting-point, and that it remains wholly dependent on the
continued renewal of the variety for its existence beyond a few years.
It appears, then, that this form of