Age of Mother at her Approximate average Marriage. Fertility. 17 9.00 = 6 × 1.5 22 7.50 = 5 × 1.5 27 6.00 = 4 × 1.5 32 4.50 = 3 × 1.5

Which shows that the relative fertility of mothers married at the ages of 17, 22, 27, and 32 respectively is as 6, 5, 4, and 3 approximately.

The increase in population by a habit of early marriages is further augmented by the greater rapidity with which the generations follow each other. By the joint effect of these two causes, a large effect is in time produced.

Let us compute a single example. Taking a group of 100 mothers married at the age of 20, whom we will designate as A, and another group of 100 mothers married at the age of 29, whom we will call B, we shall find by interpolation that the fertility of A and B respectively would be about 8.2 and 5.4. We need not, however, regard their absolute fertility, which would differ in different classes of society, but will only consider their relative production of such female children as may live and become mothers, and we will suppose the number of such descendants in the first generation to be the same as that of the A and B mothers together[17]--namely, 200. Then the number of such children in the A and B classes respectively, being in the proportion of 8.2 to 5.4, will be 115 and 85.

[Footnote 17: Fecundity, Fertility, Sterility, etc., by Dr. Matthews Duncan. A. & C. Black: Edinburgh, 1871, p. 143.]

We have next to determine the average lengths of the A and B generations, which may be roughly done by basing it on the usual estimate of an average generation, irrespectively of sex, at a third of a century, or say of an average female generation at 31.5 years. We will further take 20 years as being 4.5 years earlier than the average time of marriage, and 29 years as 4.5 years later than it, so that the length of each generation of the A group will be 27 years, and that of the B group will be 36 years. All these suppositions appear to be perfectly fair and reasonable, while it may easily be shown that any other suppositions within the bounds of probability would lead to results of the same general order.

The least common multiple of 27 and 36 is 108, at the end of which term of years A will have been multiplied four times over by the factor 1.5, and B three times over by the factor 0.85. The results are given in the following Table:--

Number of Female Descendants who themselves become Mothers.

After Number
of Years
as below.		Of 100 Mothers whose
Marriages and those of
their Daughters all take
place at the Age of
20 years.
---
Ratio of Increase in
each successive
Generation being 1.15.)
Of 100 Mothers whose
Marriages and those of
their Daughters all take
place at the age of
29 years
---
(Ratio of Decrease in
each successive
Generation being 0.85.
10817561
21629938
32453523

The general result is that the group B gradually disappears, and the group A more than supplants it. Hence if the races best fitted to occupy the land are encouraged to marry early, they will breed down the others in a very few generations.