[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 |            A             |          B                 |
of Years     | Of 100 Mothers whose     | Of 100 Mothers whose       |
as below.    | Marriages and those of   | Marriages and those of     |
| their Daughters all take | their Daughters take       |
| place at the Age of      | place at the Age of        |
| 20 Years.                | 29 Years.                  |
|          ---             |        ----                |
| (Ratio of Increase in    | (Ratio of Decrease in      |
|  each successive         | each successive Generation |
|  Generation being 1.15.) | being 0.85.)               |
-------------+--------------------------+-------------------

---------|
108      |            175           |            61              |
216      |            299           |            38              |
324      |            535           |            23              |
============================================================

==========

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.

MARKS FOR FAMILY MERIT

It may seem very reasonable to ask how the result proposed in the last paragraph is to be attained, and to add that the difficulty of carrying so laudable a proposal into effect lies wholly in the details, and therefore that until some working plan is suggested, the consideration of improving the human race is Utopian.  But this requirement is not altogether fair, because if a persuasion of the importance of any end takes possession of men’s minds, sooner or later means