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 | 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.