| Children | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 1803-1814 | 0 | 0 | 2 | 4 | 8 | 10 | 16 | 20 | 16 | 10 | 8 | 4 | 2 |
| 1865-1874 | 10 | 15 | 19 | 8 | 4 | 5 | 8 | 10 | 8 | 5 | 4 | 2 | 1 |
It would be clear that the change was due to the substitution of families of 0, 1, 2 and to a slight extent of 3, for fifty per cent. of the families over 3, that all these groups of larger families had given up the same proportion to swell the groups of small families. This would point clearly toward restriction as a cause.
Suppose that the following were the facts:
| Children | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 1803-1814 | 0 | 0 | 2 | 4 | 8 | 10 | 16 | 20 | 16 | 10 | 8 | 4 | 2 |
| 1865-1874 | 6 | 8 | 10 | 16 | 20 | 16 | 10 | 8 | 4 | 2 | 0 | 0 | 0 |
In this case it is clear that the change was due to the substitution throughout of families less in each case by three children. There is no cutting off equally from all the higher groups. Families of 4 and 5 for instance increase in number. There is no special increase of the 0, 1, 2 families. The movement has been simply a general decrease in size, a moving backward of the general tendency to produce. Such an appearance in the statistics would point toward decreased reproductive capacity.
In our second illustration there would probably be in connection with the lowered average tendency a reduction of the variability. That is the range or spread from the common occurrence (a four-children family) would be less, and our figures would be something like the following:
| Children | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 1865-1874 | 0 | 4 | 11 | 17 | 24 | 17 | 11 | 6 | 4 |
Generalizing the argument we may say:
In so far as conscious restriction is the cause of the lesser fertility of the late decades it will show itself by a disturbance of the form of distribution of the different-sized families.
1. Restriction as commonly considered would increase the 0, 1 and 2 and to some extent 3 children families at the expense of all larger families. For according to the common view there would be no influence of restriction in a family which had already five or six children.
2. Each group of large-sized families would then lose in proportion to the number of families in it, the psychological and social sources of the custom being in no way correlated with fertility.
3. The result will be the appearance in the statistics of late decades of two species of families, one showing the natural tendency and in every way comparable to the species shown in the first decades, the
