Observations on the Rate of Reproduction.

A study of the South African family CAIRNCRO SS as it was constituted in 1938 reveals a number of interesting facts, and allows of a number of equally interesting deductions.

At the end of 1938 there were 54 male Cairncrosses alive in this country, their ages ranging from 2 years to 76. Of these 54, 28 were over thirty, and therefore of marriageable age, though in point of fact, 6 were bachelors. Of the 28, no fewer than 13 had no sons, while 9 more had only one son each. Of the remaining 6, 3 had two sons each, one had three sons, and 2 had four sons each. That is, the 28 who exceeded 30 years of age had 26 sons, 22 of them contributing only 9. The inference is obvious - unless conditions change, the Cairncrosses will diminish in number with the passing of the years, after increasing from one to 42 during the 19th century. How to account for this reversal is a difficult matter. However, this is a national calamity today, for the Cairncross family is no exception to the general rule. A study of any family will reveal the same tendencies.

It may be objected that the daughters of the Cairncrosses have been omitted, and that their inclusion would alter the position outlined above. My reply is that in omitting the daughters I have also omitted the mothers, and that in including both, the figures I have quoted would merely be doubled and would therefore not alter the relative position at all.

Another interesting though depressing fact is that of the 54 Cairncrosses alive in 1938, sixteen had no brothers. This means, of course, that their branches are no longer flourishing as they did in the past century, but have been reduced to one thin and slight line in each case, in great danger of failing in each generation. Their fathers and grandfathers in nearly every instance had three, four, five or even six brothers, but for some unknown reason the branches have ceased to be fruitful, and in some cases indeed will fail with the passing of the present generation. There are several cases of a solitary Cairncross with a solitary son, and others of a solitary Cairncross with only a daughter or daughters, or with no offspring at all. These latter branches must of course cease to exist at the deaths of the present representatives.


The most striking failure is that of the branch of David (1790 - 1857). This Cairncross had no fewer than 8 sons. Of these 8, six died without male issue, the other 2 producing 5 and 6 sons respectively, i.e. 11 in all; and in 1890 there were 13 representatives of this branch. At this time David's brothers William and Thomas each had 13 and 12 representatives living. However, in the 3rd generation there were only 4 young men of David's branch - two of them are brothers, the only sons of the 6 brothers, while the other two are the solitary sons of the 5 brothers. And so David in the 3rd generation has only four descendants in the male line, although he had 8 in the first and 11 in the second. His brother Thomas, ten years his junior on the other hand, has 16 in the 3rd generation, while William has 10.

The ideal family would consist of four children, two sons and two daughters, the father having married at the age of 25. If the first son was born when the father was 26 and the second son when the father was 30, and this was repeated in each generation, then in the 5th generation there would be 32 male descendants of the originator of the branch; and the time required would be 150 years from the date of the birth of the originator.

Applying this ideal to the case of William Cairncross the Elder (1788 - 1868), we see that in 1938 there should have been 32 male descendants in the 5th generation. But in actual fact there were only two. The first of the 5th generation appeared in 1923 instead of 1918, and the second in 1925, since when there have been no more. The oldest branch of William's family did in fact approach closely to the ideal outlined above, but only through the eldest sons. The others have fallen behind lamentably, so much so that two members of the third generation, who should have been born about 1875, only appeared in 1930 and 1932 - i.e. 55 years later, being thus nine years younger than one of the 5th generation, and 65 years younger than the oldest of their own generation.

This great failure of William's branch is all the more striking when one reflects that whereas the ideal branch requires only two sons per son, William had five sons, two of whom had three sons each, two of these in their turn also having three sons each.

In the ideal scheme there should have been 4 males of the 2nd generation, 8 males of the 3rd, 16 of the 4th and 32 of the 5th. In William's branch there were 9 of the 2nd generation instead of only 10 of the 3rd instead of only 8, but in spite of this great advantage there were only 8 of the 4th generation instead of 16, and 2 (two, mark you) of the 5th instead of 32. Allowance must however be made for the fact that two of the 3rd generation are still infants and may add to the 4th and 5th generations, while five of the 4th generation may one day add to the 5th generation. However, the time lag will be great.


In the case of David (1790 - 1857) the position is much worse. In the 2nd generation there were 11 males instead of 4, but in the 3rd generation there were only 4 instead of 8; and there are none at all in the 4th and 5th generations - nor can any more be added to the 3rd generation.

In the case of Thomas (1800 - 1866) there were 7 in the 2nd generation instead of four, 17 in the 3rd instead of 8, but only 6 of the 4th instead of 16. However, there are still 11 young men of the 3rd generation to add to the 4th; though even if they do eventually bring it up to the ideal number, there will have been a very considerable time lag. In this branch none of the 5th generation has as yet appeared, although there should be 16 of them by 1940.

The following table summarises the remarks contained in the preceding paragraphs: -

1st Gen.2nd Gen.3rd Gen.4th Gen.5th Gen.
Ideal2481632 by 1918/38
William591082 by 1938
David8114 -- by 1938
Thomas57176- by 1938

Of the 54 living male Cairncrosses in South Africa in 1938, 28 were over the age of 30. Of these 28 : -

13 hadno sonsi.e., a total of ......Nil sons
9 hadone son eachi.e., a total of ......2 sons
3 had two sons eachi.e., a total of ......6 sons
1 hadthree sonsi.e., a total of ......3 sons
2 hadfour sons eachi.e., a total of ......8 sons


The ages of the 54 Cairncross males were distributed as follows: -

0 - 10 years6 children
11 - 20 years11 children
21 - 30 years10 adults
31 - 40 years7 adults
41 - 50 years8 adults
51 - 60 years4 adults
61 - 70 years5 adults
71 - 80 years3 adults

The above was written in 1938. During the twenty years that have elapsed since then, the position has deteriorated still There have been 13 male births and 17 deaths. There are males over the age of 30, 18 of them without sons, 14 with 23 sons. There is only ONE grandfather in the male line, only one grandson. Of the 32 over 30 years of age, it can safely be said that, owing mainly to age, at least 25 will not add to the present total. There are 22 males under the age of 30. No doubt half of them will also be dead wood on the family tree, in view of the fact that of the 81 males born between 1788 and 1926 and who lived to be 30 or over, 40 had no sons (33 were childless; of them 23 were bachelors) and 41 had 104 sons (20 had 20; and 21 had 84, the great majority before 1920).

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