232 



• KNOWLEDGE ♦ 



[Sept. 19, 1884. 



People generally get rather confused when they come to 

 talk about twenty or thirty millions ; they can hardly fail 

 to grasp the issues really involved when it is a mere ques- 

 tion of a poor little thousand. Let me add, also, by way of 

 preface, that I am not going to trench upon the debateable 

 ground of the Malthusian problem. My object is ethnical 

 and historical alone, not political or economical. 



It is obvious that if every one of these married couples 

 were to have two children apiece, one a boy and one a 

 girl ; and if all these children were to grow up, without a 

 single death or misadventure ; and if all of them were 

 then to marry, the population on the whole would remain 

 exactly stationary. True, there would be just one apparent 

 increase to double after the birth of the new pair into each 

 household ; and the normal number of the population 

 would ever afterwards be two thousand, instead of one : 

 but in each subsequent generation there would always be a 

 thousand children born; and the sum of parents and 

 children would never greatly exceed or fall short of the 

 round two thousand. For simplicity's sake it may be 

 added that in Barataria the children are usually born 

 when their parents are thirty, and the parents themselves 

 usually die in their sixtieth year. 



But, as a matter of fact, an average of two children to 

 each family will not, of course, suffice to keep the popula- 

 tion of the island from positively dwindling. Out of every 

 thousand children born in Barataria, as in England, 150 

 die during the first year, 53 during the second year, 28 

 during the third year, and so forth. By the time they 

 were all 21, and therefore marriageable, only 657 out of 

 the original thousand would be left, of whom 331 would be 

 young men, and 326 young women. ^Some of the men would, 

 of course, of necessity have to remain bachelors, so that 

 instead of five hundred couples, as at the beginning, we 

 should only have 326 couples to recruit the population in 

 future. It results that at this rate the population of 

 Barataria would go on decreasing in the proportion of 

 nearly two-fifths at each generation ; and as we must make 

 some small allowance for couples who do not wish to 

 marry, we may fairly say that it would become practically 

 extinct in seven generations. Roughly speaking, the 

 decrease in the number of married couples would be to 300 

 in the first generation, 180 in the second, 108 in the third, 

 63 in the fourth, 36 in the fifth, 21 in the sixth, and 12 in 

 the seventh. By that time it would be impossible to 

 carry it on much further without an importation of fresh 

 blood from outside to renew the impoverished stock. 



It is clear, then, that an average of two children in each 

 family will be quite insufiicient even to keep up the popula- 

 tion to a fixed standard. Indeed, if we are going to allow 

 for infant mortality, we must put the [average at more 

 than three ; and if we reckon the chances of invalids, 

 bachelors, old maids, and other casualties, we must put 

 it as high as four. In other words, the population of 

 Barataria will not keep stationary even, I take it, unless 

 each married couple on the average has as many as four 

 children. In that case, a generation will consist of 2,000 

 children, of whom 1,314 will reach maturity. But of these 

 only 652 will be girls ; and allowing 152 out of that number 

 (not an excessive estimate) for weaklings, nuns, old maids, 

 and girls who die unmarried, we get back exactly to our 

 original 500 couples. 



This looks a startling conclusion, but it is, nevertheless, 

 a pretty certain one. If the married couples of Barataria 

 have only two children apiece, their population will 

 decrease with surprising rapidity. If they have four 

 apiece, it will barely remain stationary. If they want it 

 to increase perceptibly, they must have five apiece or 

 more. 



Observe, too, that as some families will have only one, 

 two, or three children each, there must be some which 

 have more than four, even to keep the inhabitants of the 

 island up to the fixed number. Families which have less 

 than four children from one generation to another, are 

 families that are gradually dying out. They represent the 

 decadent element in the total population. Families that 

 have more than four children are families that are 

 gradually gaining ground. They represent the progressive 

 element in the population. After a few hundred years, 

 the population will consist of their descendants alone, or 

 almost alone. As a matter of fact, so high is the real 

 average of early death, of celibacy, and of other checks, 

 that even five children are not enough to keep a population 

 up to its normal level, under the circumstances of western 

 Europe. 



But the average fertility of married couples in real life, 

 either in Barataria or in England, is something greatly in 

 excess of this modest estimate of five children apiece. 

 And it does not remain fixed, as I have here supposed, no 

 matter at what age the women marry : it varies greatly 

 with the age at the date of marriage. Dr. Matthews Dun- 

 can has shown that when women marry at seventeen they 

 have on an average nine children each (I omit decimals, 

 which after all are far from lively to look at, and 

 seldom affect the practical result), when they many at 

 twenty-two they have seven, at twenty-seven they have 

 six, and at thirty-two they have four and a half. Even 

 this last comparatively high average is not, in the actual 

 state of England, sufficient to keep up the population to its 

 normal level. Mr. Galton has very ingeniously shown, in 

 his " Inquiries into Human Faculty," that if all the women 

 of a race were to marry at the age of twenty-nine, there 

 would be a steady decrease in the number of their descend- 

 ants from one generation to another. Let us put his case 

 a little more concretely than he has done by applying it to 

 two different classes which go to make up the population of 

 Barataria. 



Half the married couples with whom we have stocked 

 the island are Europeans, and the other half are negroes. 

 Now, we find in this particular case that our negro 

 mothers usually marry at twenty (on the average), and 

 our white mothers at twenty-nine. The result will be 

 that our negro mothers will produce about eight children 

 apiece, and our white mothers about five. This, however, 

 does not in itself sufficiently express the rate at which the 

 negroes will gain upon the whites ; for while the average 

 length of time between one generation and another among 

 the blacks will be twenty-seven years, among the whites it 

 will be thirty-six. In other words, not only wiU the 

 negresses be absolutely more fertile, but their generations 

 will follow upon one another with far greater rapidity : so 

 that at the end of any given time — say, a century — the 

 blacks will have gained doubly upon the whites — first, by 

 gi-eater number of births to each mother; second, by 

 greater number of generations to the given time. 



Mr. Galton's figures enable us to see exactly how fast 

 these two causes of relative increase and decrease would 

 tell upon the total population of our island. Let us start 

 with 100 white mothers and 100 negresses. After 108 

 years (the least common multiple of 27 and 36) the number 

 of female descendants who themselves become mothers 

 would have risen to 175 among the negresses, while it 

 would have sunk to 61 among the whites. At the end of 

 the next equal period, namely, in 216 years from now, the 

 number of negro mothers would be 299, while that of 

 white mothers would only be 38. After the third period 

 had lapsed (in 324 years) the number of black mothers 

 would have increased to 535, while the white mothers 



