tion. We can reduce all these to precise numbers, and when we do so we find that every American woman between 16 and 45 must produce 4 1-4 children, in order to replace the existing population and to prevent its decline.* Thus, if every American woman who could have children were to have 4 1-4, they would only keep up the population, but not at all enlarge it. I take America as the strongest case that can be adduced on the subject, and also as that in which the numbers have been so distinguished as to afford the elements of an exact calculation.t

Let us see next what a country in the Old World, on the German continent, exhibits on this subject. I will take Saxony in 1834. Her census has not given the numbers from 16 to 45, but it has noted them from 19 to 50, which we will take as the nearest substitute. Here we find that the same population could not be maintained, even without any increase, unless every woman between 19 and 50 had, upon the average, 4 1-2 children; but, as a large part of these would not be in wedlock, each of those who were must have many more than 4 1-2 each in order only to replace. Thus

The whole white population of 1800 of both sexes
amounted to
Deducting from this.

Leaves

4,309,656

809,760

3,499,896

as the number of all in the community who were not females between. 16 and 45; this number is about 4 1-4 times the 809,760. A similar result will be found from the amount of the other years, as stated in the preceding notes.

In the state of New-York the census in 1825 returned the population as 1,616,438, consisting of 822,897 males and 793,561 females. Of these females 361,624 were under 16, and of those above 16 the married were 200,481, and the unmarried 135,291. Thus the wedded females were but one eighth of the whole population, and nearly one fourth of their own sex. In this proportion, those actually married could not replace themselves and the rest of the community unless each, upon an average of the whole, had eight children.

The whole population of Saxony on the 1st December, 1834, was 1,595,668, or 775,244 males and 820,424 females. The number of females between 19 and 50 are thus stated:-

351,302

4 1-2 to each of these would produce 1,580,859, being nearly 15,000 short of the actual population.

the results both in North America and Saxony seem to ap proximate in this respect.

What facts have we on these points in our own country? Here I do not find a table of the female ages between 16 and 45. But Mr. Rickman has made one, with divisions, for the year 1821, that will enable us to take, as the nearest substi tutes, either 15 to 40, or 20 to 50. Let us inquire into the results of both. The results will be found to be, that every woman between 15 and 40 must have above 5 children to replace the existing population; or every woman between 20 and 50 must, on the average, be mother to 5 1-7.* Yet as a considerable portion of these would not be in the wedded' state, the existing numbers could not be kept up, unless the actually married had each as many as the American and Saxon enumerations required.

These three instances, so distinct in locality from each other, are such fair and sufficient specimens of the general process and course of the renewal of population, that it is not necessary to inquire for similar results elsewhere. These prove the impossibility of a geometrical population, and show by what gradual degrees all national multiplications must take place, and lead us to infer how much more likely population is to keep stationary or to lessen, than to make any great ad vances. Nature forbids the too rapid increase by her two laws that females only shall give the new generations to so ciety, and that only a peculiar portion of these shall, from the ages required, ever be the producing mothers.

Our next point of inquiry may be, what portion of the population of a country is usually living in the married state; and the most common rate at which we can generally estimate this appears to be about one third. In some nations there are more than one third who are married, as in Spaint and

* The whole population in England and Wales in 1821 was 10,530,671, comprising 5,151,052 males and 5,379,619 females. Those of the latter between 15 and 50 are thus stated:

500,997 1 Rick., xxxvii.

Of these, the 15 to 39 inclusive are 2,086,414, and those from 20 to 49 are 2,051,842.

La Borde stated the population of Spain in 1802 to be 10,409,879; and that of these 3,890,661 were married; and of the unmarried then,

Saxony.* In others, rather less than one third, as in the Rhine provinces of Prussia;† in a French department‡ and a Nether. land province; and still less in New-York state. Thus, as a general average, we may calculate that about one third of the whole are always living in the united state. This appears to have been the case pretty nearly in England for the last 30 years;¶ and when this is the proportion, then one sixth of the contemporary population are in the condition of becoming mothers; and this one sixth must be the reproducers of the

3,257,022 were males and 3,262,196 were females. One third of the whole people would have been 3,469,959; so that the married were a little above 3 1-3.

*In December, 1834, out of the Saxon population of 1,595,668 there were 566,837 married and 1,028,831 unmarried. The one third of all would have been 531,837.

† In 1828 the population of the Prussian provinces on the Rhine was 2,172,545. The married couples were 696,220 persons. The one third would have been 724,181. The department of L'Aisne in France in 1818, had 184,214 married persons out of a population of 459,666—Bull. Univ., 1826, p. 20. One third would have been 153,222.

In the department Du Doubs in 1826 the population was 254,314; and the married of these were 82,871.-Bull. Univ., 1831, p. 330. The one third would have been 84,771.

Guelderland in 1824 contained 283,407 people; of whom 89,305 were then married.—Bull. Univ., 1827, p. 101. One third would have been 94,469.

In the New-York state, as before mentioned, the numbers of all were 1,616,458; and the married were, of course, twice the married women, or 400,962, which is not one fourth of the whole. So that, in this flourishing province of the United States, men do not marry so much or so soon as elsewhere.

The standing marriages, if doubled, furnish us with the amount of the married population in every year, as thus calculated on Mr. Sadler's list of them in England, vol. ii., p. 240. The marriages of the year not being included and compared with the population at the time, they exhibit to us these numbers:

The exact one third of the English population in each of these years would have been :

So that the married, in England, at each of these periods, were about one third of the inhabitants, or rather less than one third in the two first ten years; rather more in the two last.

new generation.* Consequently, to do so every wedded female must, on the average, produce 6 children, in order to keep up the population to its existing number, and more than 6 before this can be augmented. This is a large average, and another circumstance hostile to the possibility of a geometrical multiplication, and indicative of the moderate ratio at which population increases, according to the natural laws of birth, and to the ordinary habit of marriage unions, It leads us to infer, likewise, that population has been much oftener stationary than multiplying in the successive ages of the world.

These limitations show that our system has been formed upon a careful plan as to this great point of our population. Limitation implies and indicates regulation; for when natural agencies and their effects arise from specific construction, who is it that limits them but the constructer? and why should he do so but for some purpose and according to some plan? A regular and continued limitation is a mark of a definite design and of an end steadily pursued. The exist ence of such a fact assures us of the superintending attention of our Creator to the subject so guarded; and we may therefore be confident, that whether our populations increase or decline, the elements and laws by which either event ensues are always obeying the direction of his guardian benevolence. We may always leave the issue unfearingly to his disposal.†

Mr. Sadler remarks that the mean amount of the population of England, as made by Mr. Rickman for the three periods of 1801, 1811, and 1821, is 9,988,666; and the total amount of the marriages of the whole term is 1,650,576.-Sadler, Law of Popul., vol. ii., p. 120. Now one sixth of the mean of the population for that time is 1,664,929; so that very nearly one sixth of the living population married in the 20 years from 1801 to 1821.

† On the subject of the marriages, I have endeavoured to trace out some rules concerning them, and will add what has occurred to me in my arithmetical calculations.

If marriages are 1 in 100, and continue to be in that proportion for 33 1-3 years, which may be taken as the average duration of a generation, then, in the course of that series of years, at that ratio, one third of the population will have married, and this portion or number will have all the births of the society among them.

The actually married, in the course of a generation, may be considered to amount to 33 1-3 times the annual number.

We may then deduce as a rule, that according as the proportion of marriages is more or less than 1 in 100, so less or more than one third of the population are in the married state.

When the ratio is 1 in 90, more than one third are married; more, by VOL. III.-I

LETTER XII.

On the Proportion of Births to Marriages.-The Variation in Different Countries.-The established Limits to these and usual Laws.

MY DEAR SYDNEY,

The proportion of BIRTHS to marriages will be always one of the chief laws of human population, because, as they must arise from the connubial associations, and are always pursued by the laws of death, they are limited by our natural system both in their origin and in their departure, and must therefore be duly adjusted to them.

More cannot arise than the marriages allow-more cannot be at any time on the earth than the local, natural, and temporary laws of death permit, in every district. Thus confined in number, on either side, by causes over which they have no control, the continuance, as well as the increase of the human race, will depend principally on the comparative ratio of the nativities to the wedlock of the parents of the community.

From this glance at the real state of this subject, your reason will perceive that the births of the human race, in every country, require the adjusting and providing care, not only at the commencement of the creation, but always afterward. The adapting government must not cease as long as the human race are to continue here under their present system of being. To make continued care on this point unnecessary might have been easily effected by establishing it as a universal and invariable law, that every woman, in her years of marriage, should everywhere, invariably, have the same number of children; and consequently, that every marriage should always have one ratio of births, proportioned

one tenth of the one third. When the ratio is, as in England, 1 in 128, then less than one third are married; less by the difference of a hundred and twenty-eighth part to a hundredth part.

The births, if known, multiplied by their proportion to the married population, will give the number of these; and this number, multiplied by their ratio to the population, will, of course, show the whole number of the community.

When the documents are not complete in all the elements, these rules may assist the calculations from them.