Here we find the period of duplication to be 27 years, as fol

If the period of matrimony be delayed to 25 years, and the productive children be born in the first, fourth, seventh, and tenth years, and the duration of life be diminished to 50 years, the period of duplication will be 30 years. To obtain a more rapid increase than is given in the above table we must have more children, or longer lives, or both.

If we suppose the unproductive children born in the second and fourth years, and to die at the age of one, five, and fifteen years, we shall obtain 43 years as the average duration of life, as follows:

* These births, resulting from the latest marriages, are here added only with a view to show that the total births correspond with the total number of marriages.

In order to ascertain what proportion the marriages, births, and deaths bear to the whole population, it is necessary to inquire how many of the unproductive births would be living in any given period, and we therefore give the following table of the births and deaths of that class, that would take place in the years from 223 to 250. In preparing it, to avoid the necessity for using fractions, we have stated the whole in thirds, so that three represent a single birth or death.

The number of unproductive births in this period would therefore be 299, and there would be 264 deaths out of the same class. The whole number of that class living in the period referred to, would be 1192, giving an annual average of 44. The average of productive population, existing between the years 223 and 250, agreeably to Table I., is That of unproductive population, per Table II.,

Average population,

890

44

934

Of these there would be, of 23 years and upwards, married, or fit to contract matrimony,

489 The number of marriages in the same period is 239, giving an annual average of 9, being 1 in 104 of the total population, or 1 in 54 of the population of mature age, estimated at 23 years. The number of births in the same period, is

annual average 43, or 1 in 22. The deaths in the same period, are

annual average 18, or 1 in 52.

1168

480

These quantities are probably the lowest in regard to deaths, and the highest in relation to marriages and births, that are likely to occur in the existing condition of man, and afford the maximum rate of increase.

We have now to consider the effect produced by emigration in diminishing the rate of increase, and of immigration in augmenting it. With the increase of population and of capital, men are enabled gradually to bring into cultivation soils that by distance, or by difference of quality, are inferior to those that were originally cultivated, with a constantly increasing return to labour; and thus while population is becoming daily more dense in the neighbourhood of the great centre of capital, it is also daily extending itself over a wider space. It is sometimes asserted, that if land would always yield in proportion to the quantity of labour and capital applied to it, there would be no need to cultivate more than a single farm, or a single district, for the supply of any number of inhabitants; and because such cannot be the case, it is assumed that every fresh application of capital and labour to cultivation, must be attended with a diminished return. If we were to attempt to erect a column of earth, or of sand, we should speedily attain the greatest elevation of which it was capable, for the simple reason that the form was artificial. If we were to compel a family and its descendants to remain permanently upon the same soil, living upon its produce, and performing no exchanges with their neighbours, we should soon find the same result. For a given time, increase of population would be attended by increase of capital and improved means of living, but when the whole land was cultivated, as well as their skill and capital permitted, every increase of population