The law governing the increase of population, as generally stated, is, that when not disturbed by extraneous causes such as emigration, wars and famines, the increase of population goes on at a constantly diminishing rate. By this is meant that the percentage of increase from decade to decade diminishes. It will be noticed that the figures just given involve such a decrease in the percentage of growth. A simple differentiation of the formula gives as the percentage of increase of the population per decade 32 per cent, in 1790, 24 per cent, in 1880, 13 per cent, in 1990, while in one thousand years it will have sunk to a little less than three per cent. But according to the formula this percentage of increase will become zero, or the population become stationary, only after the lapse of an indefinite period.
The figures just quoted are, to say the least, suggestive. Forming, as they do, the most probable estimate we can make for the population of the future, they suggest possibilities of the highest social and economic interest. Within fifty years the population of the United States (exclusive of Alaska, of Indians on reservations and of the inhabitants of the recently acquired islands) will approximate 190 millions, and by the year 2000 this number will have swelled to 385 millions of people; while should the same law of growth continue for a thousand years the number will reach the enormous total of 41 billions.
How great a change in the conditions of living this growth of population would imply is, perhaps, impossible for us to realize. Great Britain, at present one of the most densely populated countries of the globe, contains about 300 inhabitants to the square mile. Should the present law of growth continue until 2900 the United States would contain over 11,000 persons to each square mile of surface.
With the growth of population our civilization is becoming more and more complex and the drafts upon the stored energy of the earth more enormous. As a consequence of all this, it would seem that life in the future must be subject to a constantly increasing stress, which will bring to the attention of individuals and of nations economic questions which at our time seem very remote.