savings per capita multiplied by the population and capitalized at the proper rate of interest for new industries. If the population is one hundred thousand and ten per cent, of a fair rate for capitalization, the above example would produce $2,000,000 as the value of the invention. If the population had happened to be one million, the value of the invention would have been $20,000,000. Consequently, we note that the greater the population the greater will be the value of a new art.
The second theorem is, that the capitalized value of the old arts in current exercise steadily increases with increasing population, since the savings are effected for more people.
As a third theorem, we may assume that the new arts during any period are the products of the inventive or exceptional minds, and that the greater the population, the greater will be the number of exceptional minds of each degree for the various classifications, so that the value of the new arts during a year is the product of the exceptional minds and the average inventive productivity for each degree.
Suppose that in a population of one million, we may expect that the "one brain" in the million will produce an invention capable of saving one dollar per capita per annum over existing arts. Capitalized at ten per cent, the value of one year's product of this mind is ten million of dollars. Now, let us assume that in two million of people, we shall find two such men. The capitalized value of two such inventions as above will be not twenty millions, but forty millions of dollars. In other words, the capitalized value of new inventions for a given time tends to vary at least as the square of the population, and, if we may imagine that the "one brain" in two millions is of higher degree than in the one million of population, the value of inventions will be at a greater rate than the square of the population.
We, therefore, arrive at the conclusion that the comfort and the prosperity of a population tends to increase more rapidly than the population on which it depends; that society tends to progress under the law of increasing returns. It is also interesting to note that through the workings of our law of social progress, the per capita increment of value for arts varies with the population. In our illustrations above the savings for each person in a one million population would be one half that in a two-million population. We find in the above law an explanation of the rise in wages, inasmuch as exceptional men in all degrees tend to receive as wages or remuneration for services of the same per-capita saving a sum proportional to the total population.
All this reasoning is theoretical. The same is true of the writings regarding the Malthusian theory. But it would appear that the steady progress made in average comfort by all nations of the world since the remotest antiquity would favor the former rather than the latter reasoning. It would appear that there can be no more favoring circumstance
