254 THE POPULAR SCIENCE MONTHLY 
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 inven- 
tion 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 popu- 
lation 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 reason- 
ing. It would appear that there can be no more favoring circumstance 
