254 TEE 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 



