ence. At times, doubtless, the series will increase more rapidly than by a common difference of one, and at others, by a difference less than one, until, when all the land shall have been brought under cultivation, and the fertility of the soil shall have been increased up to the highest point, to which skill and labor can carry it, there can be no common difference, no farther increase at all, whatever may be the state of the population, whether increasing or decreasing.

And so, too, the "difference," or rate of increase in certain cases, may become a minus quantity, and give in succeeding quantities a smaller quantity of the products of labor with which to supply human wants. Doubtless such a thing, though possible, will be rare and most demoralizing in its influence, wherever and whenever it may occur.

255. The rate of increase of population.

Certainly the rate of increase in human population is of the nature of a geometrical ratio. Two parents, for example, may have four children, and they may, each pair of them, become parents, with four children in each family, and so on; and thus we have a geometrical series, with a ratio of two to indicate the rate of increase of population.

Of course this will not be the exact number in all cases.

But it indicates the law of the series.

256. Limits to the rate of increase of population.

But to the operation of this law there are two limits, that the advocates of the Malthusian theory seem not to have taken into account; both of them limiting, after a certain stage in the progress of the race, the rate of increase, totally irrespective of any change in the distributive wealth.

(1) Human beings, like every thing else in the animal, and even in the vegetable world, become generally less productive as they rise in the scale of culture. We are all familiar with the fact that roses and others of our most highly cultivated flowers will produce no germinating seed; sometimes they have no seed at all.

The higher ranks in any civilized society, if we take wealth and cultivation as the standard, seldom produce offspring enough to keep their numbers, as a class, good. Most of the great men of the world have had no children; very few have had descendants in any direct line for more than three or four generations.

(2) As population becomes dense large cities arise and increase in number, and in the number of their citizens. But they are great consumers of

human life.

I doubt if in cities with thirty thousand inhabitants, there are, on an average, more persons born

than die annually within their limits. In larger cities the number of deaths almost invariably exceeds the number of births. In New York it is about three to one. For some years past there have been in round numbers, births 14,000, deaths 21,000.

And this certainly not because there is not enough to live upon: not because New York State is not increasing in distributive wealth.

Dense aggregations of people, such as cities and armies, furnish an extended field for the operation of the causes tending to destroy human life.

The barrack and the camp are great nurseries of vice and disease, and far more destructive to life than the actual battle field, while the influx of fresh blood into cities and towns unprotected by sanitary precautions affords them the only refuge from depopulation and decay.

The tendency of population is to centralization. Great cities and large towns thus become pestiferous centres, absorbing the vigor and energy of the country and increasing at its expense.

The causes tending to produce disease and death are more fatal and prevalent among a dense than among a scattered population.

In England, for example, from every class of diseases except two, the deaths were more numerous in the cities and larger towns than in the rural districts.

For the diseases called zymotic, and believed to originate from over-crowding and a general sanitary condition of the people, the deaths were twice as numerous in the cities as in the country, while for the whole number of diseases the deaths were forty per cent. more among the civic than among the rural population.

Of the whole ninety-five causes of death specified in the reports of the Registrar-General, only fourteen —and these among the least destructive—were more prevalent in the country than in the cities of England.

The reports of the Registrar-General give the ratio of deaths, in each of the six hundred and twentythree registration districts, to the density of population, for twenty years, and show that the death-rate varies directly as the density and inversely as the advance of sanitary civilization. In the most crowded localities, with a population of two hundred and fifty to the acre, the death-rate was one in eighteen; while in the country, with from twenty to thirty-eight acres to the individual, the deaths. were only one in sixty-two.

As another proof that the average life of man is shorter, his vitality lower, and his physical powers less fully and perfectly developed and less vigorously sustained in the city than in the country, I cite the fact that of the recruits enlisted for the British and

French armies who fail to meet the requirements of health, strength, constitution and stature, a much greater proportion of them are from the cities than from the rural districts.

257. Statistics bearing on this point.

I find the following statistics in the Philosophical Transactions, Vol. VII, pp. 10 and 214 of the Abridgment relating to the cities on the continent of Europe, chiefly German; I could doubtless find more recent facts on the same subject, but these are sufficient, I think, to justify me in the inference I have made.