ABSTRACT
The principle enunciated by Malthus of the geometrical growth of the human population is only a tendency, as obstacles to this growth can be generated by the very increase of the population itself Hence, there are limits to the potential increase of the population, which thus tends to become stationary. Quetelet assumed the sum of obstacles that oppose the indefinite growth of the population is proportional to the square of the rate at which the population tends to increase. This implies that the impact of the obstacles grows indefinitely and that the maximum population, at its stationary level, will only be reached at an indefinitely distant time.
Data is lacking to determine the probable law of population, but formulas of speculative interest can be drawn up. The principle consists of extracting an unknown function j(p) from the formula dp/dt = mp which expresses the geometric growth of the population p. The simplest hypothesis for the form of the function j is to assume j(p) = np. This calculation thus makes it possible to determine the upper limit for the population. However, we can also take j(p) = npa where a has any value, or, yet again, j(p) = n log.p. These hypotheses are in agreement with observed growth, but give very different values for the maximum population. The tables that follow give the population growth for France, Belgium, the county of Essex and Russia (persons of the Orthodox faith) according to the calculations and according to the registry office.
