Note 246-1 — Chapter II

The so-called Populationistikers are wont to distinguish between the average and probable duration of life (vie moyenne—vie probable); and understand by the former the number of years which, on an average, have been accorded to one deceased; by the latter, the number of years after the expiration of which one-half of a given number of human beings have disappeared. If x deceased persons have lived an aggregate of s years, their average duration of life = s/x. In the case of a whole people, indeed, even the many-years' average of the duration of life of those deceased expresses the true average duration of life only when (a rare case) the aggregate population remains stationary. For, when the population is increasing, the average age of the deceased is smaller than the average duration of life, and, when population is decreasing, larger. In the saddest case of all, when there are no births whatever, and the nation is gradually dying out, there would be an increase from year to year of the average age. In all such cases, strictly speaking, only the actual observation and following up of those born, until they die; can afford a safe result. This is Hermann's method, introduced into Bavaria since 1835. Compare the XIII. and XVII. numbers of the official Bavarian statistics with G. Meyer's criticism in Hildebrand's Jahrbüchern, 1867, I. And indeed Hopf, Preuss. Statist. Zeitschr., says that a complete table of mortality can be made, according to the best method, only after centuries of observation.

Compare Kopf, in the 3d edition of Kolb's Handbuch der Statistik, and the solid works of G. F. Knapp, Ueber die Ermittelung der Sterblichkeit (1868) and Die Sterblichkeit in Sachsen (1869). Price's mode of calculation of which Deparcieux is the real author, which divides the number of the living by the arithmetical mean of the number of births and deaths is not only inaccurate (Meyer, loc. cit., 43 ff.) but erroneous in principle, since it allows two countries of equal population to be the same, the one of which has 120,000 births and a mortality of 80,000, and the other, on the contrary, 80,000 births and a mortality of 120,000. Engel recommends as the measure of real vitality the ratio between the "living years" and the "dead years," meaning by the former the sum of the years which those still living have lived through, and by the latter the sum of the years lived through by those who have died within a given period. (Preuss. Statist. Zeitschr., 1861, 348 ff.) But the inference which may be drawn from a high or a low average of life is altogether ambiguous. A high average may as well be produced by a great mortality among children as by a favorable mortality among those of mature age; and a low average as well by a relatively small number of births as by a relatively short duration of life. (Meyer, loc. cit., 23, 24.)