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through the census and the number of deaths at each age observed for as many years, generally from 10 to 20, as suffice to furnish a trustworthy average. The population thus dealt with is supposed to be stationary, that is, the loss by death at each age is at once made good by the addition of an equal number of the same age, whilst the survivors pass on to the age above. Of the many calculations set forth in these valuable tables there is only room here to refer to the “afterlifetime” for such countries as it is available, which is quoted in the last column of Table VII. It shows the average number of years which persons of a given age, or, as here, of all ages, will live, on the assumption that they are subject to the calculated probabilities of survival. It is sometimes known as the “expectation of life,” a term, however, which involves a mathematical hypothesis now discarded.

The relation between the birth and the death rates has been the subject of much analysis and controversy. Observation has demonstrated that the two rates are generally found to move along parallel lines. A high birth-rate is accompanied by high mortality; conversely, when one is low, so is the other. A birth-rate continuously in excess of the death-rate tends to lower the latter through the supply it affords of people annually reaching the more healthy ages. If the supply be diminished, the narrower field open to the risks of infancy has the immediate effect of further decreasing the mortality. In course of time, however, under the same influence, those passing from their prime into the second period of danger acquire a numerical preponderance which throws its weight upon the general death-rate and tends to raise it. It is assumed that throughout the above course the hygienic conditions of life remain unchanged. If, however, they undergo marked improvement, the duration of life is extended and both birth and death-rates, being spread over a wider field of the living, tend to decrease. On the other hand, an accidental set-back to population, such as that caused by famine or a disastrous war, leaves room which an increasing birth-rate hastens to occupy. A similar result follows in a lesser degree a wave of emigration. Examples of all the above tendencies may be gleaned from the returns of the countries named in the table, though space does not admit of their exhibition. In both France and Germany, for instance, the process of replenishment after a great war can be traced both early and late in the 19th century. In England, the decrease in “natality” is in itself enough to account for the decline in the death-rate, apart from any considerations of improved hygiene. In France, on the contrary, the low natality having been so long continued, has raised the death-rate, by reason of the balance of proportion having been shifted by it from youth and the prime of life to old age. It may be inferred from the above that a high birth-rate does not imply a high rate of increase of population, any more than does a decreasing mortality, but the two rates must be considered in their relations to each other. The death-rate, however, is often taken by itself as the measure of the relatively favourable conditions or otherwise of the different countries; but it indicates at best the maintaining power of the community, whereas the increasing power, as manifested in the birth-rate. has also to be taken into account. Here, again, it is not sufficient to rely upon the mere rate of natural growth, or the difference between the two rates, since this may be the same in a community where both the rates are very high as in one where they are relatively low, a distinction of considerable importance. It has been suggested by Dr Rubin of Copenhagen, that if the death rate (𝑑) be squared and divided by the birth-rate (𝑏), due influence is allowed to each rate respectively, as well as to the difference in the height of the rates in different countries (Journ. R. Statist. Soc., London, 1897, p. 154). The quotient thus obtained decreases as the conditions are more favourable, and, on the whole, it seems to form a good index to the merit of the respective countries from the standpoint of vital forces. The first column of Table VIII. shows the order in which the countries mentioned are found to stand according to the above test.

The three Australasian states head the list in virtue of their remarkably low death-rate, which outweighs the relative paucity of their births. The next countries in order all belong to north-western Europe, and their index-quotients are all very close to each other. Sweden falls below its geographical neighbours owing to its low birth-rate, and Finland because of its higher mortality. England and Scotland, in spite of their higher birth-rates, are kept below Scandinavia by the higher death-rate, but their birth-rate places them above Belgium. Ireland and France are pulled down by their low natality. The latter, with the same mortality as Germany, stands far below it for the above reason, as Ireland is raised by its lower death-rate above the prolific countries of eastern Europe. The rate of natural growth is given in the second part of the table. In the case of two of the Australasian states, of Holland, Finland, Spain and Italy, the order is in accord with that given by the test applied above, and the difference between the two in Austria, Ireland and France is not large. The great difference between the serial rank occupied in the respective lists by Russia, Servia and Galicia, with remarkably high rates of natural growth, as well as that found in the case of most of the other countries in question, shows that this factor is by no means a trustworthy guide in the estimate of hygienic balance.

Migration.—Passing from the internal factors in the movement of population, the influence has to be taken into account of the interchange of population between different countries. The net results of such exchange can be roughly estimated by comparing the rate of natural growth with that of the total increase of the community between one census and another, as set forth in Table VIII., in the last section of which the approximate loss by emigration, as calculated by Dr Sundbärg, is given. It will be seen that the only European country which gains by the exchange is France, and there the accretion is almost insignificant. Between many of the countries there is a good deal of migration which is only seasonal or temporary, according to the demand for labour. From Russia, too, there is a stream of colonization across the Urals into western Siberia, and amongst the western Mediterranean populations there is constant