birth-rate. It should be remembered that the birth-rate started with has been calculated on the Registrar-General's official estimate of the population; and the preceding method can therefore only be regarded as testing the consistency of his figures, and not as determining the actual population.

The conclusion from the preceding discussion on estimates of population is, that a more frequent census is required. Every calculation in vital statistics rests on the assumption that the population is accurately known, and consequently the trustworthiness of such calculations steadily diminishes as the interval from the preceding census increases.

It

It must be remembered that the mean population of the year is taken as the basis of calculation of mortality and other rates, which involves an estimate, even in the census year, for the three months between the census and midsummer. would therefore be advantageous to have the census enumerations at the end of June as well as to have them more frequently. A Quinquennial Census would go far to remedy the present uncertainties. Such a census is practised in France and Germany (triennial in some German states), in New Zealand, Queensland, Manitoba, and the North-western Territory of Canada, as well as in twelve states and three territories of the American republic. It is true that there are not as powerful reasons for a quinquennial census as on the continent, where it is required for military purposes; nor is there the same necessity as in many American states, where the increment of population is by leaps and bounds, and not steadily, as in most parts of our own country. Still, however, there are very strong reasons why a quinquennial census should be adopted.

Vital statistics must always furnish the basis on which sanitary reforms shall rest, especially in regard to legislation. Dr. Farr may in this sense be called the father of sanitary science. There are also political reasons for the change, as political representation for both imperial and local purposes will rest in future on a strictly numerical basis. In addition, a more frequent census would lead to the work being better done, owing to less difficulty in collecting a sufficient staff of

intelligent enumerators, and greater experience on their part. The chief obstacle is the expense of the enumeration; but in view of the important results obtainable, it may be hoped that the reform will be soon realized. The Government has been recently memorialised on the subject by the Statistical Society, and a deputation urging its importance has been favourably received by the Secretary of the Local Government Board (Dec., 1888).

The Requirements of a good Census from a sanitarian's standpoint are, that the enumeration shall be accurate and complete, and that it shall be rapid and simultaneous throughout the country, in order to avoid the disturbing influences of migration. The particulars stated should comprise the following items as a minimum: name, sex, age (children under two years stated in months), relation to head of household, conjugal condition, calling, religious persuasion, illiteracy, birthplace and nationality, language, residence, infirmities. The occupation should be given with such definition as will obviate confusion, and will enable different classes to be compared. The accurate enumeration of age and sex is of great importance, as on it depends the correct interpretation of mortality statistics.

Effect of Migration on Population.-Between any two censuses there is a constant inflow and outflow of population. There is first the natural increment of population due to the excess of births over deaths. Then there is the inflow caused by the presence in this country of visitors and settlers from other countries; while there is the much larger outflow due to the departure of travellers and emigrants. Probably there is no other State in Europe in which the influence of immigration and emigration is so great as in England. In the ten years 1871-80 the natural increment of the population was 3,425,982, the actual increment (as determined by the census) was 3,256,020. Thus in ten years there was a loss by excess of emigration over immigration of 169,962, which excess consisted of 138,324 males and 31,638 females.

Population Registers.-The only way in which an exact record of migration can be kept is by population registers, which

are kept in Sweden, Belgium, Holland, and Italy. The number of emigrants from England and Wales is approximately known from the annual returns of the Board of Trade, but there are no trustworthy data as to immigration.

During the year 1886 there were in England and Wales 903,866 births and 537,276 deaths, so the natural increment was 366,590, equal to 1:32 per cent of the estimated population at the beginning of the year. Now the population of England and Wales enumerated in April, 1881, was 25,974,439 persons. The excess of births over deaths (natural increment) from that date to the middle of 1886 was 1,971,600, making the population in 1886, if determined simply by natural increment, 27,946,039. We have no data, however, for checking the influence of migration, and are obliged, therefore, to assume the same rate of increase as in the previous intercensal period, on which assumption the population of England and Wales in the middle of 1886 consisted of 27,870,586 persons.

Migration not only affects the actual numbers of persons, but has an important effect on the age and sex of the resultant population. Inasmuch as the mortality differs in the two sexes and at different ages, it is evidently of great importance to know for statistical purposes the age and sex constitution of a population.

Progress of Population. The following table shows the population of England and Wales and London at each of the nine census enumerations:

Thus in England every 100 persons living in 1801 had increased to 132 in 1821, and every 100 persons living in 1821 had increased to 132 in 1841. Every 100 persons living in 1801 had increased to 175 in 1841, and at the same rate of increase would amount to 200 in the year 1850 and to 300 in the year 1879. The mean rate of increase was 0141 per unit, or 1.41 per cent. annually during these years. The method by which these facts are worked out is as follows:

Let r rate of increase per unit of population, so that 1+r=population at end of one year; and generally n years.

(1+r)"=

Let R=(1+r)

Then if P = total population in any given year.

n =number of years under observation.

P' population at end of n years.

P (1+r)"=PR"=P'

To find the time in which a population will double itself, i.e. in which P' will become equal to 2 P.

log 2

•3010300

..n= log 1.01410060808=49.5 years.

Similarly, to find in how many years the population trebles itself, we have

n=

log 3 4771213

=

log 101410060808=

The following table gives the estimated population and the area of the United Kingdom, and its several portions in the middle of 1886 :

Economic Value of Population.-Dr. Farr has shown that each individual member of the community has an actual money value represented by the wages he is capable of earning, and that this constitutes the most important factor in the wealth of the community. Deducting the amount required for subsistence, £150 is the mean net value of each member of the male population estimated by the standard of the agricultural labourer. This amount is obtained by capitalizing the income derived from wages and deducting all the expenses of subsistence. It is evident that this value will vary greatly at different ages, being partly dependent upon the expectation of life, and very low in infancy on account of the high death-rate under five years of age. On Dr. Farr's basis, the child of an agricultural labourer is worth only £5 at birth, £56 at the age of 5, £117 at the age of 10, £192 at the age of 15, increasing to £246 at the age of 25, then steadily declining to only £1 at the age of 70, while at 80 the cost of future maintenance is greater than the earnings by £41. It is evident that diseases like enteric fever and phthisis, which destroy life at its most productive period, must necessarily involve an immense waste of money, and that the economic value of the population has been increased by sanitary measures. Thus by Dr. Farr's English Life Table the mean lifetime is 40-86 years; by the Healthy Districts Life Table it is 49-0 years. It is fair to assume that if the mean lifetime in the latter case is one-fifth greater than in the former, at least onefifth has been added to the money value of a working population.