1886 the rate of natural increase per 1,000 was 13.2=0132 per unit.

Now MP R", where, as in compound interest,

Mamount when increased = principal + interest.

P=principal=original population.

R=1+rate of increase per unit.

r=rate of increase per unit.

R=1+r.

n=number of years.

Required, the time required to double the population.

CHAPTER VI.

DEATHS.

Estimation of Death-rate.-Death-rates for Short Periods.-General and Special Death-rates.-Effect of Migration on Death-rate.-Correction for Visitors.-Effect of Public Institutions. -Influence of Birth-rate on Death-rate.-Opposite Views of Letheby and Farr.-Influence of Age and Sex-distribution on Death-rate.-Proportion of Males and Females in Population. Method of Correction for Age and Sex-distribution.— Standard, Recorded, and Corrected Death-rates.-Factors for Correction. -Trustworthiness of General Death-rates.

ORTALITY statistics surpass all others in importance, whether they are considered from a social, or actuarial, or sanitary standpoint. We must therefore consider them in detail.

Estimation of Death-Rate.-The death-rate may be reckoned (1) in proportion to every thousand of the mean population; or (2) the proportion of deaths, taken as unity, to the whole population may be stated. Thus, in 1886 the death-rate per 1,000 was 19.3, which is equivalent to 1 in 51. The two are easily convertible by division.

Death-Rates for Short Periods.-It is evident that the shorter the period to which a death-rate refers the greater the liability to error, owing to accidental causes of variation. But the death-rate for a short period expresses a fact, the errors only arising when we draw wide inferences from facts relating to short periods. Large fluctuations from accidental causes occur cspecially in connection with small populations. A temporary high death-rate may, for instance, only mean that, owing to the

prevalence of inclement weather, a considerable number of unstable and fragile lives have had their deaths slightly hastened.

The death-rates for each week published by the RegistrarGeneral are annual death-rates per 1,000 of the mean population of the year; i.e., they represent the number who would die per 1,000 of the population, supposing the same proportion of deaths to population held good throughout the year. They are, therefore, not actual rates at all, and the public should be warned against the indiscriminate use of them for comparison. They may be of service in contrasting with the death-rate of the same place at the corresponding period of a preceding year, and as showing the influence of seasonal variations; but should be received with caution when used to compare one town with another.

The death-rate for a week might be obtained, if there were exactly 52 weeks in a year, by multiplying the deaths by 52, or dividing the population by 52, and then proceeding as for an annual death-rate. But the correct number of days in a natural year is 365-24226, and the correct number of weeks therefore 52.17747. The Registrar-General therefore divides, for the purposes of his weekly returns, the estimated population of each town by 52:17747, thus obtaining what may be called the weekly population of the town. Thus, if the population of a town is 143,956, its weekly population is

which is assumed to remain constant for the year for which the calculation is required. Now, if there are 35 deaths in one week; then the annual death-rate for the week in question 35 × 1,000-12.69

=

2758

It would be more logical to multiply the deaths of each week by 52.17747 than to deal with the population; but as this would require to be done each week, the former method is evidently less laborious, and produces the same results.

The Registrar-General makes his death-rates for each

quarter refer to the thirteen weeks most nearly corresponding with the natural quarter; and the quarterly population is obtained by multiplying by thirteen the population of one week.

The death-rate, expressing the proportion borne by deaths from all causes to each thousand of the population, is known as the general or crude death-rate. The fallacies detracting from its value as a test of relative vitality will be subsequently considered. It should be regarded as the first test, to be followed up by further research. It is doubtful, however, whether, in the case of large populations, any more trustworthy test is available; and its value may be regarded as remaining unimpaired, spite of numerous attacks upon it.

Special death-rates are also employed; and these may be divided into two kinds: (1) those which differentiate the persons affected as to age and sex, race, social condition, occupation, density of population, locality, season, etc.; and (2) those which differentiate the causes of mortality, as zymotic diseases, phthisis, violence, suicide, etc.

We can only discuss in this chapter the influence on the death-rate of movements of the population, of large institutions, of the birth-rate, and of the age and sex distribution of the population.

Effect of Movements of Population.-The effect produced by immigration and emigration will vary in proportion to the average age and sex of the migrants. The mortality of most large and growing towns would stand higher than it does but for the large number of young and healthy immigrants from the country. Similarly, watering-places and residential towns appear somewhat healthier than they are, because of the large proportion of young domestic servants.

The low death-rate of New Zealand-124 per 1,000 for the years 1866-75-was doubtless due partly to its equable climate and the prosperous condition of its population; but much more to the constant stream of mostly young immigrants, and to its high birth-rate.

The bulk of the immigrants to towns are probably in good

health; but a certain number go from the country into the town hospitals. On the other hand, many townspeople suffering from phthisis or other chronic disease migrate into the country, and aged persons very commonly do the same.

Dr. Ransome has proposed not to calculate the deaths over fifteen years of age, as being affected by migration, but to compare the death-rate of various towns for ages under fifteen. This might be suitable for Manchester, but not for other towns. Thus seaside towns like Margate and Brighton, which have a large number of boarding-schools, would be unfairly represented.

The only way to avoid the fallacies arising from this cause would be to have records kept of the movements of population, and the births and deaths of each place subjected to analysis before comparison is made. In order that the death-rates of two populations should be comparable on equal terms, so far as migration is concerned, it would be necessary that (a) the number of immigrants and the average duration of their residence should balance the number of emigrants and the average duration of their absence; and that (b) the proportion of sexes living at each age, their state of health and liability to disease, should be the same among both.

Such conditions are not attainable even in European States, where a record of migrants is kept, and much less so in this country; and it is satisfactory to remember, therefore, that in most instances the sources of mistake tend to counteract each other; and the most important fallacy, that arising from varying age-distribution of the population, can be avoided by giving the death-rate separately for different groups of ages.

There is another way in which migration may affect mortality statistics. In the case of districts inhabited by artisans and labourers, there is always an extraneous population pressing in to fill the vacuum caused by removal or death, so that, as pointed out in regard to Liverpool by Dr. French in 1865, the same house may in one year represent the accidents, deaths, and diseases of twenty-four persons, instead of the six persons which the census gives for each house. This is analogous to the error in hospital statistics, when the number