There are two false methods of estimating the rate of mortality at different ages. The first of these is to calculate the proportion of deaths to total deaths; and the second to calculate the proportion of deaths at various age-groups to the population at all ages. The fallacy involved in the first method arises from the fact that either a diminution in the total deaths or an increase in the deaths at any age-group would increase the proportional deaths at the age-group under consideration, though its interpretation in the two cases would be essentially different. Or if a reduction in both the total deaths and the deaths at a given age-group occurred, this reduction might be entirely hidden by the statement of the result as a proportion between the two.

The second method is equally fallacious; as apart from any conditions adverse to health, the number of deaths at various age-groups, and therefore the proportion of these to the entire population, will vary with the number living at the same agegroups.

For small populations a too minute division of age-groups is unadvisable. Deductions from a small number of individual facts are never so trustworthy as when the basis on which an inference is founded is wider, and accidental causes of variation are thus to a large extent eliminated.

The following table gives the death-rates at various agegroups per 1,000 living at these age-groups.

It will be seen that under 5 and over 55 the death-rate per 1,000 living at each group of ages is higher than the general death-rate at all ages; while at intermediate ages the mortality is lower than the general death-rate, being at its lowest ebb between 10 and 15, and much lower between 5 and 25 than at succeeding ages. It is evident, therefore, that the age-distribution which would be most favourable to a low mortality is one containing an undue proportion of persons aged 5 to 25—such a population as would naturally arise from a continuously high birth-rate.

Annual Death-rates in England and Wales at Twelve Groups of Ages in Groups of Years, 1838-87.*-Males and Females.

to 22.8 70.1 7.9 4.4 6.2 8.3 9.5 13.1 18.9 32.8 67-6 147-7 313.5

1886

1838-40 23.3 72.6 9.7 5.3 7.3 9.5 10.2 12.9 18.2 32-1 65.8 144.0 306.2 1841-50 23.1 71.2 9.2 5.1 7.1 9.5 9.9 12.9 18.2 31.8 67.5 148.3 312-3 1851-60 23.1 72-7 8-5 4.9 6.7 8.8 9.6 12.5 18.0 31.0 65.5 146.7 308.2 1861-70 23.7 73.5 8.2 4.5 6.2 8.5 9.9 13.5 19 2 33.1 67.1 147.2 315.0 1871-80 22.7 68.5 6.7 3.7 5.3 7.4 9.4 13.8 20.1 34.9 69-7 150.8 327.4 1881-85 20.4 59.6 5.8 3.2 4.6 6.0 8.2 12.7 19.4 33.6 68.8 144.6 296.4 1886 20.3 60.3 4.6 2.8 4.3 5-6 7-6 12.0 19.3 33.5 72.7 151.0 333.0 1887 19.8 57.8 4.9 2.9 4.2 5.3 7.4 11.9 18.8 33.5 72.0 146-7 303.5

FEMALES.

1838

to 208 60-3 7-7 4-6 6-7 7-9 9.5 12.1 15.6 28.0 59-8 134-3 288-1 1886

1838-40 21.5 62.4 9.4 5.8 8.3 9.1 10-3 12.7 15.8 28.1 57.3 130-0 278.4 1841-50 21.6 61.1 8.9 5-4 7-9 9-1 10-6 12.9 16.1 28.4 60.9 135.9 293.3 1851-60 21.4 63.0 8.4 5.1 7.4 8.6 1861-70 21.4 63.7 7.8 4.5 6.7 8.0 1871-80 20-1 58.4 6.3 3.7 5.5 6.8 1881-85 18.2 50.5 5.6 3.3 4.7 5.9 1886 18.3 50.9 4.7 3.1 4.5 5.3 1887 17.8 48.9 4.9 3.0 4.3 5.5

10 0 12.2 15.3 27.1 58.9 134.5 288.9 9.7 12.1 15.6 27-9 59-1 134-9 285.1 8.6 11.6 15.6 28.7 61.0 135.4 296.4 7.9 10.9 15.2 27.8 59.5 129.4 267.8 7.2 10.3 15.0 28.4 64.2 137.6 307.0 7.1 10.2 15.2 28.0 63.4 132.7 276-2

It has often been asked why, in a population with a continuously high birth-rate, these inequalities in the proportion of persons living at the different groups of ages do not in a series of years adjust themselves. This cannot be answered better than in Mr. N. A. Humphreys' words: "It must be

* The populations used are deduced from the rates of increase observed in the 40 years 1841-81, and are distributed in the several groups of ages according to the proportions found to prevail at the last five censuses.

remembered that an annually increasing number of births forms a continuously recurring wave, which is always raising the proportion of those living at the lower ages, and which cannot cease its disturbing influence unless the birth-rate were for a lengthened period to remain stationary, as is assumed in a Life-Table population."

Infantile Population.-In considering the mortality at different ages, the first group of ages (under 5) requires further consideration, and especially the mortality under one year of age (infantile mortality). In order to ascertain the infantile mortality, it is necessary to know the infantile population. And in this case the census enumerations do not give us information which is as trustworthy as in most cases. The ages of infants are very commonly incorrectly returned at the census. The number under one year old is certainly understated (many in their first year being returned as one year old). A smaller number in their second year are returned as two years old, and so on. It has been sought to explain the deficiency of infants returned at the census by omissions in enumeration, but Dr. Farr has attributed it rightly to confusion between the current year of age and the completed years of life, rather than to actual omissions. On account of this deficiency in the census number of infants, it is more trustworthy to estimate their mortality in proportion to every thousand births. A more strictly correct plan would be to take the mean of the births of the current and the immediately preceding year as giving the true infantile population; but as this plan is not usually adopted, for the sake of uniformity the births of the current year are taken.

Infantile Mortality. The infantile mortality then is the annual number of deaths of infants under one year of age to every thousand births during the same year. Dr. Rumsey regarded the infantile mortality as a most reliable test, owing to the fact that migration does not greatly affect the result at this early age. He held, however, that premature births should be struck out of account both of the living and dying. It should be remembered that still-births are in this country

thus excluded from registration, though in France they are included. Probably the best plan would be to insist on registration in every case, making a class separate from births and deaths, in which still-births and premature births would find a logical place.

A table showing the infantile mortality in the different counties of England and Wales is given at page 58. This table shows that the infantile mortality is usually lowest in agricultural neighbourhoods and highest in industrial centres. The following table compares the infantile mortality of the 28 great towns during 1887 :