The mean age at death can be employed with safety as a true test or measure only in those cases in which the calculation purport ing to embrace an entire class of persons, every member of that class is included, or in which the calculations embracing only a sec tion of an entire class, the class in question is retained in a state of perfect uniformity during the whole time comprised in the calculation. According to the first supposition, we take a given number (say 100,000) of children born in a given year, and trace them through life till they are all dead, summing up their ages at death, and dividing by the number of deaths. According to the second supposition., we ex tract from some register of deaths the ages of all who die during some term of years, having ascertained, by referring to the census, that the population has continued stationary (that is to say, constantly gaining as many by fresh births as it loses by death), during the time over which the calculations extend. The same reasoning will be found to apply to the mean age at death, taken as a measure of the true duration of life of the members of any handicraft, trade, or profession. It can only be a true measure so long as the blanks aused by death are filled by new recruits, entering at the same age as the age of entratice of the deceased. In all other cases but those now specified, the mean age at death is a more or less fallacious measure of the true duration of life.
As the mean age at death has been lately revived as a measure of the duration of human life, and a test of the sanitary condition of the population, though its fallaciousness was long since recognised and pointed out by the early constructors of life-tables, it may be well to devote some space to a statement of the cases in which the proposed test is most open to objection.
a. The mean age at death has been employed as a test of the sanitary condition of a nation, and as a measure of that condition when com pared with another nation, or with the same nation at another time, in ignorance or for getfulness of the well-ascertained fact that the living population of one nation may differ very widely in its composition from the living population of another, and that the elements of the population of the same nation may undergo very extensive changes even in a short term of years.
In illustration of the first of these state ments, it will suffice to instance the strongly contrasted populations of England and Ame rica, of which the first has 46 and the second 54 in the hundred under 20 years of age, the number above 20 being, of course, reversed. In the two populations of Denmark and Sar dinia, on the other hand, the relative pro portions at different ages are very nearly the same ; and, when expressed in round numbers, for long intervals of age, identical. As a general rule, however, there is considerable difference between one population and another in the proportion of persons living at the same ages. In support of the second of these statements, the change which took place in the population of England in the interval from 1821 to 1841 may be adduced. At the former period, the persons living under 20 years of age were 49 per cent, of the whole population, but in 1811 they had fallen to 46 per cent.
There is no room for doubt, therefore, that different populations vary in their composition, and that the same population may, in course of time, undergo considerable changes, and exhibit very striking contrasts in the number of persons living at different ages.
Such being the case, it will not be difficult to prove that the differences in question do so materially affect the mean age at death as to rob it of its alleged value as a test or measure of the sanitary condition of nations. We have only to suppose the young population of America transferred to England, and exposed to the same causes of death as determine the duration of life of its own inhabitants, in order to be fully convinced of the fallacious ness of this test. Now, according to the rate of mortality prevailing in England, little more than half its inhabitants die before com pleting their 20th year, and somewhat less than half after that age. If the mean age of all who die under 20 years of age be taken at 5 years, and of all who die above 20 at 60 years, the mean age at death of fifty persons dying out of the respective populations of England and America, will be about 31 and 30 years. These numbers, however, though correctly calculated from the rough data just assumed, much less widely than the true re sults, for the actual mean age at death, which is 29 years in England, is only 20 years in 'America.* So that two populations, subject :to the same law of mortality, and losing the same number of persons at the same ages, in consequence of the different constitution of their respective populations, may have a widely different mean age at death. Similar results to those obtained by comparing Eng land and America are arrived at if we compare England in 1821 with England in 1841. The mean age at death, which in 1821 was 25 years, became in 1841, owing to the change in the population already referred to, 29 years.*
If any further illustration of the fallacy of the mean age at death, when used as a test of the sanitary state of nations, were required, it might be found in its failure when applied to coun tries of which the true position in the sanitary scale has been ascertained by the application of unexceptionable tests. The three nations, England, France, and Sweden, for example, occupy the following relative position :— 1. England. 2. France. 3. Sweden. But if the mean age at death were taken as our guide, they would rank as 1. France. 2. Sweden. 3. England. The mean age at death being 34 for France, 31 for Sweden, and only 29 for England. t b. The mean age at death has been em ployed as a measure of the relative sanitary condition of English counties, cities, and towns, of town and country, and of the several districts of large cities. to show the fallacy of' the method as so applied, it will suffice to prove that the populations thus compared are composed of different elements. Taking, as before, the number living below 20 years of age as an illustration, it appears that while there are 47 in the hundred under 20 in Essex and Suffolk, there are only 44 in the hundred under 20 in Staffordshire ; that for 47 in the hundred in Leeds, 46 in Sheffield and Birmingham, and 94 in Manchester, there are only 42 in Liverpool, 41 in Exeter, and 40 in London ; and, lastly, that the popu lation under 20 years of age, which amounts to 47 per cent. in Bethnal Green falls as low as 41 in Clerkenwell, 40 in Kensington, 36 in St. Giles's and Marylebone, and 31 in St. George's, Hanover Square. The effect of this variable distribution of the population on the mean age at death is very well marked, and is placed in a very striking light by sup posing the population of the metropolis to be transferred to some of these counties and cities, and to be exposed to the influences for good or evil which are brought to bear on the duration of life of their actual populations. Thus, if the population of' London, of which 40 per cent. are under 20 years of age, were to be transferred to the county of Hereford, where the average age at death is nearly 381 years, the mean age at death would become 301 years, or a year and a half in excess of the mean age at death of the existing inhabit ants of London. The advantage, therefore, which the county of Hereford enjoys over the metropolis, in a sanitary point of view, instead of being represented by the difference between and 29 years, or 94. years, is really not more than a year and a half. Again, the average age at death in the metropolis is 29 years, and in Sheffield 23 years ; but if the population of the metropolis were transferred to Sheffield, the average age at death would be 28 years. So that the difference of 6 years, which, according to this test of the mean age at death, marks the sanitary su periority of London over Sheffield, dwindles, under this very obvious correction, to one year. If we apply the same correction to the several districts of the metropolis, we obtain similar results. Bethnal Green is the district in which the mean age at death is lowest, while in Kensington it attains its maximum. In Bethnal Green the mean age at death is 26', in Kensington 32. But the population of Bethnal Green transferred to Kensington, would have a mean age at death of 27 years ; so that in this case also a difference of six years in favour of the more aristocratic quarter dwindles down to one year. In some eases the use of this corrective actually re verses the position of the two populations submitted to comparison. Thus, the mean age at death in the united parishes of St. Giles's and St. George's Bloomsbury is 28 years, and in Bethnal Green, as has just been stated, 26 ; but transfer the population of Bethnal Green to St. Giles's, and the mean age at death becomes 24, years. The application, therefore, of this correction completely alters the relative position of the two parishes, so that the parish which, when tested by the mean age at death, seemed the healthiest, proves to be the most unhealthy. Serious errors and exaggerations have also been committed in comparing the smaller districts of our large towns with each other. The meanest and most squalid districts are as naturally the resort of those who marry early, and of those who are sunk into poverty by the burden of large families of young children, as better districts are the abodes of the more prudent and least encumbered members of society. The lowest districts of the large towns of England are also the resort of that part of our population which indulges most habitually in intemperance, and in all the habits that engender poverty, misery, and disease. It is, therefore, inevitable that in comparing the worst districts with those of a somewhat better class, we should be comparing popula tions containing a large proportion of persons liable to a high mortality for reasons other than the insalubrity of the districts themselves with those containing a smaller proportion.