Some curious instances will be found in a paper by an American author, J. E. Worcester (Remarks on Longevity, &c., 1833): “In a magazine published at Philadelphia in 1804, it was stated that Samuel Bartrow died at Boothbay, Maine, at the age of 135. But instead of this it appears that a man of the name of Barter died at that place at the age of 105. Several newspapers and journals, in 1823, mentioned the death of a Moor, of the name of Yarrow, at Georgetown, Columbia, at the age of 135, but it has been found that his age was only about 85."

Undoubtedly several other records of centenarians are tolerably accurate. If we confine ourselves to the comparatively youthful persons of 100-105 years, we shall find many reliable cases, as that of Sir Moses Montefiore, or of the French naturalist Chevreuil, and even if we go to much higher ages, there is often good evidence, as in the case of the Norwegian Drakenberg (1626-1772), who married when 111 years old, and as a widower of 130 proposed to marry again, though without success.1 But these records are neutralised by other more or less doubtful cases, and at the end of the 19th century statistics of longevity are still in a very incomplete condition.

No wonder then that life tables generally take very small notice of extreme old ages. Sometimes they stop abruptly, for instance at 100 years of age, or the rates of mortality in the highest ages of life are not based on observations, but on some fiction, generally that mortality is increasing with age according to a simple mathematical function till all have died out. But probably none of the authors of life tables would look upon this scale of probabilities otherwise than as a conventional fashion of bringing a tale to an end, nor is it of any practical consequence in life assurance or similar matters what are the rates of mortality among very aged persons, the number surviving being so small that it is of nearly no influence on the premiums charged by the life offices what is the law of mortality in this period of life. No wonder therefore that modern statisticians have taken so small notice of this question.

But even if life tables have no great value for business purposes, they may have an intrinsic value, and I hope the following investigation will be found of some interest for students of vital statistics.

If we consult the unadjusted life tables we sometimes find a curious interruption in the general law of mortality. The following table shows the probabilities of dying in the course of a year for males of various ages according to the German and Norwegian life tables 1871-1881.

It will be seen on inspection of these numbers, that the chances of dying within the next year are not increasing according to the German unadjusted table and, from 95 years of age, rather decreasing according to the Norwegian table. The question arises whether this must be ascribed to the defects of the numerical observations or whether there 1 Dansk Biografisk Lexikon, IV, 1890, pp. 327-8.

is a real influence counteracting the general tendency to an increase in mortality according to age.

It is evident that a person like Drakenberg could hardly have existed if 50 per cent. or more of the old persons alive died every year. Very few persons in a million will reach 100 years of age, but if out of these one half died yearly, only 100 of the centenarians would reach 110 years, and one out of a million 120. If there are some rare cases of persons with an extraordinary age, the law of mortality must have a form which renders it possible to meet these exceptions every now and then.

But, on the other hand, we cannot rely on the official statistical data without any revision. For instance, if only a few persons were erroneously made 20 years older than they are, we might observe a conspicuous influence on the law of mortality in the very old ages. According to the Norwegian table there will be 33,695 males alive at 70, 15,347 at 80, 2,440 at 90, and 70 at 100. Let us now suppose that only 1 per mille of males, 70 years old, was erroneously registered as 90 years old, the number of males of this age would be 2474 instead of 2440; the error would thus be of little consequence. Ten years later there would be about 15 persons alive out of the 34 persons whose age was wrongly registered, and if the mistake is still undiscovered, the number of centenarians will be increased from 70 to 85. The influence of this apparently insignificant error will thus be constantly greater every year. The probability of dying before a year for a person of 95 years would be nearly unaltered, but for a centenarian it would sink from 41 to 36 per cent., and 5 years later it would be about 30 per cent. instead of 60 per cent. It will thus be necessary to be very careful in order to draw correct conclusions out of such observations. The Norwegian Central Office of Statistics adopted the good plan

of revising the observations from the census 1st January, 1891, on aged persons above 95 years of age, with the help of the church registers, and to follow these persons closely through the following 5 years till the end of 1895. The list has been afterwards carefully revised once more and even if there are possibly still some inaccuracies left, these observations seem trustworthy enough to allow conclusions as to mortality in these ages.2

Altogether, 323 persons came under observation, 111 males, 212 females; out of these about gave their age incorrectly. One of them was 12 years younger than according to the census, but on the whole the errors are much more inconsiderable, and the collective result of all the errors is that the average age both of males and females is overstated with only about 10 months. There is even a chance that this difference may be still a little reduced, for there may have been some persons above 95, but registered by the census as younger, who are therefore not on the list. Still there is evidently a much greater inclination to overstating the age than to giving a smaller age than the real one, so these cases are probably not very numerous.

Generally, in statistical investigations, the year is used as unit of time. In dealing with these observations I have preferred the quarter of a year as unit, the after life-time allotted to these aged persons being so short. Each person has been taken under observation from the first day after January 1st, 1891, when a fresh quarter of a year began, and till the end of the last quarter before December 31st, 1895, if he did not die before; fractions of quarters of a year thus being left out of consideration. If a man is born 1st February, 1790, and is still alive on 31st October, 1895, I have thus taken him under observation from 1st February, 1891, till 31st October, 1895, i.e., 19 quarters of a year.

A quarter of a year has been, under this supposition, commenced altogether 2457 times by the persons observed, viz., 756 by males, 1701 by females, with 82 and 147 cases of death. Out of 100 persons there consequently died 9 before the end of a quarter, viz., 8.6 per cent. of females, 10-8 of males. The difference between the mortality of males and females is not particularly striking, and I have therefore preferred to deal with both sexes combined, in order to secure somewhat larger numbers.

According to these observations about of the aged persons died within a year, but the mortality seems to be decreasing instead of increasing according to age, and the above-mentioned stoppage in the general movement of mortality seems to be evidenced by these observations, few as they are in number.

These observations are, however, open to an objection. Mortality

1 A similar proceeding has been followed for years by the Swedish Central Office of Statistics.

2 In a contribution to Nationalókonomisk Tidsskrift I have dealt with these observations before the additional list of corrections was published; the numerical results here given therefore differ a little from what was stated in that article.

in this period of life is evidently rather variable, according to the more or less favourable meteorological character of the year. During the first 4 quarters of a year mortality was 1037 per cent., in the next 4 quarters 11.20, and then 6.82, 6·60, and 8.70. On the whole the two first years were unfavourable, whereas the rest of the period had a relatively small mortality. But during these five years the persons under observation have grown older, and it may therefore be objected that the peculiar features of mortality only arise from this circumstance. If we, however, calculate the number of deaths expected during each year of age according to the above-named rates, supposing 10.37 per cent. to die in the first 4 quarters, 11.20 in the next, and so on, we shall find the following result :

:

There is no marked difference between the actual and expected numbers; and there is evidently more probability that mortality after 101 is smaller than in younger ages, than for the opposite theory. What has been observed above thus holds good if we take the various aspects of the year in consideration. On the whole these 5 years have been favourable to the old persons, for at the close of the period of observation there were 2-3 times as many persons above 100 as before It is not uncommon to observe interruptions like this in the general law of increasing mortality according to age. Mr. A. N. Kjær, Director of the Norwegian Bureau of Statistics, points out a remarkable connection between mortality and marriages, in the ages 22-32 years. During this period of life the greater part

of the male population enters marriage with its generally healthy influence on the chances of life. According to the unadjusted Norwegian life-table the rates of mortality of males are, during these 10 years constantly decreasing from 9-3 per m. to 7.9 per m. But at the same period of life we shall find that mortality of bachelors is on the whole increasing, of married men likewise, or at least not essentially decreasing. The fact that there is a constant stream from the comparatively unhealthy class of bachelors to the more settled class of married men with their smaller rates of mortality, explains the considerable reduction of mortality in this period of life.

A similar interruption of the increase of mortality may be observed among persons with a consumptive family history after the age of about 40 years. Another striking fact is the mortality of retired civil or military officers, or on the total of persons retiring on account of age or debility from their usual activity. In a report on the pensions of the Danish clergy, I have pointed out a curious influence of the time elapsed since the retirement. On an average, Danish clergymen retire when 69 years old; on the whole we should presuppose that mortality would be increasing with the distance in time since retiring, though not in the same degree as according to a common life table, as some of the retiring clergymen are comparatively young with greater chances of surviving, whereas others are very aged, and may soon be expected to die out.

But if we group the observations according to the time elapsed since retiring we shall find the following numbers (1857-85).

From the first year with its rather exceptional conditions to the second one, there is thus a considerable increase of mortality, but afterwards the chances of life are improving (or at least they do not get worse) with the advancing age, till a minimum is reached after 4-5 years. On the whole there died, proportionately, more during the first 5 years than during the next quinquennium, but after that time considerable increase can be observed.