5. Decrement of Life. Assuming, as before, that a million of male children are born alive (for the still-born must be excluded from the calculation) if it be found that 180,492 would die in the first year, it follows that the difference, namely, 819,508, will enter upon the age of one year. Suppose the law of mortality indicate that the proportion that will die, out of a million, between the age of one and two, is 30,000; it is plain that the number who would die out of 819,508 will by the rule of three be 27,863, and consequently that the residue, namely, 791,615, will remain alive, and so enter on the age of two years. This method being pursued through each and every age to the extreme term of life, when none of the original million survive, the result is a table of mortality in the form in which it is commonly presented in the works of writers on this branch of science. In the table thus constructed there is a column containing the number of living persons who, out of the original million, lived to enter upon each and every year. Of this rank of numbers the difference between each term and its next succeeding one, is the number who die in that particular interval: that number is the measure of what is technically called the decrement of life for that particular year, and the whole of the decrements for each and every year taken collectively is termed the decrement of life. The decrement of life, then, is not only not the same as the law of mortality, but is carefully to be distinguished from it. The law of mortality is derived from observing the number who die out of one and the same number which is always supposed to enter on each and every year. The decrement of life constitutes a rank of numbers arising out of the successive deaths; that is, out of the original million in the first year; out of the survivors of that million in the second year; out of the survivors of those survivors in the third year, and so on. In the first case the number of the living is always the same; the number that die is the variable quantity: in the second case the number of the living is the variable quantity, while the number that die may remain pretty much the same for a succession of years; and on casting the eye on the tables constructed in the ordinary mode, it will be seen that the number often does remain the same for a considerable series of years.
We have said that life is a fluctuating quantity. It fluctuates in different countries at the same period; in the same country at different periods; in the same country, at the same period, in different places; in the same country, at the same period, in the same place, among different classes; in the same country, at the same period, in the same place, among the same class, at the different determinate stages of life. Some few of these fluctuations, and more especially the last, depend on the primary constitution of the organization in which life itself has its seat, over which man has little or no control. The greater part of them depend on external and adventitious agencies over which man has complete control. Human ignorance, apathy, and indolence, may render the duration of life, in regard to large classes and entire countries, short; human knowledge, energy and perseverance, may extend the duration of life far beyond what is commonly imagined. It will be interesting and instructive to select a few of the more striking examples of this from the records we possess, few and imperfect as they are, in relation to this subject.
Of the duration of life in the earlier periods of the history of the human race we know nothing with exactness, though there are incidental statements which afford the means of deducing with some probability the rate of mortality in particular situations. There has come down to us one document through Domitius Ulpianus, a judge, who flourished in the reign of Alexander Severus, which enables us to form a probable conjecture at least of the opinion of the Roman people of the value of life among the citizens of Rome in that age. It happened at Rome as in other countries, that when an estate came into the possession of an individual it was burthened with a provision for another person during the life of the latter, a younger brother, for example. This provision was called by the Romans an aliment. No estate, burthened with such a provision, could be sold by the heir in possession, unless the purchaser retained in his hands so much of the price as was deemed adequate to secure the regular and continuous payment of the aliment. This imposed upon the Romans the necessity of considering what the term of life would probably be from and after any given age. What they did conceive that term to be is stated in a document of Ulpianus, recorded by Justinian, and given in the note below.[1] This document imports that from infancy up to the age of
| 20, | there should be allowed | 30 | years | |
| From | 20 to 25 | "" "" | 28 | " |
| 25 to 30 | "" "" | 25 | " | |
| 30 to 35 | "" "" | 22 | " | |
| 35 to 40 | "" "" | 20 | " | |
| ———— | ||||
| From | 50 to 55 | "" "" | 9 | " |
| 55 to 60 | "" "" | 7 | " | |
| And at all ages | above 60 | "" "" | 5 | " |
But between 40 and 50, as many years were to be allowed as the age of the party fell short of 60, deducting one year.
No clue has hitherto been obtained to the discovery of the real meaning of this document. It is, however, highly probable that the Romans had fallen on one of the two methods of measuring the value of life already explained; namely, that termed the Probability of Life. Of the two modes of determining the value of life, the probability was more likely to occur to a Roman judge than the expectation. He had no tables, no registers to guide him. What course, then, would he be likely to take? Probably he would form a list of his own school-fellows and others within his own knowledge, of the age, say, of twenty. By prevailing on persons of his own age, on whose correctness he could rely, to draw out similar lists, he might accumulate some thousand names. In this list it is probable that the male sex alone would be included, on account of the greater ease of ascertaining both their exact age and the exact date of their death. For the same reason, it is probable that the list would consist only of the nobility and the inhabitants of towns. Having thus completed his list, the next step would be to frame another list of all who died at the age of twenty-one; and next, another list of all who died at the age of twenty-two, and so on through each and every year of life. Now by subtracting the number in the list, No. 1, that is, those who died between twenty and twenty-one, from the number who originally started at twenty, which, in other words, would be to find the decrement of life, in the mode already explained, he would see how many lived to commence the age of twenty-one, and so on, through each year of life. But this would be to construct a table, showing the probable duration of life; that is, a table from which he could observe at what advanced age the number originally starting at twenty, and so on, came to diminish to one-half, when it would naturally occur to him that it is an equal wager whether such younger life would or would not be in existence at the advanced age so ascertained. If we suppose this to have been the method actually adopted by the Roman judge, and apply it to the table of Ulpianus, the result obtained is consistent in an extraordinary degree, and is highly interesting.
There is reason to believe that the mortality at present throughout Europe, taking all countries together, including towns and villages, and combining all classes into one aggregate, is one in thirty-six. Süssmilch, a celebrated German writer, who flourished about the middle of the last century, estimated it at this average at that period. The result of all Mr. Finlaison's investigations is a conviction that the average for the whole of Europe does not materially differ at the present time. He has ascertained by an actual observation, that in the year 1832 it was precisely this in the town of Ostend. Taking this town, then, as the subject of comparison, it is found that the probable duration of life among the male sex at Ostend exceeds the Roman allowance by the following number of years; namely,
At the age of 17, the excess in round
| numbers is | 5 | years. | |
| 22 | "" | 5 | |
| 27 | "" | 5 | |
| 32 | "" | 5 | |
| 37 | "" | 3 | |
| 42 | "" | 3 | |
| 47 | "" | 5 | |
| 52 | "" | 5 | |
| 57 | "" | 4 | |
| 62 | "" | 4 | |
| 67 | "" | 2 | |
| 72 | "" | 1 | |
| 77 | "" | 0 |