The observation, No. 15, is founded on the large mass of 9,347 lives and 4,870 deaths. From this observation, it appears that, at the age of thirteen, the mortality out of a million is 5,742, being 174,750 less than in the first year of infancy At the age of twenty-three, it is 15,074, being 9,332 more than at the close of childhood. At the age of thirty-four, the period of complete manhood, it falls to 11,707, being 3,367 less than at the close of adolescence. At the age of forty-eight, the mortality returns to 14,870, all but identically the same as at twenty-three, the adult age. From the age of forty-eight, when, as has been stated, life just begins to decline from its meridian, the mortality advances slowly, but in a steady and regular progression. Thus, at the age of fifty-eight it is 29,185, being 14,315 more than at the preceding decade, or almost exactly double. At the age of sixty-eight, it is 61,741, being 32,556 more than at the preceding decade, or more than double. At the age of seventy-eight, it is 114,255, being 52,514 more than at the preceding decade. At the age of eighty-eight, it is 246,803, being 132,548 more than at the preceding decade.

During the first year of infancy, as has been shown, the mortality out of a million is 180,492. At the extreme age of eighty-four, it is 178,130, very nearly the same as in the first year of infancy. Greatly as the mortality of all the other epochs of life is affected by country, by station, by a multitude of influences arising out of these and similar circumstances; yet the concurrent evidence of all observation shows that at this and the like advanced ages the mean term of existence is nearly the same in all countries, at all periods, and among all classes of society. Thus, among the nobility and gentry of England, the expectation of life at eighty-four is four years; among the poor fishermen of Ostend, it is precisely the same. M. De Parcieux, who wrote just ninety years ago, establishes the expectation of life at that time in France, at the same age, to have been three and a half years; and Halley, who wrote 120 years ago, and whose observations are derived from documents which go back to the end of the seventeenth century, states the expectation of life at eighty-four to be two years and nine months.

From these statements, then, it is obvious, that from the termination of infancy at three years of age, a decade of years brings childhood to a close, during which the mortality, steadily decreasing, comes to its minimum. Another decade terminates the period of adolescence, during which the mortality as steadily advances. A third decade changes the young adult into a perfect man, and during this period, the golden decade of human life, the mortality again diminishes; while, during another decade and a half, the mortality slowly rises, and returns at the close of the period to the precise point at which it stood at adult age. Thus the interval between the period of birth and that of adult age includes a term of twenty-three years. The interval between the period of adult age and that when life just begins to decline from its meridian, includes a term of twenty-four years: consequently, a period more than equal to all the other epochs of life from birth to adult age is enjoyed, during which mortality makes no advance whatever. Now the term of years included in the several epochs that intervene between birth and adult age is rigidly fixed. Thus the period of infancy includes precisely three years, that of childhood ten years, and that of adolescence ten years. Within the space of time comprehended in these intervals, physiological changes take place, on which depend every thing that is peculiar to the epochs. These changes cannot be anticipated, cannot be retarded, except in a very slight degree. In all countries, among all classes, they take place in the same order and nearly in the same space of time. In like manner, in extreme old age, or the age of decrepitude, which may be safely assumed to commence at the period when the mortality equals that of the first year of infancy, namely, the age of eighty-four, physiological changes take place, which, within a given space of time, inevitably bring life to a close. That space of time, in all countries, in all ranks, in all ages, or rather as far back as any records enable us to trace the facts, appears to be the same. As within a given time the boy must ripen into manhood, so within a given time the man of extreme old age must be the victim of death. Consequently, it is the interval between the adult age and the age of decrepitude, and only this, that is capable of extension. During the interval between adult age and the perfect meridian of life, comprehending at present, as we have seen, a period of twenty-four years, the constitution remains stationary, mortality making no sensible inroad upon it. But there is no known reason why this stationary or mature period of life should, like the determinate epochs, be limited to a fixed term of years. On the contrary, we do in fact know that it is not fixed; for we know that the physiological changes on which age depends are, in some cases, greatly anticipated, and in others, proportionately postponed; so that some persons are younger at sixty, and even at seventy, than others are at fifty; whereas, an analogous anticipation or postponement of the other epochs of life is never witnessed. So complete is the proof, that the extension of human life can consist in the protraction neither of the period of juvenility, nor in that of senility, but only in that of maturity.

Were it necessary to adduce further evidence of this most interesting fact, it would be found equally in the statistics of disease as in those of mortality. Indeed, the evidence derived from both these sources must be analogous, because mortality is invariably proportionate to the causes of mortality, of which causes, sickness, in all its forms, may be taken as the general or collective expression.

We do not possess the same means of illustrating the prevalence of disease through all the epochs of life as we do of showing the intensity of mortality; yet the report of Mr. Finlaison, already referred to, enables us to show its comparative prevalence at several of those stages. Thus, from this document, it appears, that among the industrious poor of London, members of benefit societies, out of a million of males, the proportion constantly sick at the age of twenty-three, is 19,410; at the age of twenty-eight, it is 19,670; at the age of thirty-three, it is 19,400; at the age of thirty-eight, it is 23,870; at the age of forty-three, it is 26,260; at the age of forty-eight, it is 26,140; at the age of fifty-three, it is 27,060; at the age of fifty-eight, it is 36,980; at the age of sixty-three, it is 57,000; at the age of sixty-eight, it is 108,040; at the age of seventy-three and upwards, it is 317,230. The prevalence of sickness is not an exact and invariable measure of the intensity of mortality; but there is a close connexion between them, as is manifest from the progressively increasing amount of sickness, as age advances. Thus, in the first ten years from the age of twenty-three to that of thirty-three, there is no increase of sickness, its prevalence is all but identically the same; in the next ten years from the age of thirty-three to that of forty-three, the increase of sickness, as compared with that of the preceding decade, is 6,860; in the next ten years from the age of forty-three to that of fifty-three, the increase is only 800; in the next ten years from the age of fifty-three to that of sixty-three, the increase is 29,940, while from the age of sixty-three to seventy-three, it is 260,230.

Such are the results derived from the experience of disease considered in the aggregate, all its varied forms taken together. I am enabled further to present an exact and most instructive proof, that one particular disease which, in this point of view, may be considered as more important than any other, because it is the grand agent of death, namely fever, carries on its ravages in a ratio which steadily and uniformly increases as the age of its victim advances. Having submitted the experience of the London Fever Hospital for the ten years preceding January 1834, an observation including nearly 6,000 patients affected with this malady, to Mr. Finlaison, it was subjected by him to calculation. Among other curious and instructive results to be stated hereafter, it was found that the mortality of fever resolves itself into the following remarkable progression. Thus suppose 100,000 patients to be attacked with this disease between the ages of 5 and 16, of these there would die - 8,266 and of an equal number

Thus the risk of life from this malady is twice as great at the age of thirty-one as it is at eleven. It is also nearly twice as great at forty-one as it is at twenty-one. It is five times as great at sixty-one as it is at eleven, and nearly four times as great above sixty-five as it is at twenty-one.

From the whole of the foregoing statements, it is manifest that life is a fluctuating quantity. In order to compare this fluctuating quantity under different circumstances, writers on this branch of statistics use several terms, the exact meaning of which it is desirable to explain. It is, for example, very important to have a clear understanding of what is meant by such expressions as the following: the expectation, the probability, the value, the decrement of life, and the law of mortality.

1. The Expectation of Life. It is important to bear in mind that several expressions in common use have a signification perfectly synonymous with this: namely, share of existence; mean duration of life; la vie moyenne.

By these terms is expressed the total number of years, including also the fractional parts of a year, ordinarily attained by human beings from and after any given age. Suppose, for example, that one thousand persons enter on the eighty-sixth year of their age: suppose the number of years and days which each one of them lives afterwards be observed and recorded; suppose the number ultimately attained by each be formed into a sum total; suppose this total be divided equally among the thousand, the quotient of this division is said to be each one's share of existence, or his mean duration of life, or his expectation of life. Thus, of the thousand persons in the present case supposed to commence the age of eighty-five, suppose the number of years they collectively attain amount to 3,500 years: the one-thousandth part of 3,500 is three and a half: three years and a half then is said to be the expectation of life at the age of eighty-five, because, of all the persons originally starting, this is the equal share of existence that falls to the lot of each.

2. Probability of Life; or the probable duration of life, la vie probable. These are synonymous terms, in use chiefly among continental writers as an expression of the comparative duration of life. The tabular methods of setting forth the duration of life consist, for the most part, in assuming that 10,000 infants are born; and that at the age of one, two, three, and each successive year of life, there are so many still remaining in existence. Fix on any age; observe what number remain alive to commence that age; note at what age this number decreases to one-half; the age at which they so come to one-half is called the probable term of life; because, say the continental writers, it is an equal wager whether a person shall or shall not be alive at that period. Thus, suppose one thousand males commence together the age of eighty-four; suppose the table indicate that there will be alive at the age of eighty-five, 817; at the age of eighty-six, 648; at the age of eighty-seven, 493; at the age of eighty-eight, 357, and so on. In the present case, the probable duration of life at eighty-four is said to be very nearly three years, because, at the age of eighty-seven there are left alive 493, very nearly one-half of the thousand that originally started together.

3. Value of Life. This term, when used accurately, expresses the duration of life as measured by one or other of the methods already expounded. But it is sometimes popularly used in a loose and singularly inaccurate sense. Thus it is very commonly said—"Such a man's life is not worth ten years' purchase," which is the same thing as to say, that an annuity, suppose a hundred pounds a year, payable during the life of the person in question, is not worth ten times its magnitude, that is one thousand pounds. If a thousand pounds be put into a bank at some rate of interest to be agreed upon, and if a hundred pounds be drawn every year from the stock, the expression under consideration affirms that the person in question will be dead before the principal and interest are exhausted. For instance, at four per cent., the value of an annuity of one hundred pounds to a man of the age of twenty-five is 1694l., which is 16-9/10 years' purchase; whereas, his expectation of life at that age is 35-9/10 years.

4. Law of Mortality. By this term is expressed the proportion out of any determinate number of human beings who enter on a given year of age, that will die in that year. Every observation on the duration of life presents certain numbers, which, by recorded facts, are found to pass through each year of age, and also shows how many have died or failed to pass through every year of age. Those numbers, by the rule of three, are converted into the proportions who would die at each age out of one million of persons, if such a number had commenced it. Suppose, then, a million of persons to be in existence at the first year of age; suppose a million to be in existence at the second year of age; suppose a million to be in existence at the third year of age; and in this manner suppose an equal number to be in existence at the commencement of each and every year to the extreme term of human life. Now, the proportions that by actual observation are found to die at each and every year out of the million that were alive at the commencement of it, form separately the law of mortality for each year, and collectively for the whole of life.

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