A well-known contributor to the Assurance Magazine has drawn attention, at pp. 167 and 168 of the Number for April, 1859, to “the incongruity existing between the rates of premium charged at certain ages on bonus policies, and the benefits to which they entitle the holder.”

In a note in the introduction to Milne's Treatise on Annuities, the author remarks—“There can, I think, be no doubt but that the mortality is greater among the higher than the middle classes of society. They form too small a proportion of the population to have any sensible effect here; but it would be of importance to the Life Offices to determine the law of mortality among them.” Since the publication of this work, forty-six years ago, some attempts have been made to test the accuracy of this assertion, and to supply the desideratum; but none with which we are acquainted are by any means conclusive.

By this I do not mean what is usually called Newton's Table, but something which has a better right. First, however, I will speak of the table which, having Newton's certificate of accuracy, is (or was) usually called by his name.

Mr. Edleston, Fellow of Trinity College, in making researches for his biography of Newton, found out the author of the old table. His name was Mabbot, and he was manciple (mancipium) or caterer of King's College. Mabbot published his table in 1686, with the well-known attestation of Newton opposite to the titlepage. There seems to have been a special reason for procuring this certificate. The church lessors were beginning to open their eyes to the leniency of their terms, and Mabbot's tables were certainly intended both to urge them to raise their fines, &c., and to point out the proper way of doing it. Subsequent editions of these tables had attached to them the well-known letter which pointed out the advantage under which the tenant was living. As it was natural that the lessees should oppose the new scheme, and they would probably question its accuracy, it seems that Newton was applied to for the testimonial which, as is well known, he gave.

In the former papers upon this subject1 which I had the honour to lay before the Institute, I described the vehement controversy carried on in earlier ages as to the propriety of allowing any interest to be taken for the use of money, and I alluded to the discussion which, after interest to a limited extent had been allowed by law, arose as to the advantages to be derived from a reduction of the legal rate.

The Transactions of the Royal Society contain the first Life Table. It was constructed by Halley, who discovered its remarkable properties, and illustrated some of its applications. The Breslau observations did not supply Halley with the data to frame an accurate table, for reasons which will be immediately apparent; but the conception is full of ingenuity, and the form is one of the great inventions which adorn the annals of the Royal Society.

The operation of the clearing has the effect of enabling all the payments from one bank to another to be performed without the passing of bank-notes; and the result is, that if any bank has to receive from the clearing, say, £50,000, the account of that bank at the Bank of England is better by £50,000 at 9 o'clock the next morning; and if a bank has to pay into the clearing £50,000, the amount of that bank is worse by £50,000.

In the last number of the Assurance Magazine (April, 1861), there appears a letter from Mr. Gompertz, in which reference is made to his and my claims to the discovery of the law, or part of the law, of human mortality. In this letter, Mr. Gompertz declares that my claim cannot interfere with his claim, because I had acknowledged the priority of his discovery. I admit the truth of this declaration, and can add thereto, that I also am able to declare, with equal truth, that his claim, as now described by himself, cannot interfere with any claim hitherto advanced by me. The law of human mortality, now claimed to be discovered by Mr. Gompertz, differs materially from the law which I have declared to exist. The two laws are in accordance with one another only at one period of life (extending, say, from the age of 15 to the age of 55 years), and then only in a partial degree. It is in this partial agreement, at this particular period of life, that the priority of Mr. Gompertz's discovery consists. The description of the law of human mortality, as now believed by Mr. Gompertz to exist, is contained in a paper, referred to in the letter above mentioned, and since published (page 454) in the Appendix to the Report of Proceedings of the Fourth International Statistical Congress, held in London in the year 1860.

In 1839, in the Penny Cyclopædia (article “Mortality”), I wrote as follows, referring to Mr. Gompertz's well-known hypothesis on the law of mortality:—

“We enter into some detail of it the more readily, that it is necessary as an act of justice to Mr. Gompertz, whose ideas have been adopted by a recent writer on the subject, without anything approaching to a sufficient acknowledgment.”

The series lx has been constructed, and from that series others are deduced to complete the Life Table, consisting now of six columns.

(1.) dx=lx−lx+1=number of deaths in the year of age following, out of lx alive at the age x. By taking x successively at 0, 1, 2, 3…to the last age in the Table, the numbers dying in every year of age are obtained.

A principal use of logarithms is to solve all the cases of compound interest which are not, without great difficulty, attainable by the rules of common arithmetic. But before we proceed to the practical part, it may, perhaps, not be improper to say something of the foundation or demonstration of the rules we are to give.

The following letter from M. Réboul will serve to introduce the several subjects upon which he has addressed the Institute:—

“Gentlemen,—The Institute of Actuaries being the most competent tribunal in matters of assurance, it is to you, as to my natural judges, that I have conceived it proper to submit my first essays in that science.

The annuity tables accompanying M. Réboul's communication are sufficiently described by that gentleman himself. The rate of mortality, and the rates of interest upon which they are based, will, no doubt, be considered by our readers as circumstances affording sufficient reason for not reproducing them here.

As regards the hereditary transmission of phthisis, another investigation of the statistics of the Hospital for Consumption at Brompton showed, that where one parent only was affected with pulmonary disease, the fathers being so affected transmitted the disease to their sons in 63 out of 106 cases, being 59·4 per cent. of the whole number observed; and to their daughters in 47 cases only out of 108, being 43½ per cent.: while the mothers being phthisical transmitted the disease to their sons in 43 cases, being 40·6 per cent.; and to their daughters in 61 cases, being 56½ per cent. of the cases under observation. Judging, therefore, from these figures, it would probably appear, if a large number of cases were registered, that the power of transmission of disease by phthisical fathers to their sons, and by phthisical mothers to their daughters, is about the same.

Upon perusal of the Annual Reports of the Registrar-General, and of the valuable analyses by Dr. Farr that accompany them, we can scarcely fail to be struck with the alarming fatality which appears to prevail in this country from certain classes of diseases; and the inquiry naturally arises in our minds, whether we have any control over this excessive mortality: is, in fact, any proportion thereof preventable?

With respect to the inhalation of woolly matter, Mr. Leigh, a surgeon at Manchester, and Registrar of Deaths for the Deans-gate sub-district of that city, in which cotton-mills are so numerous, states, in one of his Reports to the Registrar-General, that in certain trades in Manchester almost every member above 40 is affected with emphysema of the lungs; and that persons who work in dust—as fustian-cutters, cotton-carders, and the like—are almost all affected with it, after working at their occupations for a few years.

I have a suspicion that Mr. Edmonds intends the fifteen pages on the “Law of Human Mortality,” which appear in the last Number of this Journal, to stand in place of an answer to my remarks “On an unfair suppression of due acknowledgment to the writings of Mr. Benjamin Gompertz,” printed in the July Number; for though no allusion is made to the charge, still less statement of it or answer to the evidence produced, there is one mention of me which looks so like a distortion of my paper, that I think the suspicion is justified. Mr. Edmonds says (p. 181), “Mr. De Morgan, in his office of self-constituted judge between Mr. Gompertz and me, overlooks this important error …” Now, though my paper does not deal with the truths or errors of either, but only with the question whether Mr. Edmonds's mention of Mr. Gompertz was suppressive; and though I never said, and certainly never thought, that there was or could be any question pending between Mr. Gompertz and Mr. Edmonds; and though I was not the judge, either self-constituted or otherwise, but only the promoter of an accusation of unfair suppression for others to judge of;—there is in the quotation that remote likeness to an account of my proceeding which often exists between that which cannot be answered and that which it is convenient to substitute for it.

There is, probably, no department of an actuary's pursuits where there is such diversity of practice as that of which this paper treats. After the calculation of the premiums and the periodical valuations, the distribution of surplus is infinitely the most important duty that an actuary has to perform. The premium income of the various Life Offices now exceeds £8,000,000 a year, and probably not less than £l,000,000 is annually divided as surplus. Within the last 14 years, one Office alone has divided upwards of £1,200,000; and another, for many years past, has annually distributed as surplus more than £100,000. This will be sufficient to show the magnitude of the interests concerned; and yet, as will be seen in the sequel, these distributions are, in some cases, made in a most arbitrary manner—without reference to principles of justice and equity, and without the basis of accurate reasoning. After what has been written on this subject by Mr. Jellicoe and Professor De Morgan, it is not to be supposed that any actuary would defend the schemes here referred to as equitable; those who do follow them, content themselves with stating their advantages.