Gentlemen,—I have to thank you sincerely for the honour you have conferred upon me in calling me to fill the office of Honorary President this Session. I accepted the honour with hesitation, recollecting the long list of distinguished men who have occupied and adorned the high office since the year 1859, and whose Inaugural Addresses we cherish as a valuable heritage. I felt, however, under such great obligations to the Society for having opened up to me in the past so many new fields of study that I could not refuse to undertake any service to which by your goodwill I might be called.

The subject of State Pensions for the Aged Poor, which I propose to bring under your notice to-night, is one which has occupied public interest and attention to a large extent during recent years. Suggestions numerous and varied have been made for the solution of the difficulties which surround the question, but the problem unsolved still holds the field. This winter it will be again much in evidence, as a Committee on Old Age Pensions, appointed by Government, will meet at the Treasury from time to time under the presidency of Lord Rothschild. It has been remitted to this Committee.

In July 1880 there appeared in the Journal of the Institute of Actuaries certain “Remarks as to the Influence of Marriage on the Death-Kates of Males and Females, abridged from Dr. James Stark's Letters to the Kegistrar-General of Births, Deaths, and Marriages in Scotland” (J.I.A. xxii. 233). In these letters Dr. Stark compares the mortality of the married and unmarried females at different ages in Scotland in the years 1861 and 1862; and calls attention to the fact, that the excessive mortality of the former, as compared with that of the latter class of lives, appears to be confined to the ages under thirty years. He offers, as an explanation of this, the great danger—well known, as he says, to every medical practitioner—which attends the delivery of the first child; and then proceeds to demonstrate its effect by means of two tables, showing (1) “the number and ages of mothers and the number of children which they had on the birth of their last child,” and (2) the “proportion of mothers bearing their first child to every 100 mothers.” The figures given in the former table show that nearly as many women above thirty years as under that age bear children; and yet the marked difference between the mortalityof the married and unmarried is only apparent below that age. From inspection of the second table, which shows the number of mothers bearing their first child to be, after age thirty, very small as compared with those under that age, he concludes that not only is the view that the risk to the mother is far greater at her first confinement, than at any subsequent delivery, rendered almost a certainty, but that the increased mortality of the married females is almost solely due to this cause.

Many valuable papers have from time to time appeared among our own Transactions and in the Journal of the Institute of Actuaries bearing upon the Amounts invested by Life Offices in various securities, and the rates of interest yielded by such investments at different epochs. So far as I can discover, however, with the exception of a short, but very instructive, paper on Railway Debenture Stock by Mr. Coles in the 15th vol. of the Journal, nothing has been written in description of the origin and character of the various securities which are usually selected for the investment of Life Offices' and other Funds. Having discovered that many others besides myself have experienced difficulty in obtaining information on this subject, I have ventured to put down in an elementary way the results of my own research in regard to it.

The President of the Institute of Actuaries, in his Inaugural Address, delivered recently, impressed upon his hearers the imperative necessity for the Actuary being now a practical financier also, and I am sure that every one of us knows sufficient about the difficulties that beset the investment of money at the present day to fully indorse his remarks. No one can, however, it seems to me, be a “practical financier” without having an intelligent knowledge of the character of various securities, and it is my desire to-night to try to help in some small measure towards the attainment of that knowledge.

Mr. President and Gentlemen,—I accepted with some misgiving the invitation with which your President honoured me to read a paper before your Society on some medical subject connected with Life Assurance, because I doubted my ability to deal with it in any way worthy of the audience. When I further reflected that some of those present might be the Managers and Actuaries and even the Chief Medical Officers of Companies for which I have examined in London, I sought a loophole for honourable escape. Now, when the eyes of some of these officials are upon me, I feel inclined to beat a dishonourable retreat.

Many valuable contributions have been made to this subject, and subjects bearing upon it, of late years; and if I gave you an account of the bibliography alone, it would occupy the time at my disposal. The President probably thought that the study of this literature would be of educational advantage to me; and, if so, I can assure him that it has fulfilled the object he had in view.

The title of Some Medical Aspects of Life Assurance seemed to be one which would enable me to escape the dangers of attempting to give you a statistical dissertation on my own experience, while it would admit of some general remarks on the method of Life Assurance examination.

The lives which present themselves for assurance are, in the process of selection, divided into three main groups or classes:—

I. Lives insurable at the ordinary rate.

II. Lives insurable only at extra rates.

III. Uninsurable lives.

Although, in measuring what we call “extra risk,” only the subdivisions of Class II. are of practical significance, yet each of the three classes admits of almost indefinite subdivision in respect of the quality of the lives embraced in it.

In the first class, some lives present no flaw of any kind in health, physical condition, occupation, or family history; others, at the further end of the scale, present flaws which bring them close to the border line of Class II.; and between those two extremes there is every degree of variation. Using terms that are not unfamiliar, Class I. may be subdivided into three distinct groups:—

(a) Unexceptionable lives, presenting no unfavourable feature.

(b) Good average lives, in which the personal or family history, or the physical condition, is not entirely faultless, but which present no feature likely to tell against the life-prospects.

(c) Fair average lives, presenting some flaw or imperfection, or some combination of unfavourable circumstances, which only falls short of requiring an extra premium.

Eleven years have elapsed since anything on the subject of Office Books was before you. Mr. M'Lauchlan's paper, which was read in April 1886, has long since become a classic, and has been of incalculable service as a text-book for the Faculty and Institute Examinations. All-embracing as it is, however, its great scope rendered it impossible to treat, within the limits of one paper, all aspects of Life Office Book-keeping and its kindred topic Life Office Records, so fully as may be done by taking the subjects in sections. I shall be glad, therefore, if my contribution be looked upon as a practical tribute of my sense of indebtedness to Mr. M'Lauchlan's paper, and as an attempt to expand a small portion of it. I hope my example may be the means of inducing others to do likewise.

Mr. R. P. Hardy recently said (J.I.A., vol. xxxii, p. 443) that to frame a scheme of books and forms that were at once analytical and interlocking, presenting at the same time the maximum of convenience for the needs of to-day, encumbered by the mere minimum of what was indispensable for the emerging wants of the future, was in itself a liberal and highly stimulating education.

Gentlemen,—It is with feelings of diffidence and trepidation that I venture to address you to-night. I have been informed that it is almost impossible to write a paper on anything new in connection with Actuarial matters, as everything bearing on the theory and practice of Life Assurance has already been written, read, and understood by all those interested in the business. However, although nowadays every Actuarial student can graduate a Mortality Table in about three different ways, and can run off lists of the Securities, in which the funds of an Office should and should not be invested, with reasons as to their choice or rejection, I think that perhaps in the department of Life Office Accounting there are still a few suggestions which can be made. I allow that the subject is not so scientific as, say, the calculation of the probable future profit to be received on a Reversion, which has been bought at an auction, or the valuation of conflicting interests in a Disentail. I am also afraid that Accounting is not thought of much importance by Actuaries, but is regarded rather, may I say, as a prosy, though easily crammed subject, to be read up before examinations.

The Actuarial Society of Edinburgh was formed more particularly for the benefit of students, to assist them in their studies of actuarial and mathematical subjects; and it is therefore unnecessary to make any apology for submitting a paper of an elementary character, which makes no pretence at originality of thought, but which is designed simply to bring together some of those practical questions which have been dealt with by Actuaries of ripe experience, and to place them before students in a compact form. Those questions which do not appear to have been discussed by others, are well known to Actuaries who have had any considerable experience in the practical calculation of office premiums; but yet the following notes may be of service to students who, in many cases, have little opportunity for gathering such information.

In order to deal clearly with the subject, it is desirable to state, in the first place, one or two of the fundamental principles which should regulate the calculation of office premiums. The premium payable by the policyholder forms the foundation upon which the whole structure of life assurance is built; and if the premiums be inadequate, as in the case of Assessment Companies, the structure must sooner or later collapse.

Exactly twenty years have elapsed since I first had the honour of addressing the members of the Actuarial Society as their Honorary President, being then but on the threshold of my official life.

Again ten years later I once more occupied this chair.

And now after the lapse of another ten years, as my professional career draws somewhat near its close, and you have again kindly asked me to become your President, there comes on me in meeting you at the beginning of your session for the purpose of offering to you a few words of welcome, a desire, on the one hand, to look back over the past—to get out of the trees, as it were, and see the forest,—and on the other, already throwing loose the trammels of daily routine, to turn in the forward direction with an endeavour to peer some way into the future and see what is in store for us there.

I will accordingly endeavour to ascertain in what way our science and the great practical businesses built upon it—and to promote which actuarial science mainly exists—have been tending during these more recent years, and, by carrying on the lines in the same direction, to make some forecast of the conditions that will prevail when you, who are entering on the actuarial profession, in your turn take the helm of management.

Gentlemen,—Allow me in the first place to thank you most sincerely for the honour which you have conferred upon me, in electing me President of the Actuarial Society for this Session. A consideration of the long list of those who have been my predecessors in the Chair, makes me all the more sensible of the honour, and it is therefore with diffidence though with great pleasure that I accept the post. While my residence out of Edinburgh will prevent me from presiding at as many ordinary meetings of the Society as I should like, I think I may assert with confidence, that no one takes a deeper interest in its progress. I have been a member of it for thirty-three years, and have experienced the varied benefits which a Society conducted as yours has been, is able to bestow, and to which many here are largely indebted for assistance in their career. The main benefits to which I refer are (first) the stimulating effect of intercourse with men desirous to raise the standard of our profession, founded as it is on the threefold basis of exact science, true benevolence, and honest business principles—a combined foundation which few professions are able to claim; (second) the information and culture which are gained from the perusal and study of the papers read to the Society; and (third) what is perhaps more valuable than either of the other two, and which therefore I would more emphatically impress upon the younger members—the training which is obtained in preparing papers for a Society like this.

The Supplement to the fifty-fifth annual report of the Registrar-General for England, issued early in 1898, contains a mass of statistical material bearing on the mortality among persons engaged in various occupations, much more important and complete than any previously available. The principal object of the following Paper, is to examine the information therein contained bearing on the mortality in certain hazardous or unhealthy occupations, with a view to obtaining some guidance in fixing the extra premiums which should be charged for insurances on the lives of persons engaged in these occupations. In some cases, the information obtained from the Supplement to the fifty-fifth report has been supplemented from other official sources.

For the purpose of comparing the mortality of persons in different occupations, Dr. Tatham, the Superintendent of Statistics at the General Register Office, has, following his predecessor, Dr. Ogle, made use of the method of ‘comparative mortality figures.’

The subject of Valuation is one of such superlative importance to the actuary that possibly even a merely repetitional paper may not be wholly without interest. Two of the most important contributions to the practical side of the science have appeared but recently in the Journal of the Institute of Actuaries—Mr. Chatham's paper on the books to be used in scheduling the particulars of the risks of a Life Assurance Company J.I.A., xxxii. 393), and that by Mr. Lidstone on the Valuation of Endowment Assurances in groups J.I.A., xxxiv. 61). What follows is in great measure an attempt, on the basis of these papers, to present forms for valuation purposes adapted to an Office declaring quinquennial reversionary bonuses on the Sum Assured or on the Sum Assured and Existing Bonuses—furnishing the particulars essential to an annual investigation, while at the same time providing for a quinquennial return to the Board of Trade.

Although the subject we are about to discuss is frequently referred to as “Health” Insurance, I venture to submit that as a mere question of exactness Sickness Insurance is the correct term. The common method of naming systems of Insurance is not, however, too exact, but that is no sufficient reason for being inexact where exactness is possible. Insurance against fire, insurance against accident, and insurance against sickness are expressions, each of which carries with it a precise meaning; but to speak of “insurance against health” would be a contradiction and an impossibility. In Life work we refer to Life Assurance, while in reality we mean insurance against death, and in respect of this particular business, whoever may have been responsible for the primary use of the term was wise in his generation. To write or speak perpetually upon the subject of death even in its relation to insurance would be a lugubrious vocation to engage in. The subject itself would not only be uninviting but repellent, and therefore as far as possible men would seek to avoid its discussion. For the same reason I imagine “Health” Insurance is preferred by some to Sickness Insurance; but the description cannot be supported by the same reasoning, while, as I have said, it is incorrect and therefore unnecessary.

My principal object in presenting this paper is to assist the student in his endeavour to obtain a knowledge of Life Insurance as it is practised in the United States of America, and to correct certain misconceptions regarding it among many of the older members of the profession.

The casual reader is apt to receive wrong impressions of Insurance in America through a want of knowledge of the conditions surrounding it. He is probably under the impression that nearly all American companies do business on the tontine plan, that new assurance is obtained at enormous cost, and that “Assessment Insurance” of the original type is the only system practised. Before proceeding to discuss these matters, it will be well to give a brief review of the history of Insurance in the United States. Without historical knowledge it is difficult to understand the legislative enactments regarding “Old Line” Insurance, or to realise the astonishingly large proportions to which Assessment Insurance has grown.

One of the most remarkable features in the history of the nineteenth century has been the rapidity with which some scientific discovery made in one country has been followed, and often eclipsed, by one on similar lines in another country. The reason for this is not far to seek, for he who would excel in any branch of science or learning must keep himself thoroughly acquainted with its latest developments, and with the progress it is making in all parts of the world. Thus, we find that a rivalry has sprung up, which grows keener every day, between this and the Continental countries in Science and Philosophy, as well as in Commerce and Politics. In this country, however, until quite recently, the insurance world in general, and the actuarial student in particular, have not considered it worth while to inquire how and upon what lines insurance business is carried on across the Channel. So far as I have been able to ascertain, the only books in the Faculty Library dealing with the subject of Life Assurance in France are Walford's Insurance Cyclopœdia, published in 1876, and a pamphlet by H. S. Washburn in 1879. The object of this paper is to supplement to some small extent the information contained in these volumes, and to place materials in the hands of the Actuarial Society which will enable its members to form some idea of the progress and nature of life assurance business in France.

Gentlemen,—When you did me the honour to appoint me your President, and gave me for the fourth time the privilege of addressing you from this chair, I was within a few weeks of completing the fiftieth year of my business life, and my thoughts dwelt much upon the changes I had seen in that time.

Such being the case, you will not be surprised that I decided to offer you a retrospect of some one important branch of our business. I selected Life Office Investment, of which I think I can claim to have had an unusually long and varied experience.

In the treatment of my subject I shall endeavour to confine myself to a narration of such facts, and to draw such inferences from them, as I can reasonably hope will interest and instruct the younger members of the Society, and which, at the same time, will serve to remind their seniors of the steps by which our present notions of what is safe and advisable in the investment of the funds of a Life Assurance Office have been arrived at.

Gentlemen,—Allow me to thank you very cordially for electing me to preside over your meetings during the ensuing Session It is an honour very greatly appreciated by every one who has been selected to fill this chair. Indeed I feel doubly honoured, seeing that I am the first to address you in the new Hall of the Faculty of Actuaries under the gaze of the stony eyes of our own immortal Napier. Your election reminds me that I had the honour of presiding over your earliest meetings and that I also had the pleasure of reading the earliest papers that were presented for your consideration. These three papers I am proud to believe have been diligently perused by nearly every student of Actuarial Science, forming as they do the wicket opening into wider fields, the earliest lessons of the course. They have, as I have been told, been the guiding rays of light which induced some of our most eminent Actuarial stars, presently shining in our firmament, to follow in the pursuit of higher knowledge, and to join the profession. These simple papers have been printed three times, and are again out of print. Gentlemen, I do wish I were able to repeat that enthusiasm. It seems to me now to be a much more simple matter to find language to describe something which one is striving to understand for oneself, and labouring to make clear to one's own comprehension, than to write an essay upon something which appears so plain and so palpable that the wonder is how any one could fail to interpret the language of the symbols.

Graduation of all kinds is most attractive. The highest mathematical minds have apparently lingered upon it with delight, and when I glance down the weighty list, I feel that I, of all persons, should have shrunk from touching it. Most of these men have treated the subject in a highly theoretical manner, and have furnished formulæ that are extremely difficult to apply. A few, however, have followed in their footsteps and elaborated something that is practical. Other enthusiasts have searched for and have thought that they had found a ‘Law of Mortality.’ Some are still searching for it, and more will continue the search in all time coming. A Law of Mortality seems to me to be as illusive as the rainbow. The law found is only the law of some mathemathical process of summation.

The method of graduation indeed should vary with the matter to be graduated. When applied to the probability curve, it is intensely fascinating, and there appears to me to be occasional opportunities in our business of so applying it. I do not profess to put forward any new scheme. I do not propose to electrify the subject. I possess no wizard's wand. All I propose to do is to elaborate a very simple exposition of the most elementary principles on the subject of differences, but I am bold enough to state that, in my opinion, it is all that is necessary in the graduation of a table of mortality.

In the paper that I had the pleasure of reading before this Society in the course of last Session, I brought forward a problem to which I promised to recur on an early occasion. That problem was a consideration of the present method of dealing with observations of various magnitudes when striking the rates of mortality experienced in each year of life. Our early mortality tables were derived from observations of a very general nature. The gross number of lives passing through each year of age and the number of deaths arising out of that number furnished the whole of the materials for producing the desired rate of mortality. Indeed in some instances these numbers at each age may have been ascertained by some mathematical interpolation from larger groups at younger and older ages. There was no discrimination as to the relative weights that may be allotted to any sections of these numbers. Thus in the tables derived from the numbers of the population there was no distinction between the numbers dying out of the sick and the numbers dying of the healthy. In more recent researches, however, we have improved upon our former methods of tabulation. The exact problem to be solved was not that of finding the general average rate of mortality for each year of life, but rather to ascertain the flow of mortality emanating from each group of healthy lives enrolled at each age and carefully tracing their mortalities year by year during all the subsequent years of their lives.