The distinction which this Society has conferred on me by electing me its Honorary President for the year is one that is much enhanced by repetition; and I have to acknowledge with peculiar gratitude that this is the sixth occasion on which I have had the privilege of addressing you in that character. Twenty-one years ago, in the infancy of the Society, I selected for a topic “The Profession of an Actuary.” On looking back, I find that since then I have brought under your notice the subjects of “Fire Insurance,” of “The Future Interest of Money in connection with Life Assurance Institutions,” and of “Some of the Principles to be observed in Life Office Valuations;” and I ventured on the last occasion, a few years ago, to select a wider and less technical theme, and to invite attention to a general view of the Philosophy and Ethics of Business. I propose now to recur to the topic of our Profession, and to try whether an acquaintance with it of now forty years may not offer a few suggestions, that may possibly be of service to some of you who are engaged in fitting yourselves for its highest duties.

Although more than half a century has elapsed since attention was first drawn to the effect of selection upon the mortality among insured lives, the subject seems to have received but little consideration, partly on account of the numerous other questions pressing for solution, and partly, I dare say, on account of the scanty materials in existence; and it is only within the last decade that interest in it has been revived, and it has taken the place in the actuarial world which its importance demands. This is, in a great measure, due to the valuable collection of statistics published by the Institute of Actuaries in 1869, which has been the fountain-head of many interesting papers, as it furnished investigators with ample materials for their researches into the mortality among insured lives, and especially in the determination of the vexed question of “selection.” Before selection was understood, or rather, I should say, given effect to, it was thought sufficient to group together all the lives of the same age irrespective of the length of time for which they had been assured, and then to deduce the rate of mortality; but the introduction of select lives at old ages reduced the rate of mortality among those who had entered at young ages, and thus an exaggerated view of the probable longevity of young lives was obtained. Consequently, as the annuity-values for young ages by this method are greater than those obtained when selection is taken into account, it follows that young lives were charged too low a rate of premium, while old lives were charged too high a rate.

In welcoming you once again as your Honorary President, at the beginning of another Session, I would fain that it were allowed me merely to refer you back to one or other of the Opening Addresses of past years—the classics of your Society—which tell, many of them in terms much more eloquent than I could hope to do, what lines the Actuary had better follow in setting out on his professional career, and what goal he should steer for once he is fairly started on it.

But, as the old order changes yielding place to new, each year brings round with it some altered phase of thought, turns up to the surface some fresh and suggestive idea, and in so doing compels one forcibly to remember—notwithstanding there may be nothing altogether new under the sun—that the world still moves on ever more rapidly with kaleidoscopic effect, bringing old developments within the field of view in some fresh and altered light. Wherefore I am in duty bound in my turn, if I can, within our own sphere of observation, to draw notice to the new forces that are there at work, and to indicate the direction to which our attention should be turned.

1. Book-keeping by Double Entry is now universally admitted to be the only complete and satisfactory system, and its general principles have been shown to be adapted to all kinds of commercial or public accounts. The work of the accountant in arranging a special system adapted to the purposes of a Life Assurance Office, is therefore principally confined to fixing the number and forms of the subsidiary books which serve either to receive the original entries of transactions, or to relieve the Principal Ledger of the particulars of individual accounts.

In Life Assurance Book-keeping, as in that of Mercantile Houses, Banks, or Government Departments, these subsidiary books must be specially adapted to the various classes of transactions or other financial facts which occur in the business. I have therefore found it convenient to deal with the subject of Life Assurance Book-keeping by considering in succession the various classes of financial facts that fall to be recorded in conducting the business, and in the case of each class, describing the books required for receiving the original entries, and the subsequent progress of these entries through the books.

At so striking an epoch in the history of our times as the Jubilee of our Most Gracious Queen, it seems natural that those who are engaged in any special branch of trade, or commerce, or science, should look back with interest at the records of the progress of that branch during the period then completed; and I therefore venture to hope that the particulars which I have collected regarding the progress of Life Assurance Business in the United Kingdom during the last half-century, and which I propose to lay before you this evening, may prove in some degree interesting to you.

Before submitting to you these particulars, I think it may be useful if I refer for a few minutes to the condition of the United Kingdom in 1837, and to the changes which have occurred since then in matters which have had an important, though indirect, bearing on Life Assurance Business.

The Reports of the Registrar-General of Births, Deaths, and Marriages, and the writings of the late Mr. F. G. P. Neison and others, abound with statistical information regarding the influence of occupation on health and the duration of life. These statistics, the most of which are derived from observations made upon the general population, or the members of Friendly Societies, are useful in many ways. From them we learn that there are certain occupations which tend to preserve health and prolong life, and that there are other occupations which tend as decidedly to injure health and shorten life. But these statistics are not applicable to the business of Life Assurance, and are not appropriate data for the purpose of determining the amount of premium which persons of different occupations should pay for Life Assurance. We still desiderate reliable data for this purpose, and it can best be obtained from the Life Assurance Companies themselves.

Some years have now elapsed since I had the honour of addressing you from this chair. In the paper which I then read to you I urged on our younger members the necessity of studying finance, and especially of endeavouring to form a just estimate of the value of money, and of the rate of interest which will obtain in the future, so far as that future forms an element in our calculations. Without this knowledge we shall build with insufficient materials, and in the absence of its thoughtful application to our daily work, and to our periodical investigations and valuations, we shall rear a fabric which, although it may last during our lives, and look to all appearance as if it were carefully and substantially built, will certainly, before its time, show symptoms of decay, and finally fall about the ears of too confiding policy-holders.

That the subject of the extra risk incurred by dealers in intoxicating liquors is still open for discussion is evidenced by the fact that, on inquiry at over thirty of the principal Scotch and English Life Offices as to the rates of extra premium charged for assurances on innkeepers and publicans, it has been found that the practices of the various Offices in treating such cases differ so much and so widely, that to give a table showing the results of the inquiries would almost necessitate the practice of each individual Office being detailed. Some offices, it appears, charge no extra premium on either innkeepers or publicans, while one or two other Offices will not, as a rule, entertain proposals on either class of lives. Some Offices, again, charge no extra for innkeepers, but a very considerable extra for publicans, while others require the same extra from both classes—such extra varying from 10s. to 20s. per £100. A few Offices charge 10s. for innkeepers and 20s. for publicans, while one or two others make the extra take the form of an addition to the age, varying from five to seven years for both classes.

What was probably the beginning of knowledge in this country in regard to the subject of Life Annuities and Assurance was the publication, in 1661, by John Graunt, of his Natural and Political Observations on the Bills of Mortality. In that publication we have no doubt the primary data on which the business of Life Assurance is founded. By the gradual development and extension of that business, it soon came to be recognised that in all calculations connected with the subject it was needful to proceed on a sound fundamental basis. For not only was it seen to be necessary that the affairs of an institution conducting such business required to be administered for the immediate benefit of those concerned; but it was also observed that there were many prospective liabilities, and that therefore it required to be built on such a solid and substantial foundation as to be able to meet all obligations in the future. This is appreciated by all who are in any way interested in Assurance.

Having been a member of the Actuarial Society of Edinburgh for something like a quarter of a century, and having been during that period anything but a working bee, in so far as the interests of the Society are concerned, I felt, when I was asked to be its Honorary President for this session, that I had no claim whatever to the honour proposed to be conferred upon me.

Further reflection, however, led me to see that wrong-doing in the past formed no valid reason for a continuance of the same line of conduct in the future, but rather that the reverse should be the case. It seemed to me that, having hitherto failed to take my fair share of the work of the Society, I should best expiate my guilt by trying to do better in the future.

In coming to this conclusion, I was quite aware that the first mark of penitence I would be called upon to show would be the delivery of an Inaugural Address at the opening of this session, and that meant time for preparation, which, in a busy life otherwise, was not so easily secured. However, the time between the election of the Honorary President and the opening of the session was considerable, and I trusted to opportunity presenting itself.

Gentlemen,—At the time you did me the honour to elect me President of your Society, I was collecting information regard-the land laws and conveyancing systems of our Australasian Colonies, and also endeavouring to master the details of the legislation for Ireland which gradually led up to the passing of the Ashbourne Act, and left us with the prospect of still more sweeping measures.

It appeared to me that information on these matters could not fail to be of interest, and might be of use to you, so I determined to make them the subject of my Address, and that my paper might be more worthy of the occasion, and might better show my appreciation of the honour you have for the third time conferred on me, I decided to widen the subject and give you a sketch of the “Tenure of Land in the United Kingdom and its principal Colonies,” and in doing so to touch on cognate subjects of interest to all concerned in land as a security.

1. In the following Paper I propose to investigate formulas for use in the valuation of ordinary whole-term policies, endowment assurance policies, and limited-payment policies; with special reference to the modifications which these of formulas are subject, when the next premium Paper is due, not immediately, but at the end of some fractional portion of a year, and when the premiums are payable half-yearly or quarterly.

2. It may be well to point out that it is no part of my plan to deal with the more important questions of principle that arise in connection with a Life Office Valuation, such as:—What mortality table or rate of interest should be used, Whether the valuation ought to be a net premium or a gross premium valuation, How the effect of selection should be allowed for, or whether any allowance should be made for the special expenditure of the first year.

In the Introduction to his famous Théorie Analytique des Probabilités, Laplace, after an eloquent summary of the progress of Astronomy from the days when every rare celestial phenomenon was regarded as a portent of human misery, to the verification in April 1759 of the perihelion passage of Halley's Comet, proceeds to say :—

“The regularity which Astronomy shows us in the movement of Comets exists, beyond doubt, in every phenomenon of nature. The curve described by a simple molecule of air or of vapour is regulated in a manner as certain as the planetary orbits: there is no difference between the two cases save our ignorance.