The idea of reducing the ordinary with-profit premiums in anticipation of such future bonuses as past experience shows may be safely reckoned upon, is not a modern one. The adoption of such tables has, however, become more common in recent years; and since their use involves the consideration of various practical points of importance—such as the basis upon which the reductions should be computed, the reserves and surrender-values attaching to the policies, the course to be pursued when the profits exceed or fall short of their anticipated amount, and the manner in which the calculations are affected by changes in the rate of interest and mortality—the subject appears to be one well suitable for discussion by this Institute.

The value, to the practical actuary, of Makeham's formula for the law of mortality, as a means of facilitating the calculation of joint-life benefits, is well established. Considerable use, for instance, is undoubtedly made of the tables appended to the second volume of the Institute Text-Book, in questions of everyday occurrence involving the computation by the HM Tables of annuities on three or four lives. In like manner, where the employment of Carlisle annuities is desirable, the tables prepared in 1880 (see J.I.A., xxii, 191), by Messrs. George King and G. F. Hardy, afford a ready means of obtaining results which are at once consistent, and substantially in agreement with values derived directly from the parent table. With regard, however, to the calculation of contingent survivorship benefits, it seems worthy of consideration whether something may not be done to render expressions based upon Makeham's formula better adapted than they are, in the shape in which they are usually presented, to meet the exigencies of practical requirements.

In venturing to bring this subject before the Institute to-night, I am conscious of inviting attention to a matter which has been frequently treated before and by far abler hands than mine. I at once confess that I have little original matter to bring forward; indeed, the main object of this paper is to endeavour to bring into one focus and to a common standard of criticism the various formulas for ascertaining the rate of mortality, which have already been so often discussed in this room. The expression “rate of mortality” is advisedly used here instead of “exposed to risk”, because it would seem that attention has hitherto been unduly centred in the latter.

The subject upon which, at the suggestion of your Council, I have undertaken to address you to-night is “Some of the Modern Developments of the Life Assurance System”, including under this heading not only those which most of us will regard as improvements, but others which some among us may consider mere excrescences and eccentricities. The subject, as I have found somewhat to my cost, is a very large one, needing for its full elucidation an enormous mass of detail, which, were your patience equal to its due exposition, would not, I think, bring with it any corresponding pleasure or profit. I propose, therefore, to treat the subject on somewhat broader lines, in which I shall use details only so far as they may illustrate principles.

Having on several occasions been employed to investigate and report upon the Widows' Funds of certain Banks in Scotland, and having found no available tables specially suited to work of that kind, Mr. Hewat had, like other actuaries, to fall back upon existing tables which have been considered more or less appropriate and presumably safe enough for the purpose in view. Not being quite satisfied that these tables are sufficiently reliable for use in the actuarial investigations of these increasingly important Funds, and holding the opinion that the actuary, like other skilled workmen, should never allow his work to suffer for want of a proper instrument or tool, he resolved to emulate the intelligent and enterprising workman in other professions—the surgeon and the engineer, for example—and manufacture an instrument specially adapted to the particular class of work in hand.

Considering the important part played in the social system by the various Friendly Societies of the Empire, both as fosterers of the inestimable principle of self-reliance and as trainers in the art of practical government, it appears to me strange that hardly anything respecting their aims, or their working or experience, has been brought before this Institute.

In the course of an investigation I have lately made, into the rate of mortality that has prevailed among the female lives insured in the Scottish Equitable Life Assurance Society, I have tried various methods of arranging the facts furnisht by the books of the office; and I think it may be useful to persons engaged in similar investigations, if I describe these methods, and state the conclusions at which I have arrived as to the best course of procedure.

A careful study of the prospectuses of the leading life offices discloses so great a variety of practice in minor details that the question naturally arises whether something cannot be done to secure uniformity. I propose in the following pages to discuss a few illustrations of this diversity of practice with a view to showing that the requisite combination on our part could not fail to exercise a beneficial influence by the simplification of a naturally complex branch of business, by the withdrawal of unnecessary and vexatious restrictions, as well as by the resistance which could be offered to the demands for unwise concessions.

In venturing to direct the attention of the Institute of Actuaries once more to the subject of contingent reversionary interests, I am deeply sensible that the topic has been treated by some of the most brilliant and experienced members of our profession, and that it may therefore seem presumptuous of me to choose it for further comment. I can but plead in extenuation the very great practical importance of the subject—so great as to make it one upon which we can hardly confer too freely or too often. The only other prefatory remark I would make is a disclaimer of any ambitious design, or plea for originality, as regards the paper itself. Its purpose, so far as I am concerned, will be amply fulfilled should it succeed in eliciting a useful discussion.

As stated in the foregoing paper, the number of persons to whom the observations relate was 2,205, and the total years of life 30,521. The average time for which the lives were under observation was therefore 13·84 years. The number of deaths was 668; the number of discontinuances 730; and the number of existing 807. The experience may therefore be described as an unusually mature one. The numbers at risk and the deaths in each insurance year have been calculated separately for each age at entry; but, as the numbers at individual ages are small, it is probably not worth while to publish them. The following are the figures irrespective of the age at entry.