When I accepted the suggestion of my friend, Mr. Woods, that I should open a discussion on this subject, I was in hopes that I should do so before the passage of the Bill for the Census of next year. As, however, that measure was added to the Statute Book at the end of last month, I have been compelled to approach my subject in a somewhat different manner. I shall, therefore, endeavour to set forth briefly my own views on the requisites of a successful Census and then examine the present Act to see how far the approaching Census promises to fulfil those conditions. That I shall have anything new to tell you, I do not for a moment expect, but I venture to hope that, as I regard the subject from a totally different standpoint to that which an actuary would adopt, I may be able to suggest points which will serve for an interesting, if not particularly useful discussion.

The objects which I have set before myself in writing this paper are (1) to advocate a more elastic interpretation than has hitherto been usual, of the requirements of the Act of 1870 in regard to Valuation Returns; (2) to discuss some points that arise in the classification and valuation of Special Policies. The connection between these two objects consists in the fact that the necessity, or the supposed necessity, of conforming to the stereotyped schedules in which valuation returns under the Act are usually made, and the labour entailed by the individual valuation of special policies, constitute, jointly and severally, a serious obstacle to the rapid conduct of a life-office valuation. This may not be a matter of very great importance if or so long as a valuation is looked upon as a quinquennial or septennial event, for which special and extensive preparations must be made, and upon which months of overtime are to be spent, but it becomes a very different matter if a valuation is to be regarded—as it should, I think, be regarded, and as it undoubtedly is regarded in an increasing number of offices—as little more than an incident in the actuarial routine.

The first object of the present paper is to bring before the members of the Institute some model tables, which I have constructed shewing the force of mortality and the expectations of life based on a single value of log c, combined with certain constant values of A in the formula

Finding some time since, in connection with some work then in hand, that many conveniences would result from model tables on Makeham's hypothesis with which to compare the deduced functions of an ungraduated table, I gave some consideration to the most general form in which such a work could best be accomplished, resulting in the Tables, Nos. I, II, III, and IV, which I have the honour to lay before you this evening.

Some years ago I had the privilege of reading a paper on Contingent Reversions, &c., before this Institute, and the proposals I then made for the treatment of the premiums on the insurances to be set up in connection with reversionary transactions were received with general condemnation, nor have they since, so far as I know, met with any practical support, although I have seen no reason to alter my opinion of the soundness and practicability of the views I then put forward. I am not afraid on this occasion of meeting with like opposition, as the methods I am now going to deal with have been carried into practice already by the Society with which I am connected, and by way of reassurance, if not otherwise, have examples on the books of many of the life offices, both in England and Scotland.

The two leading formulæ at present in use for interpolation by central differences are due to Newton‡ (Methodus Differentialis, Prop. III), though often called by the name of Stirling, who republished them about 20 years later.

It would appear, from some of the answers given by candidates in the recent Final Examination for the Fellowship of the Institute of Actuaries, that considerable misapprehension exists as to the effect of the latest decision of the Courts with reference to the subject of this note. It may, therefore, be useful to deal briefly with the question in the pages of the Journal.

According to Wallace and Weisman the duration of life in any organism is determined by natural selection. An organism lives so long as it is advantageous, not to itself, but to its species, that it should live. But it would be impossible for natural selection to determine the fit duration of life, as it would be impossible for it to fix any other character, unless that character were inherited. Accordingly the hypothesis above referred to supposes that duration of life is an inherited character. So far as we are aware, however, neither of the above-mentioned naturalists, nor any other investigators, have published researches bearing on the problem of whether duration of life is or is not inherited. We are accustomed to hear of a particular man that “he comes of a long-lived family”, but the quantitative measure of the inheritance of life's duration does not yet seem to have been determined. This absence of investigation appears the more remarkable as a knowledge of the magnitude of inheritance in this respect would, we should conceive, be of primary commercial importance in the consideration of life insurance and of annuities. The biological interest of the problem, as we have already noticed, is very great.

The President in his inaugural address last session, expressed the opinion that “the time is ripe for another discussion on surrender-values.” In accordance with that suggestion, I have ventured to bring to your notice some considerations bearing on the subject of surrender-values and the principles which, it would appear, should underlie their calculation.

The publication of the Sickness and Mortality Experience of Registered Friendly Societies, the work of our late distinguished member, Mr. W. Sutton, has directed the serious attention of the Manchester Unity of Oddfellows to the question of the continued reliability of the Tables on which the Society has been accustomed to base its financial estimates, and as the result of the interest thus awakened, the Actuaries of the Order have been instructed to make a complete investigation of its experience during the five years 1893–97. From the immensity of the data to be handled in this investigation (these being contributed by about 3,500 branches and comprising, inter alia, some three million years of life and 40,000 deaths) it has been necessary, at the outset, to closely consider the methods of tabulation and classification to be adopted, and preliminary experiments on a somewhat elaborate scale have accordingly been required. The results of these experiments appear to possess a definite value in relation to the subject of friendly society experience, and I am emboldened on this account to offer the following notes respecting them for the consideration of this meeting.

The Institute of Actuaries had been in existence forty-one years when the first decisive steps were taken by the actuaries of America to form an Association for the promotion of the Science of Life Insurance. It happened that in February 1889, Messrs. David Parks Fackler, Clayton C. Hall, Sheppard Homans, Emory McClintock, and Howell W. St. John (the third and fourth being respectively a Corresponding Member and a Fellow of the Institute), independently thought of proposing an organization of actuaries. Somewhat by accident their ideas were intercommunicated. On the request of the four other gentlemen, Mr. Fackler sent letters to the actuaries of the regular Life Insurance Companies in the United States and Canada, which called forth replies cordially favourable to the project. Accordingly, in response to an invitation of actuaries resident in New York, on 24 April 1889 twenty-nine of the actuaries met at the Astor House in New York, and, after a conference which exhibited a marked unanimity, founded the Actuarial Society of America. On 25 April, they adopted a Constitution and elected officers.

According to the Darwinian theory of evolution the members of a community less fitted to their environment are removed by death. But this process of natural selection would not permanently modify a race, if the members thus removed were able before death to propagate their species in average numbers. It then becomes an important question to ascertain how far duration of life is related to fertility. In the case of many insects death can interfere only with their single chance of offspring; they live or not for their one breeding season only. A similar statement holds good with regard to annual and biennial plants. In such cases there might still be a correlation between duration of life and fertility, but it would be of the indirect character, which we actually find in the case of men and women living beyond sixty years of age—a long life means better physique and better physique increased fertility. On the other hand, there is a direct correlation of fertility and duration of life in the case of those animals which generally survive a number of breeding seasons, and it is this correlation which we had at first in view when investigating the influence of duration of life on fertility in man. The discovery of the indirect factor in the correlation referred to above was therefore a point of much interest. For it seems to show that the physique fittest to survive is really the physique which is in itself (and independently of the duration of life) most fecund.