Some time ago, the writer had occasion to examine the principal methods adopted by life assurance companies in the distribution of surplus, and particularly the plan which is known as “Sprague's Method”, from the name of its inventor, Dr. Sprague, or the “Equity and Law Method”, from the name of the company to which it was first applied. The plan is at present employed by comparatively few British offices, but it has recently been adopted by several companies in substitution for systems previously in vogue, and it appears to be rapidly growing in theoretical importance as a standard by which to test the effect of other systems of distribution. Nevertheless, it would appear that, apart from the brief description of the method originally given by Dr. Sprague (and quoted below), there is no systematic discussion of the principles of the method in the pages of the Journal of the Institute of Actuaries, and it is therefore thought that a few notes respecting some of the points which arise in connection with the practical application of the method may be of service to those who are studying the subject, but who may share the experience that little information is to be gleaned from the Journal.

At a sessional meeting of the Institute held during the period allocated to the collection of the information required for the compilation of the New Mortality Tables, a discussion may not, I think, inappropriately be raised on various points arising in connection with the nature and adaptability for the purpose of the materials used in the construction of the principal Institute Table at present in use, and it is with this view that I venture to submit to the members of the Institute the results of some attempts which I have recently been making to trace the effects produced on the HM Table by the fact that, at the close of the observations from which the Table is derived, there were still in existence nearly 75,000 out of 130,000 males who had come under observation; I have also endeavoured to obtain from the details given in the Mortality Experience published by the Institute some approximate figures as to the new business of the Twenty Offices which supplied the experience upon which the HM Table is based.

The general subject of extra risks, and the special method of meeting such risks by making temporary deductions from the sum assured in lieu of charging an extra premium, have been more than once under discussion at this Institute. The latter problem in particular was somewhat exhaustively considered upon the occasion of a paper by the late Mr. Sunderland, “On a Method frequently adopted of treating Under-Average Lives for Assurance purposes, &c.” (J.I.A., xxix, 419).

The first International Congress of Actuaries that has been held since the profession of Actuary has been generally recognised, was opened on 2 September 1895, at the Palais des Académies, at Brussels, under the patronage of the Belgian Government, by the Belgian Finance Minister, M. de Smet de Naeyer, who had previously acted as honorary president of the organizing committee. This organizing committee had skilfully performed the laborious duty of collecting the materials and settling the procedure which so largely contributed to the success which attended the meetings of the Congress.

In dealing with the valuation of a large number of policies, the method of grouping is of very great importance, and although there is probably nothing new in any of the suggested methods, I venture to hope that a discussion of this subject will be of some utility.

In the list of names of the Permanent Committee, given on page 237 of the present volume, the following corrections should be made, namely:

For Wolterbuck read Wolterbeek.

Many valuable papers have been read before this Institute in recent years on the subject of the sources of surplus, on various methods of bonus distribution and on kindred subjects, notably those of Mr. Sunderland in 1887 and 1890 (J.I.A., xxvi, 357, and xxviii, 257); Mr. Rothery in 1892 (J.I.A., xxx, 131); Mr. G. F. Hardy in 1894 (J.I.A., xxxi, 261); and Mr. G. J. Lidstone in 1895 (J.I.A., xxxii, 73); which are, in my opinion, contributions to actuarial science of the utmost value and models of concise language and elegant demonstration for the actuarial student.

The method of valuation to be adopted in any office, and the books and forms to be used in scheduling the particulars necessary for it, must be regulated to a great extent by the requirements of “The Life Assurance Companies Act, 1870”; and it will be convenient here to give a brief summary of those requirements so far as they relate to the subject of this essay.

The standard of solvency in life assurance companies is a question of such importance that any new light, however small, that can be thrown upon it may well engage our attention. Hence, anyone who can contribute to the illumination in the most insignificant degree may escape the reproach of having intruded himself and his views unnecessarily upon the profession. It is in this spirit that I submit the following short note to the Institute.

The subject of Insurance, theoretical and practical, has been so copiously and minutely discussed of late, especially in Lectures and Essays, that serious perplexity awaited me when I began to meditate upon my Introductory Address. I felt, under these circumstances, that a Paper constructed on the usual lines must either weary you with tedious repetition or discredit myself with the reproach of platitudes. I accordingly determined to see whether I could not,—at all events, partially,—succeed in adding some novelty and interest to our proceedings by an attempt to ascertain whether the vast Doctrine of Evolution applied in any valid degree to the business in which we are engaged. Such an investigation possesses at least the merit,—however I may fail in my exposition,—of appealing to the sympathy and thought of all concerned in the several Departments of our common work, for results which may be found to bear upon Life Assurance will also, mutatis mutandis, apply to other Branches. I confess, moreover, that the subject strongly attracted my attention on the ground that an enquiry of this interesting character had not previously been attempted.

The method about to be described is based upon a special application of the principle involved in the slide-rule. As this instrument is less familiar now than it was formerly, and as its working presents many points of interest, I propose to begin with a short account of its construction and use.

In view of the present movement on the part of life assurance companies towards a reduction in the rate of interest used in calculating their reserves, it is desirable to have some easily applied method of measuring approximately, with sufficient accuracy for the purpose of a preliminary estimate, or a rough check on fully computed valuation figures, the effect of such a change. The process is simple as regards whole-life policies, classified according to age attained, if the premiums valued represent some stated proportions of the gross premiums; but difficulty arises when the premiums used vary with the rate of interest, as in the case of a net-premium valuation. The following Tables I to VI (see pages 268-271) supply the means of approximating from the net-premium reserves for whole-life policies, under the HM or combined HM and HM(5) Tables, at most rates of interest presently used, to the corresponding reserves at rates one-half or one-quarter per-cent less.