In two previous papers (vol. li, p. 77 and p. 211) an account has been given, of the published work of Newton on the subject of Interpolation by means of formulas of Finite Differences, and references have been made to the important letter which Newton sent on 24 October 1676, to Oldenburg, the Secretary of the Royal Society, with the intention that it should be communicated to Leibnitz. The second paper closed with a quotation from this letter, in which Newton mentions “a method [for the “construction of tables by interpolation] which I had almost “decided to describe here for the use of computers.” It has been my good fortune to discover that Newton had prepared an account of his method for inclusion in the letter and that the draft is preserved in the University Library at Cambridge among the Portsmouth Collection of Books and Papers written by or belonging to Sir Isaac Newton. By the freely granted permission of the Syndicate of the Library, I am able to give a reproduction and transcription of the manuscript, and I have added a translation.

Reference is made in the introductory remarks to the appointment of Investment Research Committees by the Faculty and Institute of Actuaries to undertake, in the first instance, the compilation of a comprehensive service of Index Numbers relating to British Stock Exchange Securities which will be suitable for Insurance Companies, Trust Companies, and so on. The Committees have been at work for some time, and it is hoped that publication of the results will be commenced at an early date. The Paper discusses the purposes of such indexes and the most suitable form of index numbers for the purposes decided upon. The difficulties arise from two sources ; the variety of uses for which the index must cater, and the requirement that the results must be comparable between any two dates in the series.

At every point in compilation the objects of the results must be carefully kept in view. These objects are divided under three headings : (a) uses directly connected with current investment activities ; (b) investigation of the effect of economic financial and political events on the level of security prices ; and (c) assistance in measuring approximately changes in the value of a portfolio of investments. It is suggested that securities should be divided into homogeneous classes, and a separate index calculated for each class. The wide groups “Fixed Interest” and “Variable Dividend” are not suitable for the purposes involved. The weighting system should approximate to the distribution likely to be found in an Insurance or Trust Company's investments.

Within each class companies' holdings will tend to approximate more nearly to equal amounts of money in each security than to any other distribution for which a system of varied weights would cater. Simple weights are accordingly advocated.

Various methods of averaging are discussed and reasons given for preferring the geometric average of price ratios to other methods. The dangers of adopting the arithmetic average—where the resulting figures are always dependent on the base prices—are illustrated in Table I. The geometric results are independent of base. Even using the geometric average great care must be exercised in applying the results to valuation purposes in groups where individual price movements show wide divergencies. The “error” involved by the geometric method, however, is always in the same direction. Capital appreciation is never overstated and depreciation never understated.

The foregoing remarks refer to price indexes. To obtain maximum utility from the results yield statistics also are required. The very different nature of the problem of yields is stated and an arithmetic average of individual yields in each group is advocated. While the price index should be related to 100 at the starting-point it is obviously preferable to publish actual yield averages.

In his paper of 1941, Seal included details of some experiments he performed in an attempt to estimate the appropriate number of degrees of freedom for the chi-square goodness-of-fit test of a summation formula graduation. These results are referred to by Tetley and by Benjamin and Haycocks in their textbooks when they mention the difficulty of determining the number of degrees of freedom or mean chi-square value.

The new series of Financial Times–Actuaries fixed interest indices commenced in 1977 with the first publication in the Financial Times of the British Government Securities Indices. These were described on behalf of the Joint Index and Classification Committee of the Institute and the Faculty in the paper by G. M. Dobbie and A. D. Wilkie, “The F.T.–Actuaries Fixed Interest Indices”, J.I.A. 105, 15 and T.F.A. 36, 203. Subsequent notes in J.I.A. and T.F.A. have given annual reviews, the last, for 1980, appearing in T.F.A. 37, 327. Part 1 of the present note continues the history of the B.G.S. Indices up to the end. of 1984.

The rate of mortality experienced by residents in India will supply an answer to an enquiry of the highest interest in an actuarial sense. The enquiry may even be considered of national importance so long as our countrymen seek their fortunes in a region where the effects of the climate on their prospects of health and longevity continue to be regarded as uncertain and hazardous.

Considering the undeniable importance of a conformity to correct principles in carrying out the processes which must he resorted to for the purposes above mentioned, it is not a little remarkable that no work exclusively on the subject has hitherto appeared. If we except Mr. De Morgan’s and Mr. Sang’s Essays and the Observations scattered through the writings of Mr. Babbage, Mr. David Jones, Mr. Samuel Brown, and one or two others, we believe it may be truly said that scarcely any allusion to it is to be found.

Most of the 350,000 persons who are actively engaged in the service of the General Post Office are established civil servants to whom the provisions of the Superannuation Acts, 1834–1957, apply. Arrangements for pensioning civil servants when they retire are of long standing, and the number of former Post Office employees drawing pension has now risen to about 70,000, most of whom are men.

1. Mr. James John M’Lauchlan has done excellent service, in his Presidential Address to the Faculty of Actuaries on the 30th of November 1908, by drawing attention to the natural growth of a normal Pension Fund, and the necessity of accumulating large invested funds during the first 40 or 50 years of its existence, in order to provide for the heavy liabilities which will then be maturing for payment. He has done this by a few simple and easily understood illustrations involving a very considerable amount of accurate calculations which do not appear in the work.

This note continues a regular series on mortality rates in Great Britain, showing the mortality experienced in each age-group in 1990 and comparing this for broad age-groups, on a standardised basis, with mortality in earlier years.

My intention is to give some simple illustrations of the difficulties which arise when the market rate of interest has sunk below the limit of solvency for parts of a company's stock of life contracts. In fact, the “partial liquidation” which at such a contingency would appear most natural to the unbiased mind of an actuary, does not seem to be seriously contemplated in insurance legislation. As regards Sweden, this mathematically correct reduction of the liabilities of some of the contracts could perhaps be realized within the legal frame in Mutual Offices. But it is impossible for other companies. It seems therefore necessary to attack the problem from the purely actuarial point of view. If we can find a technically satisfactory solution, it might then be possible to go farther with the question of giving the procedure legal shape.

The measure by which the Chancellor of the Exchequer proposes to extend the benefits of life assurance and annuities to the nation at large has now been before the public some time. Few Bills have of late attracted so much attention, and have been so earnestly discussed by all classes, as this. But beyond what was elicited at an interview that took place between the Chancellor of the Exchequer and the Actuaries of several Offices, and some passing remarks on the subject made at the last meeting of the Institute of Actuaries, when we had the advantage of hearing Mr. Samuel Brown's excellent paper on Friendly Societies, the public have as yet had no opportunity of hearing the opinions of those, who after all are best able to judge. It now appears, that the Chancellor of the Exchequer is opposed to a general inquiry and the calling for “persons, papers and records” by the Select Committee, to whom the Bill has been referred, and it therefore becomes all the more desirable that the merits of the proposition of the Chancellor should be calmly and impartially discussed by the members of this Institute.

This presidential address looks at the current state of affairs, the opportunities and threats to our traditional areas of interest and the importance of developing in wider fields. It pays tribute to all the volunteers who help make it the organisation that it is whilst highlighting the need for all Fellows and students to be engaged with its future.

This summary relates to the following paper:

ForoughiKMarket-consistent valuations and Solvency II: Implications of the recent financial crisis ‐ Summary of the London discussion. British Actuarial Journal, doi:10.1017/S1357321712000025

An Open Meeting was held by the Faculty of Actuaries on 15 October 2001, when Mr Myners addressed his audience on a number of the issues raised in his review, Institutional Investment in the United Kingdom: a Review. This was followed by a discussion. The lecture and an abstract of the discussion are printed after this introduction.

A second meeting on the subject was held on 16 October. This was a joint Seminar, arranged by the Faculty of Actuaries and the Centre for Financial Markets Research, University of Edinburgh. This seminar covered a number of issues raised by the Myners Review. The purpose of the seminar was to open up to discussion a number of the issues raised by the review where there appeared to be differences of opinion amongst practitioners. In particular, the investment process, investment performance and fees, especially commissions, were discussed. Academics, investment, performance measurement and pension specialists attended the seminar.