Any attempt to cover in a single paper the whole field of the present and future problems which the placing on the Statute Book of the “Local Government and other Officers’ “Superannuation Act 1922”, presents to the actuary would be a highly ambitious task, and as so many of these problems will be solved far more readily and more accurately a few years hence’ than can be the case to-day, I have deliberately limited my comments on the present occasion to two important aspects of these questions. The first section of the paper gives an explanatory summary of the main provisions of the Act, so far as they affect our profession : the second section is an attempt to devise a simple method of valuation, suitable for adoption in the case of a small body of benefit members, where the ordinary valuation procedure, based on salary averages, does not seem to me to be applicable at the outset.

The question whether the number of mixed lives at any age in the ultimate column of a select table can be subdivided into the number of lives still select and the number of damaged lives is a point of considerable interest in the practical use of mortality tables. And it was in connexion with a difference of opinion on this problem that the late Dr. Sprague made his last contribution to actuarial literature. Moreover, this was one of the few discussions in which he was apparently unable to carry conviction that his views were sound.

The arithmetical method adopted in these notes is to assume that the level premium to cover a certain under-average life is known; to work out some of the different rates of mortality that might lead to it and then see what consequences follow. The numerical work, in connection with which I have to thank Mr. Sidney J. Perry, F.I.A., for help, will be confined to an unloaded level premium on a 4 per-cent basis of ·01914 for a life entering at age 30. This premium might result from the rates of mortality set out in Table I.

Although many tables have been graduated in order to study the trend of mortality or express it mathematically, the real object of graduation in practical actuarial work is to provide a sufficiently smooth series of rates of mortality to avoid inconvenience in the calculation of monetary values, particularly perhaps, in the case of joint life functions. The importance of making tables available for practical calculation as soon as possible after the expiration of the period to which the rates of mortality relate necessitates the postponement of any attempt at an extensive mathematical study of the material and we feel that the alternative lies between (1) the use of the rates of mortality already found from the material adjusted as little as is necessary and (2) a Gompertz or Makeham graduation.

The scheme of National Health Insurance, apart from its general interest to the student of social questions, presents many technical features of special interest to the actuary, and it has been suggested that the completion of the first valuations of approved societies, i.e., the societies administering the monetary benefits of the system, affords an opportunity for discussion of the scientific problems to which these features give rise. With the Government Actuary's consent, I therefore submit in the following paper an examination of some of the more important points of actuarial interest which have emerged in the course of the valuation work. Before approaching the main theme of the paper, however, I have described briefly certain factors, such as the principal alterations made in the financial structure of the scheme by the Act of 1918, a knowledge of which is essential to an understanding of the later part of the paper. These preliminary remarks are placed in Part I, the main subject being dealt with in Part II.

We are now able to give the first results obtained from the investigation into the mortality of annuitants since 1900. It may be well at the outset to recall a few points affecting the investigation which have been acted upon throughout.

In October 1921, I had the honour of submitting to the Institute the results of an investigation into the mortality experienced by life tenants under reversions (J.I.A., vol. liii, pp. 1-42).

The investigation led to certain interesting and, I hope, useful conclusions, among them being the fact that there was no evidence that vendors of reversions exercise selection against purchasers to a significant extent and that in consequence the mortality of life tenants could be sufficiently represented by a full aggregate table.