The Registrar-General's Decennial Supplement, England and Wales, 1951, Life Tables, was published in February of last year. Following the established custom, it includes the report of the Government Actuary, Sir George Maddex, who was asked to prepare National Life Tables showing the level of mortality at the time of the 1951 census. The new life tables are presented in Appendix IV, and it is the aim of this paper to draw attention to the features which are of interest to actuaries concerned with Industrial Life Assurance.

When closing the discussion on the Finance Act, 1956, at the Sessional Meeting held at the Institute in November 1956, A. G. Simons commented that the Act would take a little while to settle down and really be appreciated, and it was a pity, therefore, that some of the younger members of the Institute had not given their views, because they were the ones who would have to handle it in the future.

If the thoughts expressed in this paper encourage a lively discussion amongst the younger members then it will have achieved its object.

The original purpose of this paper was to help students working for Parts IIIC and IVB of the Institute examinations and the equivalent sections of the Faculty examinations. The large majority of students have never been inside a consultant's office, have little or no practical experience of the subjects involved and seem to find these parts of the examinations extremely difficult because of their lack of practical knowledge. The paper does, however, seem to have expanded beyond its original aim into a general discussion of the practice and organization of a consultant's office, but it is hoped that at least part of the original intention has been fulfilled. It is written largely from the point of view of the staff carrying out the technical work in such an office. Perhaps it should be stated at the outset that it also refers mainly to one particular firm of consultants. The first part of the paper is concerned with a broad description of the services provided by a full-time consulting actuary and the necessary office organization and the remainder describes the particular features of the various types of work undertaken.

In a recent paper to the Students' Society (J.S.S. 15, 43), D. F. Gilley and D. Funnell pointed out that it would be theoretically possible, though normally impracticable, to make a valuation of a pension fund by projecting the fund membership year by year, in order to obtain a series of notional revenue accounts for each future year of the Fund's existence, and that the algebraic sum of the discounted values of the expected future current surpluses and/or deficits would be equal to the surplus or deficiency revealed by a valuation made in the normal way.

It is frequently possible, when an estimate of the future trend of the fund is required, to reverse this process. Instead of directly estimating the future income and outgo of the fund, and so building up the expected amount of the fund year by year, we may extend the normal valuation technique, and use a series of notional valuations to determine the future trend of the Fund. In other words, the growth or decline of a pension fund between two future dates may be expressed as the difference between the net liabilities of the fund, as revealed by notional valuations, on these two dates.

The technique described by Miss Merriman in the preceding note can be applied, with suitable alterations, to many different types of life assurance and annuity funds as well as to pension funds. By the use of approximate methods it is possible to abbreviate the working within a comparatively small compass, whilst retaining sufficient accuracy to afford a guide for investment policy. This note describes a particular application of these methods.

The Management Committee of a large Widows' and Orphans' Fund sought the Actuary's advice on the probable future progress of the Fund. The Fund was established many years ago, but the membership has been expanding and both contributions and benefits have been increased from time to time. It was clear on general grounds that, if sufficient new entrants were admitted to maintain the present membership without limit of time, financial maturity would not be reached for many years. On these assumptions the Fund would eventually reach stability, but it would never decrease, so that from this point of view irredeemable investments could be purchased in the belief that they would never have to be sold. The adoption of this theory, however, would be tantamount to making the future surplus or deficiency of the Fund in some way contingent upon the future flow of new entrants.

Three of the writer's earlier notes in this Journal (see References) have discussed respectively the effect, upon pension fund contribution rates, of changes in the salary scale, the rate of interest and the entry age, and approximate methods have been supplied for estimating rapidly the effects of the two last-mentioned changes. The object of the present note is to propose a method for estimating the effect on the survivorship ratio ly/lx according to a service table, of changing one of the sets of decremental rates in the same proportion at all ages, or of removing a set altogether, or of introducing a new set in addition to those already present. For example, given a service table based on certain rates of mortality and withdrawal, we shall be able to estimate, with a negligible amount of arithmetical work, the new values of such ratios as l60/l25 resulting from removing the mortality rates altogether, from doubling or halving the withdrawal rates or from introducing a new set of decremental rates.