The following remarks do not purport to contain any original matter but are merely an attempt to outline the routine followed in the valuation of a pension fund and to indicate certain problems which must be dealt with by the Actuary undertaking the valuation.

The method of valuation is in the nature of an exercise in the use of the salary scale to give actual increases and not rates of increase.

For the purposes of illustration a fund providing the following benefits is taken as an example.

Since games of chance have always exercised a fascination for people of all countries and at all times it is not to be wondered at that the theory of probability was first evolved from the dice-table. Possibly the earliest problem was to find the different probabilities of the various throws which can be made with three dice: this occurs in a document published in the fifteenth century, and the problem was taken up again by Cardan about a hundred years later. The first serious investigation into the laws of chance was, however, due to Pascal, who may be considered as the founder of the science. Pascal's attention was first drawn to the subject by a gambler who put to him problems relating to the game of ‘hasard.’ One particular problem seemed to Pascal of the utmost importance and led to a series of discussions between Pascal and Fermat, another equally eminent mathematician. The problem was the ‘Problem of Points’ and may be stated thus: Two players want each a given number of points to win a game; if they separate without finishing the game, how should the stakes be divided? Many variations of this were considered, even those where the players were not of equal skill, and although the problems would not be difficult of solution in light of modern knowledge, there was considerable divergence of opinion as to the correct methods to be applied.

This Lecture was given with the object of explaining the preliminary steps to be taken in ascertaining the mortality experienced by a body of lives, commencing with the extraction of particulars from the records of individual cases and leading up to the point where the rates of mortality are calculated from the raw material (usually referred to as the unadjusted rates of mortality) before any smoothing process is adopted for the purpose of preparing monetary Tables based on the experience. The lecture was given with particular reference to the Mortality of Annuitants 1900–1920, the first report on which had just been published.

No discussion of Life Office Investments before the Students' Society would be complete without reference to the five canons laid down by Mr A. H. Bailey. Their influence on the investment practice of Life Offices has been almost universal and continuous since they were enumerated in 1862, and when it is reflected that the great majority of Life Offices, although their annual profits are comparatively very small in relation to the very large accumulated funds which they administer, nevertheless emerged from the War period, and the enormous depreciation of securities which it entailed, stronger than ever before, no apology need be made for restating the principles which have been followed with such successful results.

They are as follows:

1. That the first consideration should invariably be the security of the capital.

2. That the highest practicable rate of interest be obtained, but that this principle should always be subordinate to the previous one, the security of the capital.