On 29 December 1902 I had the honour of reading a paper before the Institute on the “Comparative Reserves of Life Assurance Companies according to various Tables of Mortality at various Rates of Interest.” That paper was intended to complete up to date the investigations which had been made in 1876 and 1877 on the same subject, by bringing in the New British Offices Experience Tables, OM and OM(5). When that paper was read, the Select Tables, based on the British Offices data, were not available, and in the comparisons then instituted they could not be included. The case is now different, and a valuation has been made of the Model Office, on the basis of the O[M] Select Tables, at 3 per-cent interest, and in Table I of the Appendix the results are given, and compared with the results of the valuation by the OM Aggregate Table, at the same rate of interest. The valuations by the OM and OM(5) Tables in their various combinations are also repeated, so that reference to the previous paper may not be necessary.

The subject dealt with in this paper has already been introduced by a letter to the Insurance Record, of 24 February 1905, but I am now able to put forward certain further developments of the theory and method there set out.

The object of the following notes is to state somewhat more fully and formally a method (first published in the Insurance Record for 10 March 1905) of approximating to the reserves required for whole-life assurances, with due regard to the influence of selection; and to illustrate the practical application of the method.