In proceeding to make a valuation of a class of policies effecting whole-life assurances, the first step is to collect and arrange the amounts of sums assured, inclusive of bonuses, and the corresponding annual premiums under the present ages of the lives assured: that is, under the ages brought up to the date of the proposed valuation. The whole of the data for the class of policies under consideration is thus condensed, and finally exhibited, in a list showing the several amounts for every separate year of present age. The subsequent valuation of these numbers by the proper factors, so as to obtain the respective present values and thence the totals of the present values, involves necessarily a certain amount of calculation, the accuracy of which it becomes very desirable to check; more especially if the figures are considerable and there are many of such computations to make.

In the course of a paper read before the Institute in January 1885 (J.I.A., xxv, 141), I suggested a certain method of making approximate valuations on different bases of the liabilities of a life assurance company under its whole-life policies. Shortly afterwards I had occasion to make a valuation of the liabilities of a particular company, and I took the opportunity of testing the suggested method of approximate valuation by actual comparison of the results arrived at by its application with those derived from a rigidly accurate class valuation, and I have thought that it would be interesting to the members of the Institute to have an explanation of the process employed in making use of the approximate method, and a statement of the results of the comparison.

The Registrar-General's mortality statistics prove beyond doubt that a marked decline has occurred in the national death rate in recent years. There appears, however, to prevail a singular reluctance to accept this decline of mortality as evidence of the improved health and sanitary condition of the English people, or to recognize that it necessarily implies an increase of the mean duration of life in England.