Most persons who have dealt with mortality experiences have, no doubt, observed the variation in the average rates deduced according to the grouping of the exposures, but a few observations thereon, for the benefit of students of life contingencies, may, perhaps, be acceptable.

The first process in the investigation of the rate of mortality among lives assured in an office, or a special class, as annuitants, is to obtain the number exposed to risk of mortality, and the deaths which have actually occurred, at each age, during a certain period of time, as, say, the past five years, or since the company was established. The method to be used for deducing the numbers exposed to risk will depend on the special circumstances of the experience under observation, and need not here be discussed; but, assuming the exposures and deaths to have been ascertained, the mortality experience of the company is deduced by dividing the number of deaths at each age by the corresponding exposures.

The first part of this paper was devoted to an investigation of the actual rates charged by the different companies, with a view of showing how important a bearing they have upon a valuation. Before commencing the second part of my subject, which deals with different modes of distributing profits when placed side by side with the rates charged, I would recapitulate the conclusions drawn from the first part of my paper, and, in addition, refer to some of the observations which were made thereon when the paper was read before the Institute last session.

By the assessment of life-risks, I mean the gathering together all the scattered influences that bear on the duration of life of particular individuals; the connoting in the mind the weight to be attached to the several factors that make up such influences; and, finally, the fixing the price of assurance for each individual life which approximately puts all upon a level.

We commence our third epoch with the year 1721, and with the fact that there was at that period but one Life Assurance Office in existence in Great Britain—the Amicable, founded 1706. That too, so far as we have the means of knowing, was the only Life Assurance Association in the world. It was very defective in its mode of working, at the best; but it stood alone. The Society had at this date an accumulated fund of about £50,000; it had distributed in death claims £118,000. Thus it had obtained a solid hold upon public confidence, but I suspect its business suffered considerably from the general shock to public credit. The days of Mutual Contribution Life Assurance Associations, as such, were gone for ever in England. This Society had to take steps to mitigate the element of uncertainty, or it would most probably have died out. Solidity was now the one thing sought for.