The subject proposed for discussion this evening is one of considerable importance to all who engage in the pursuits of an actuary. The old practice of valuing life contingencies by a pet table of mortality and at one fixed rate of interest has long since been found to work unprofitably; and parties seeking investments in securities of this description have been compelled, for their own safety and advantage, to adjust the valuation of the actuary before determining the price to be given for the particular property under consideration. If such a state of things is unsatisfactory to the public, it must be equally so to the actuary to find his calculations used only as a partial guide, instead of being, as in fact they ought to be, the index by which a proposed purchaser may know the rate of interest and the other advantages to be derived by obtaining the security in question at the price fixed by the actuary. In the ordinary transactions of a Life Assurance Office, where the fluctuation in the rate of mortality is protected by the admission of large numbers, it is necessary also to protect its pecuniary interests by limiting the amount to be assured on each life. Even with this precaution, it not unfrequently happens that particular years have proved less favourable than might have been expected—not so much from an increase in the number of deaths, as from the average amount of the sums insured by the policies so lapsed being greater than the average of the whole number. When, however, the average of a number of years is taken, and the amount insured upon any one risk is properly limited, these fluctuations become less apparent and generally disappear.