The idea of reducing the ordinary with-profit premiums in anticipation of such future bonuses as past experience shows may be safely reckoned upon, is not a modern one. The adoption of such tables has, however, become more common in recent years; and since their use involves the consideration of various practical points of importance—such as the basis upon which the reductions should be computed, the reserves and surrender-values attaching to the policies, the course to be pursued when the profits exceed or fall short of their anticipated amount, and the manner in which the calculations are affected by changes in the rate of interest and mortality—the subject appears to be one well suitable for discussion by this Institute.

In venturing to direct the attention of the Institute of Actuaries once more to the subject of contingent reversionary interests, I am deeply sensible that the topic has been treated by some of the most brilliant and experienced members of our profession, and that it may therefore seem presumptuous of me to choose it for further comment. I can but plead in extenuation the very great practical importance of the subject—so great as to make it one upon which we can hardly confer too freely or too often. The only other prefatory remark I would make is a disclaimer of any ambitious design, or plea for originality, as regards the paper itself. Its purpose, so far as I am concerned, will be amply fulfilled should it succeed in eliciting a useful discussion.