Not much seems to have been written on the subject of the Mortality of the West Indies as compared with that of the mother country. The following contribution, being the experience of the Scottish Amicable Life Assurance Society in these colonies during the last thirty years, may therefore, perhaps, be useful as well as interesting. The Directors of the Society have cordially adopted the suggestion that the figures should now be made public.

Perhaps the most important lesson many of you can learn—one that is frequently lost sight of by persons who are solely or mainly engaged in theoretical studies—is that the researches which you are pursuing, by the aid of a variety of complicated symbols, are, after all, not merely elaborate mathematical puzzles to be solved principally for the purpose of awakening or sharpening the intellect, but have, for you at least, an eminently practical aim as well, and are insisted on as part of the education of an Actuary, with a view to their serving as the framework on which, when afterwards called upon, he must be prepared to base actual business transactions involving large sums of money, or, it may be, to lay down principles for the regulation in all its various details of a life assurance office.

Although much has been written in recent years on the comparative merits of different methods of valuation, I am not aware that any attempt has yet been made to ascertain the ultimate bearing on the Pure Premium Method, of the facts that have been recently brought forward as to the pressure of the expenses and the effects of selection in an assurance company. Speaking generally, it will, I think, be found that proposals to diminish the pure premium reserve on account of the necessarily heavy expenses of new business, have been made without reference to the mortality profit that may be expected to arise from the recent selection of the lives, and vice versa. This being the case, it occurred to me that it might be of considerable practical interest to make an investigation in which effect would be given to the influence both of expenses and of selection, for it would enable us to estimate how far the one neutralized the other. In order to render the inquiry more clear, however, it will be well to begin by considering each separately.

Mr. Artemas Martin has solicited my opinion in regard to the following problem, the true solutions of which have, he informs me, been much discussed in America. I give, first of all, Mr. Martin's solution, and append thereto my own remarks in regard to the accuracy, or otherwise, of the solution.