The question of the reserve which a life assurance society should hold, in order to meet the claims under the policies issued by it as they mature, is one of such vital importance that I am led to hope that, notwithstanding the many and valuable papers on the subject which have from time to time appeared in the Journal of the Institute of Actuaries, the following reflections may not be without interest, even though they may not throw much fresh light on the subject. I may premise by stating that the conclusions arrived at, and hereafter referred to, are the result of an investigation undertaken as a matter of curiosity, and carried on in the midst of laborious and urgent official duty; consequently the scheme propounded may appear somewhat crude and ill-defined, and doubtless lacks the completeness which a more mature consideration of the point taken up would possibly have developed. Further, the results given here were arrived at before Mr. Sprague's paper “On the Construction of Select Mortality Tables” (Journal of the Institute, vol. xxi, p. 229) appeared in print; otherwise I should probably not have undertaken the investigation.

What I have aimed at is the discovery of some method of arriving at the requisite reserves for new policies, which shall be somewhat further removed from the realm of pure theory than some others which have been suggested; a method which can be readily applied in practice; and, what is of more importance, one which can be made intelligible to the ordinary man of business.