The question which it is proposed to consider in the present paper is the correct mode of valuation of current policies, or true measure of proof to which claimants thereon are entitled in the liquidation of a Life Office. The subject is of especial interest at the present time, because its solution is even now waiting settlement by the Court of Chancery; and the interest is heightened by the fact, that conflicting judgments have been delivered by two eminent equity Judges, namely, by Lord Justice James, in Bell's case, when sitting as Vice-Chancellor in the Court of Chancery, and by Lord Cairns, in Lancaster's case, when sitting as Arbitrator in the Albert Arbitration. It does not appear that among actuaries there is a complete agreement. Nevertheless, the case ought not to present any great difficulty, and whether among actuaries or in a Court of Equity must be decided by argument alone. It is therefore proposed to consider the question, in the first instance, upon principle; and secondly, with reference to the doctrines laid down in the cases to which we have referred.

The desirableness of obtaining trustworthy statistics as to the mortality prevailing in Infancy and Childhood has been frequently insisted upon by Actuaries; no apology therefore is needed for placing before the Members of the Institute the results of some original investigations into the subject. Whilst regretting that the materials at my disposal are not very extensive, I trust that this contribution to the subject of Vital Statistics will, nevertheless, be found to possess some degree of value and interest.

Statistics, generally considered, is a term of very comprehensive import, and is to be understood as having reference to an important collection of facts properly arranged and systematized in the form of numerical tables, for the purpose of conveying such information or data as may best assist in the investigation and discussion of particular subjects of inquiry. The general principles applicable to these investigations are, for the most part, intimately allied with the mathematical theory of probabilities, and constitute the true science of statistics. It will, moreover, be found, on examination, that the same identical principles lie at the foundation of all the physical and inductive sciences so far as they originally and necessarily depend upon experiment and observation.

If a classification be made of any considerable number of life policies according to age at issue, a cursory inspection will show that the numbers at the different ages are not fortuitous, but are subject to some unknown, though plainly marked, mathematical relation; and the amenity of the results to law will be more evident as the number of policies employed in the classification is larger, and the effect of merely accidental fluctuations is consequently more nearly eliminated.