The present paper is essentially elementary, and must therefore in a great measure be considered as addressed to the junior members of the Institute, although, perhaps, even to those more experienced persons to whom in the course of years these things have become familiar, a recapitulation, such as I now propose, may not be wholly uninstructive.

Problem V.—To construct a complete table of the Values of Temporary Annuities; that is, a table which shall comprise all ages and all durations.

This benefit, being a function of the ages at commencement and cessation, say x and w (to the former of which ages also its value is referred), it will be here for convenience denoted, in accordance with the usual functional notation, by ϕ(x, w); and its duration, consequently, will be w–x=n

The manner in which current policies should be valued for proof upon the insolvency of a Life Office has been much discussed in our pages, and under cover of the conflicting decisions in Bell's and Lancaster's cases has given rise to much diversity of opinion. The interest of the question can scarcely be said to be exhausted. We are, therefore, glad to be able to present to our readers an elaborate judgment on the subject delivered by Lord Romilly, the late Master of the Rolls, which is not only interesting from the eminence of its author, but important as carrying the weight of a judicial decision. It will be best apprehended by perusal, and we will therefore only state that it unhesitatingly decides in accordance with the rule laid down by Lord Justice James in Bell's case, and against that of Lord Cairns in Lancaster's case. In order, however, to bring the whole matter down to the present time, we must remind our readers that it has been dealt with in the Life Assurance Companies Amendment Act, 1872, and again by the determination of Lord Westbury in the European Arbitration.

In 1793 the first Act “for the encouragement of Friendly Societies” was passed, and its preamble gave as the reason for passing it, that the encouragement of such societies was likely to be attended with very beneficial results, “by promoting the happiness of individuals, and at the same time diminishing the public burdens”. The encouragement given by the State consisted of exemptions from fees and stamps, facilities in recovering debts and settling disputes, and exemption of members from removal under the Poor Law until they became actually chargeable to the parish. The next Act of any consequence was that of 1819. Another Act had become needed. Since the passing of the former Act the population had increast from 9,000,000 to 11,500,000, but the amount annually expended in poor-law relief had risen to more than £7,500,000—within half a million of the amount annually expended now with nearly a doubled population. In other words, while since 1750 the population had increast by one half, the amount of poor-law relief had increast tenfold, or twenty times as fast as population.

A correct knowledge of the rate of mortality among mankind is of such importance for answering many interesting questions, that we might hav expected it would hav been diligently studied from the earliest times. This, however, appears not to hav been the case, the reason probably being that questions as to the expectation of life arise in the first instance with reference to particular persons, and not to men in general. The proverbial uncertainty of human life—so often seen in the occurrence of death when least expected—is unfavourable to the notion of a general law of mortality, but naturally suggests the search after a means of predicting the duration of individual life. As thus understood, the question of the duration of life has at all times attracted great attention. Soothsayers and magicians claimd to hav the power of discerning from signs and omens of many kinds every event of life, its termination not excepted, and astrologers pretended to read in the stars the precise hour of each man's death.