This subject, as it left the hands of Simpson, Halley, Dodson, &c., is fully discussed in the appendices of Francis Baily's work on interest and annuities. These, with Milne's note on the subject (vol. ii., p. 680), Jones's notice of the problem, and the various modes of approximation announced in the pages of this Journal, give all I have found written about the matter in modern times. Referring to the citations in Baily for the history of the question subsequent to 1680, I give what I have found in previous time; and I add a few new formulæ for consideration. The problem is, I doubt not, of infrequent occurrence. It never occurred to myself to want more than a look at the tables would furnish; but it may be suspected that, as the requirements of business become closer, inverse problems will acquire more importance than they now possess.

The steady and gradual diminution in the rate of interest that took place from towards the end of the sixteenth to the middle of the eighteenth century, was generally attributed, during the period, to the great additions made, after the discovery of America, to the amount of gold and silver circulating in Europe.

The extent to which the interchange of risks is made by Assurance Companies at the present day, renders it of no small importance that a clear understanding should exist as to the terms upon which these contracts are to be carried out. There was a time, we believe, when a proposition from one Company to effect an assurance with another was looked upon with coldness, if not with suspicion; and the fact that such proposals were often made when the proposing Office declined to assume any portion of the risk itself, would seem, very naturally, to give rise to such a sentiment. This practice, however, we believe, is now quite on the decline; and with well-conducted Companies it is pretty clearly understood that these transactions must be in every respect perfectly bonâ fide, and that the arrangement of them must be entirely just and equal, as between all the parties concerned. As the wealth of the country increases, the cases are becoming more frequent in which the sums to be assured upon individual lives are larger than any single Company would care to sustain the liability of; and as propositions of this nature are being at intervals made to all, each becomes sensible of the advantages of the system of reassurance, and of the necessity of its being based upon principles of perfect fairness and equality.

The remarkable change which has taken place within the last two or three years in the position and circumstances of these institutions has very much tended to allay the desire, so generally expressed formerly, for legislative interference, with a view to their better regulation. The impression, by which so many well-informed persons seemed to be actuated, that they might be multiplied with advantage almost indefinitely, appears now to have become thoroughly eradicated; and in its place a conviction seems to have arisen that the country cannot support a very large number of these Companies, and that the sooner the existing ones even are reduced in number the better. Be this as it may, we cannot but regard the rational and moderate ideas now prevailing on this subject as a vast improvement on the extravagant notions heretofore generally entertained with regard to it; and, if reliance could be placed on the continuance of this better disposition, we think our readers will agree that the necessity for legislative interference has, in a great measure, passed away, and that the Assurance Companies might now be left to pursue their course guided by their own discretion and untrammelled by further restrictions.