1. A Short time back I transmitted to the Philosophical Society of Cambridge some remarks upon the construction of tables of annuities: my object in that paper was to show how the probabilities upon which annuities depend should be deduced from tables of mortality, and I gave in illustration some tables of annuities calculated from observations of the mortality at Chester, by Dr. Haygarth, which appear to have been made with very great care. I have since compared these tables with a great many others, and I now present the result of this comparison.

It is now somewhat more than twelve months ago that the decimal coinage question was brought under the notice of this Institute, and that a resolution was thereupon unanimously come to approving of the plan recommended by the Committee of the House of Commons. Since that decision, public attention has been repeatedly called to the subject; and although various plans have been proposed and discussed, founded on a different basis from the one thus recommended, it must, I think, be conceded, that none of them have made any serious impression on the public mind, but that, on the contrary, the one proposed by the Committee has made some if not considerable progress in the course of the sifting which the question generally has undergone.

Let us suppose France and the United States to enter into a convention with us to issue pieces of gold of the same weight and fineness as our sovereign—that is, containing 113 grains of fine gold; the three countries would then have a common standard of gold money. Let us examine whether, in the face of the operations of commerce, the international quality of value of these coins could at all times be maintained. The temporary balance of trade is always fluctuating in favour of one or the other country; a permanent balance against any country is impossible.

Among the indirect advantages to be derived by the public from the establishment of Life Assurance Companies, may be fairly cited that of fostering a system of elaborate calculation so closely allied to the fiscal requirements of the times, that, allowing for hyperbole, the nation's finance minister might in the present day be in some degree characterized as the nation's actuary. Whether the incidental possession of analogous qualifications to those expected in insurance managers will ever be indirectly exacted by the general community from its finance ministers, would perhaps be presumptuous in us as actuaries to further discuss; but certain it is that, apart from insurance and its ramifications, no other definite school has hitherto been presented in which financial questions, and especially those relating to contingent finance, have ever been so elaborately and usefully developed. The interest and annuity tables alone, of insurance writers, form indeed an addition to financial literature of considerable importance.

I have not found it easy to select a proper title for this paper; and I am very conscious of the difficulty of explaining my reasons for instituting the somewhat laborious experiments of which I am now to state the results. Perhaps, indeed, I ought to apologize for offering to the Institute of Actuaries a communication which some of its members, who are conversant with the leading treatises on the doctrine of probabilities, may know to have been anticipated and rendered unnecessary by the labours of men much better qualified than I can pretend to be, to do justice to so profound a subject. I have some reason, however, to believe that the experiments I am about to describe are new; inasmuch as, though I have consulted one or two works which are likely to have contained some reference to such experiments, had they been already made, and have questioned more than one eminent member of your Society upon the subject, I have not been able to learn that any such experiments are upon record.

The Gotha Life Assurance Bank was founded at a time when there existed scarcely any knowledge of life assurance in Germany. Some former attempts to found such a Company had failed for this reason, and the few life assurances which were sought at that time by Germans, especially in the Hanseatic towns, could only be effected with English Companies. An essential change has taken place in this respect since the year 1827, when, by the establishment of the Life Assurance Bank for Germany at Gotha, the desire for life assurance was awakened, and its signification and meaning were explained and advanced by numerous publications. Since that time life assurance has risen in Germany as in no other country, with the exception of England. Excepting England, no country so abounds as Germany in self-denying heads of families, who find an impulse upon their minds to provide for their families beyond their own dissolution, and who endeavour to satisfy this impulse even with slender means. Such a susceptible soil could not but prove fertile to such as understood how to cultivate it.