Most writers on the subject of life annuities have had occasion to lament the paucity of tables available for the performance of calculations involving two or more lives. The late Mr. David Jones has done much to supply this deficiency by the publication of complete sets of tables for two lives at various rates of interest; but, beyond this, it is extremely improbable that, under the present system, any considerable progress will be made, owing to the multiplicity of the different combinations when three or more lives are concerned, and the consequent magnitude of the task involved in the construction of complete sets of tables for such cases.

Some three or four years ago, I submitted to the members of the Institute a few observations on the valuation of property held for life and in reversion, and on the due apportionment of it when questions arise between the life tenant and the owner of the fee. I was induced to bring this subject under the notice of the members from observing the great difference of opinion prevailing in regard to it generally, and especially in the discussions on the subject of church leases and of other property similarly circumstanced—in which discussions no sort of agreement appears to have been come to as to the true principles upon which the value of the interests of the several parties concerned should be estimated. In the paper in question, I endeavoured to point out some of these principles; and my object now is to enlarge somewhat on the arguments therein laid down, to show that the question at issue almost always resolves itself into one whether a property is to be bought or sold, to call attention to the vast difference in value which arises under the two conditions, and to point out the imperative character of the causes, from which this difference originates; finally, to urge the necessity of great care and circumspection in dealing with the questions submitted to us, so that all risk of confounding one of the conditions above referred to with the other may be avoided.

The following problem was suggested by certain remarks in Mr. Buckle's introductory chapter to his History of Civilisation. In that chapter Mr. Buckle remarks upon the striking uniformity usually exhibited by classes of phenomena—such as not only births, deaths, marriages, but such things as those apparently depending upon mere caprice—such as the number of letters annually sent without directions through the Post-office, or those which appear likely to depend on the most capricious and irregular causes, such as murders and suicides; and he proceeds to draw certain moral conclusions from the fact of this uniformity, namely, the existence of certain moral laws, by which a section of the community, definite in number, is always impelled to such acts. But before entering upon a discussion of the legitimacy of such results, there appears to me always a previous question to be solved, namely, whether the observed degree of uniformity is remarkable or not. For supposing the observed uniformity to be not more than that which might be expected from events, the occurrence of which to individuals was conceived of as perfectly fortuitous, the whole argument would resolve itself into a pure metaphysical question, from which it would be hopeless to expect any practical issue.

An allusion made by Mr. Jellicoe to this subject, in a paper read before the Institute of Actuaries on the 28th November, has induced me to place on record the conclusions at which I had arrived after a somewhat recent consideration of the question.

It appears to me that the buyer of a policy by way of investment, in considering the price at which he should purchase, should come to his decision entirely independent of what might be the Office value. The two values have no connexion whatever one with another. In the one case the purchaser is about to make an investment; in the other, the Office proposes to redeem a liability.

Having thus glanced at different occupations as elements in the medical estimate of life, it may not be out of place to introduce the following table by M. Lombard, exhibiting trades in relation to consumption. In 1,000 deaths in each of the different occupations noticed, the following proportions were furnished by this disease:—