A great deal has been written about Endowment Assurances, which now form so large a proportion of the new business of life assurance offices, but their effect upon the business has been only partially investigated, and much yet remains to be done. It is generally admitted that the mortality in this class is better than that prevailing in other classes, and recently Mr. R. P. Hardy brought before the Congress of Actuaries in New York an interesting paper, in which he stated that “while probably the results would vary in their incidence according to the tables brought into contrast, it appears to me that one effect of a better mortality is to show a gradually reduced surplus. And if this be the case, some care is necessary in relying upon future profits according to their past experience.” He appended a table showing the quinquennial surplus or deficiency arising when the premiums are charged, and the reserves made, according to the American table as adjusted by Mr. Arthur Hunter, while the mortality experienced is that of the OM table; and the results show that, for endowment assurances of 15, 20 and 25 years, the surplus at each quinquennium, as a rule, diminishes very rapidly. It should be noted that these calculations were made at 3 per cent interest throughout.

The Faculty of Actuaries in Scotland celebrated the Jubilee of its foundation by a Dinner on Friday, 19th January 1906, in the North British Station Hotel, Edinburgh, at which one hundred gentlemen were present. Mr. Niel B. Gunn, Manager of the Scottish Widows' Fund, President of the Faculty, occupied the Ghair. He was supported on the right by The Right Hon. Sir J. H. A. Macdonald, Lord Justice-Clerk of Scotland; Mr. Henry Cockburn, President of the Institute of Actuaries; Mr. William Campbell, K.C., Dean of the Faculty of Advocates; and Mr. C. D. Higham, Chairman of the Life Offices Association; and on the left by The Hon. Lord Ardwall; Mr. R. P. Hardy; Sir George Anderson, Treasurer of the Bank of Scotland; and the Very Rev Dr. Gray. The Croupiers were Messrs. George M. Low, Archibald Hewat, J. J. M'Lauchlan, and W. G. Walton.

One element underlying the whole theory of Life Contingencies is that of a Series. Thus in the Life Table we have a collection of the more usual and elementary functions, every column forming a series, and it will at once suggest itself that as soon as the actual calculation of any problem is faced, we must sooner or later arrive at a Series, and the solution of the problem will finally depend on our ability to deal with this Series. The same is obviously true of other branches of our Science, such as those derived from statistics of Sickness, of Marriage and of Issue, and, of course, in the purely algebraical theory of Compound Interest.

In 1893 Mr. William Harvey delivered to the Actuarial Society of Edinburgh a paper on “Misrepresentation and Concealment as affecting policies of Insurance,” and in the following year a series of “Lectures on Insurance Law.” I have no desire to trench upon the ground covered in these lectures, but what I now propose is to supplement them by putting before you, briefly, the results of the more important decisions relating to life assurance which have occurred in the English and Scottish Courts since these lectures were delivered. In dealing with the decisions I propose to follow the order of treatment adopted by Mr. Harvey, and I shall endeavour, also following him, to notice the American cases, and to indicate how far these are likely to be useful as authorities in our law. The subject of Trust and Settlement Policies has been separately dealt with by Mr. Constable in his paper on “The Married Women's Policies of Assurance (Scotland) Act, 1880”; but there are a number of decisions since that paper was delivered which also I think it right to bring under your notice.

When some time ago I was flattered with an invitation to read a paper before the Faculty of Actuaries, it was suggested that I should deal with the question of the amount to be deducted, in valuing reversions, for duties which, will be payable out of the funds, in reversion.

This is a somewhat difficult question to deal with directly, and I fear it will be thought that in the following pages the raison d'être of my paper has been forgotten. I may say, however, that while not overlooking the ostensible object in view, I have felt that the best way of giving effect to it is to write a short account of the various death duties which will have to be considered in making such valuations. The only alternative method of dealing with the subject which occurred to me, was to give a series of examples, but this would involve such a large number of instances to meet even a small fraction of the possible cases that may arise, in practice, that I had to abandon all idea of treating the subject in this way. I must fall back upon general principles and not rely on concrete instances, although examples of the general principles are given in a few cases.

The principles upon which surrender values should be calculated are discussed at length in papers by Mr. Macfadyen (J. I. A., xvii, 381); Mr. Crisford (J. I. A., xxi, 301); and Mr. Fulford (J. I. A., xxxv, 199), but none of the methods proposed appear entirely satisfactory in practice, and I have therefore attempted to devise a scheme which shall not only give results in reasonable accordance with strict theory, but also prove simple and easily worked in its practical application.

In response to the invitation of your President to prepare and submit a Paper to the Faculty during the present session, I thought that it would be appropriate, and I hope also of some interest to the Members, if I endeavoured to deal with a section of that important Investigation, recently completed, into the mortality of Assured Lives and Annuitants, in which the Faculty and the Institute so happily collaborated, to the great advantage of the actuarial profession.