The following pages have been written with a view to complying, in some measure, with a request that an early account of the Fourth International Congress of Actuaries should be prepared for the information of those connected with the Faculty of Actuaries who had not an opportunity of attending the meetings and of becoming acquainted with the proceedings. The exceptional length of the programme of the Congress, and the limitations of this occasion, conspired to render impracticable any attempt to present epitomes of more than a comparatively small number of the papers and discussions. It is, perhaps, unnecessary to say that no fragmentary and unannotated compilation, such as this perforce is, can take the place or claim the authority of the full revised official reports, which have yet to be issued.

The growth and development of life assurance has formed the subject of many papers read by Presidents and other distinguished members of the Faculty and of the Institute of Actuaries, who have traced in their writings its progress from very feeble beginnings to the position of importance it now occupies in the public mind, and have shown how a great system based upon large experience has evolved by degrees from the arbitrary methods of earlier days. The life assurance funds of the companies having their head offices in Great Britain and Ireland, according to the returns published by the Board of Trade last year, now exceed £255,000,000, their annual premium income £22,400,000, and the sums assured on their books £660,000,000—figures which demonstrate in a practical and conclusive way the immense confidence with which these institutions are regarded, especially when it is remembered that the contracts, the fulfilment of which is relied upon, are in most cases either lifelong or maturing only after many years. Even prior to the passing of the Life Assurance Companies Act, 1870, the hold that the companies had obtained upon public esteem was by no means insignificant, as life assurance funds of £87,000,000 and a premium income of over £9,000,000 testify; but without the publicity which the returns prescribed by the Act have secured, it would have been much more difficult, if not altogether impossible, to put forward the appeal to have the contracts of life offices admitted as trustee investments which it is the object of this paper to initiate. The advantages that have accrued from the Act are, I believe, recognised by all insurance men, and there is no occasion to enlarge upon them here, beyond the simple statement that the security afforded by the contract of an insurance company has been greatly enhanced thereby, and that the means of discrimination essential for the present purpose have been adequately supplied through its provisions.

Within quite recent years many schemes of life assurance without medical examination have been brought before the public by different offices, and have on the whole been very well received. No apology, therefore, seems necessary in submitting this paper to a meeting of the Faculty of Actuaries, more especially as, so far as we are aware, the matter has not previously been dealt with by any one.

It would be a mistake to look upon our subject merely as one out of many innovations in assurance practice of late years. As every one knows, it belongs to the earliest times of life assurance, though it is only during the last few years that it has again been introduced into the sphere of practical business. While that is so, it must be admitted that the circumstances and conditions under which it existed formerly are very, or even altogether, different from those which have seemed to warrant or necessitate its resuscitation at the present day. To make this as clear as possible, it may be well, in the first place, to trace shortly, as far as it can be done, the origin and history of the medical examination of proposers for life assurance.

As many of you are aware, I received my early training in this city. Well do I remember the meetings of the Actuarial Society and the growing interest I took in its proceedings; but in which on account of my inexperience I was seldom able to take part. After an absence of nearly twenty years in Australia, where I read with interest and undoubtedly profited by the papers published by the Society from time to time, it seemed fitting, when I had the honour to be asked to contribute to your proceedings on my return to this country, that I should choose a subject distinctively Australian, in the hope that my fellow-members might in return profit in some degree by my experience on the other side of the world. The fact that several Scottish offices had lent large sums on mortgage in Australia led me to choose “Investments” as my subject. The addresses of Mr. A. H. Turnbull, Mr. David Paulin, and others, to the Actuarial Society and elsewhere, render it unnecessary for me to enlarge upon the principles and practices of British life offices in this respect, although I propose to make use of figures previously submitted, for purposes of comparison.

It is generally admitted that select tables should be used for the calculation of office premiums, the tendency of aggregate tables being to underestimate the risk for the younger and to overestimate it for the older ages, so that, in the case of survivorship benefits, where the risk is that of a young life predeceasing an old one, a double error is introduced. In one of the earliest papers read before the Faculty (T. F. A., i, 49), Mr. A. E. Sprague considered the applicability of select tables to the calculation of continuous benefits; but it seems that the ordinary method of approximation, if applied without modification, may lead to an error of some importance. Most of the well-known quadrature formulas can be obtained by direct integration from Everett's Interpolation Theorem, which assumes that the law is continuous throughout; but it is well known that the rate of mortality changes very quickly during the few years following selection, and that it in fact follows a different law from that which prevails later on. The H[M] table is not a very good one by which to test this method of approximation, for the graduation of the HM(5) portion is not very smooth; and, as the method depends on selected values of the function, any irregularities of the table will be reflected in the final result, and it is not possible to say to what extent an error is due to this cause.

In a paper read before the Actuarial Society of Edinburgh more than thirty years ago, the late Mr. D. Deuchar discussed the question of expenses and its relation to new business, and advocated the subdivision between new and renewal premiums of the items Premiums received, Expenses, and Commission in the revenue account. From a table compiled by him, relating to fifteen Scottish offices, it appeared that commission and expenses amounted to 13¼ per cent of the premium income; or that, if 7¼ per cent be allowed for renewal expenses, initial expenditure absorbed about 80 per cent of the (estimated) new premiums. The question subsequently received much attention from Dr. Sprague, who stated (J. I. A., xix, 313) that about 7½ per cent of renewal premiums was “generally amply sufficient for the purpose of administering the existing business of a company that pays commission and employs agencies; and that any expenditure beyond this must be considered as incurred exclusively on account of the new business”; while more recently (Transactions of the First International Congress of Actuaries, p. 190) he has expressed the opinion that “the average expenditure of prosperous and well-managed offices may be taken as 80 per cent of the new premiums and 7½ per cent of the renewal premiums”.

In submitting a revised edition of the paper which I read before the Actuarial Society of Edinburgh more than six years ago, I wish to express the pleasure I feel that this, my first effort, should not only have proved of benefit to students, but that the Faculty of Actuaries consider it worthy of a place in their Transactions. The subject was taken up originally to condense the best actuarial opinions and bring together some of those practical questions which had been dealt with by actuaries of ripe experience. Premiums can be profitably discussed at almost any time, because an exchange of views is sure to shed light on some obscure point of more or less importance. The present time is peculiarly opportune for further discussion, because of the recent publication of the New Mortality Experience, and the knowledge of such statistics which we have all been gradually absorbing.

It has become important for members of our profession to know something of the English Land Registration system. Our future practice in dealing with mortgages may be materially affected by it; moreover, the question of its extension has reached a stage at which nearly every one, in England at least, is called upon to consider and form an opinion as to its merits. Here, too, the public has some practical interest in the question. It is quite probable there may be a demand for the extension of the system to this part of the kingdom; in fact, I am told that a deputation from Glasgow has already inspected the London Registry with this idea in view. In the following remarks, therefore, I shall try to bring together the chief features of registration of title to land according to the English system, and explain the circumstances under which it is being worked at the present time. The treatment of such a subject is not without difficulties. It necessarily involves a number of intricate legal points, and without a thorough knowledge and experience of English land laws, one is not in the position to follow it in all its bearings. But although I cannot attempt to deal with all the legal questions that arise, I think there may even be some advantage in a paper by one who is not a lawyer. There cannot be the same charge of bias; and it is possible that the points more particularly affecting such a profession as ours, may be more prominently brought out by one of its own members.

The Liabilities of a Widows' Fund in respect of Annuities to Widows of members may, for the purpose of actuarial valuation, be divided into two classes:—First, the liability relating to annuities which are actually payable to the widows of former members; and Second, that for annuities which may become payable on the deaths of existing members.

The chief object for which insurance offices exist is to pay claims; but before any claim can be paid, the question arises—who is the proper person to receive the payment ? If any mistake be made in this, the office may find itself involved in troublesome and expensive legal proceedings, and be compelled to pay the claim twice over. This consideration shows the necessity of insurance officials having some knowledge of law, as it is almost impracticable for them to refer every legal question to their solicitors; and my present object is to draw attention to some of the elementary points which arise in the ordinary course of our business. On the shelves of the library there are to be found papers by Mr. Barrand, Mr. Warren Crosbie, and Mr. Hayter, which should be studied carefully (in addition to the text books) by every one desirous of qualifying himself for a position of responsibility in the claims or law department of his office; but these papers do not exhaust the subject, and I do not propose to allude to the points discussed therein, except in the cases where some further explanation seems desirable or where there has been an alteration in the law or in the practice of the offices.

Public Debts, whether national or local, belong to modern history. Our National Debt dates from the Revolution of 1688. It is five years after that event until we find the item “Interest and Management of the Public Debt” figuring in the accounts of the Exchequer. At William's death in 1702 the debt was twelve millions, an amount which was increased threefold during the twelve years of the reign of Anne. George the First's thirteen years raised our national obligations to fifty-two millions, while by 1760, when George the Second died, they exceeded one hundred millions. During the long reign of George the Third the burden swelled enormously. The rise was just a geometrical progression, from twelve to a hundred millions in fifty-eight years, and from one to nine hundred millions in the sixty years succeeding. The explanation, of course, is war. We spent a hundred millions in a vain attempt to compel the allegiance of the United States, and more than eight hundred millions in avenging Louis XVI., overthrowing Napoleon, and restoring the Bourbons to the throne of France.