In pursuing the traditional practice of introducing myself officially by an Inaugural Address, I desire unaffectedly to state that any conventionality, which this course may have acquired from custom, is merged and lost in a deep feeling of grateful recognition of your generous confidence and goodwill.

In adventuring upon a Second Presidential Address, the energy of hope and freshness which stimulated me in the former effort have vanished into trepidation of feeling. For I am unhappily conscious that I then exhausted any meagre resources I possessed of novel presentation of thought and research, and was reduced to virtual bankruptcy of serviceable suggestiveness which the interval of time has failed to annul.

The subject I have chosen for my paper may seem to call for some apology, on the ground that it is more suitable for discussion at a legal institute than by a body of Actuaries. There would doubtless be some force in such a criticism, and yet I venture to think that in many respects the subject is not an unsuitable one to be brought before this Institute. The time has gone by, if indeed it ever existed, when the ordinary legal incidents arising in connection with life assurance business were submitted to the company's solicitors for advice and direction. In a large life assurance institution it would be impossible, in practice, to submit every question as to title, in the case of claims and surrenders, to a solicitor, on account of the expense and delay thereby occasioned, if for no other reasons, and at least as great practical difficulties would arise if, in order to get over the difficulty of the expense of such a reference, it were sought to saddle the applicant with such legal expenses as might be incurred. Questions of title, unless they be of a peculiarly complicated nature, are therefore usually settled by an official of the company, and since amongst the officials the Actuary will, as a rule, stand almost alone as having, of necessity, some legal knowledge, the ultimate decision on such points will, in most cases, devolve upon him.

The favour with which the convening of the present Congress has been received by actuaries of all nations, and the very questions submitted to it by the members, fully show that everywhere the same desire has sprung up, namely that actuaries should know each other personally, so that later on there may be more effective inter-communication of ideas by the interchange of the writings which are periodically published. The question of language is a great obstacle, which it is in our interest to reduce to a minimum. A foreign tongue becomes easier to us, when the technical symbols employed, assuming a form which is familiar to us, indicate the drift of the paragraph. On the other hand, when the same symbol represents, according to the author using it, diametrically opposite ideas, the passage is made more difficult to understand, and the formulas, instead of being an index to its meaning, become a source of error.

The subject of lost policies is one that is constantly coming before Life Insurance Companies in different ways, and it is one regarding which it seems very desirable that they should all act on the same principles. At present, however, I believe there is a good deal of diversity of practice; and I think it may therefore be useful if I submit to my professional brethren the conclusions to which I have been led by my business experience and careful consideration of the various points involved.

As the published facts concerning the rate of mortality in tropical Africa are very scanty, and Insurance Offices are therefore often compelled to fix the extra premiums for African risks in an almost purely arbitrary manner, I venture to lay the following investigation before the members of the Institute as a contribution to our knowledge of the subject. So far as I am aware, the only publications dealing with the subject are a note by my father, Dr. T. B. Sprague, on the Rate of Mortality on the Congo (J.I.A. xxv, 437); a note read by myself before the Actuarial Society of Edinburgh on the Rate of Mortality in Sierra Leone (Transactions, iii, 365); a paper by Mr. J. R. Hart on the Mortality on the West Coast of Africa, which appeared in the Insurance Record of 2 October 1896; and a paper by Dr. T. Glover Lyon on the Mortality amongst Europeans in certain Unhealthy Districts (J.I.A., xxix, 541).

The publication of the tables of mortality based upon the experience, collected by the Committee representing the four principal insurance companies of France, puts us in possession of an extensive and valuable body of statistics bearing upon the mortality of assured lives and annuitants in that country, and at the same time places the Actuarial profession under a considerable obligation to the Committee of French Actuaries to whom we are indebted for the collection and publication of the data and the resulting monetary tables. As in this country, the life assurance companies on the Continent had for a long time, necessarily, to depend upon statistics of mortality based upon observations of the population generally, which, whatever the skill with which they were prepared, were not only affected by the uncertainty attaching to all such statistics, but were not in any case specially suited to represent the probable mortality, either of assured lives or annuitants. The earliest of these tables, to which any value could be attached, are those of Deparcieux and Duvillard, corresponding in point of date, approximately, to the Northampton and Carlisle Tables in England, and it was not until 1860 that the three companies, the Compagnie d'Assurances Generales, Union, and Nationale, published their annuity experience, nor until 1874 that the first of these companies published a table representing the mortality experience of their assurants.

This subject may be conveniently considered under two headings; (1) as to the actual or assumed age at entry (2) as to the distribution of entrants and emergents over the year of duration current at entry and exit.

A few statistics relating to this subject recently came into my hands, and although the results obtained from them cannot be considered to be of great weight, a short communication may be of interest. In the hope that useful information might be forthcoming, I made enquiry as to whether any record is kept of the dates of departure, death, or retirement of persons who go out in the employment of African merchants to the West Coast; and ascertained that it was unlikely that data could be supplied from that source. But I thought it worth while to make similar enquiry at the Colonial Office; and although the West African department could not officially furnish me with information, as they had none here of which they could vouch for the accuracy, I obtained, through the courtesy of one of the officials, the particulars given below. These were contained in a list of all the Europeans employed by the Governments of the four West African Colonies—the Gambia, Sierra Leone, the Gold Coast, and Lagos—during the ten years, 1 January 1881 to 31 December 1890, showing when their service began, and, if ended before 31 December 1890, when and why it ended.

In applying the method of Least Squares a peculiar difficulty is often experienced whenever the function, of which we have a series of observed values, is not linear with respect to the unknown constants to be determined and is therefore either of a higher algebraic order or is transcendental.

The question of the rate of mortality experienced by residents on the West Coast of Africa, has recently attracted considerable attention among actuaries. And indeed it is one of increasing importance. Partly owing to the growth of the Liverpool trade with the West Coast, partly owing to the spread of European ideas (including that of life assurance) among the natives, the number of proposals to life offices from residents in Africa is each year becoming greater. It is most desirable, therefore, that some attempt should be made as soon as possible to measure the extra risk of residence on the West Coast, and it is with the object of assisting such an attempt that the present note is offered to the readers of the Journal

In the various references in the Journal to the subject of the approximate evaluation of compound survivorship annuities and assurances, the possibility of using Mr. Emory McClintock's expression for the continuous annuity (J.I.A. xviii, 242) does not appear to have been noticed. By substituting Mr. McClintock's expression for the annuity under the integral sign, and integrating by parts, many compound survivorship benefits can be expressed more or less approximately in terms of simple survivorship benefits; but it may be admitted that the labour necessary to obtain a result as accurate as that obtainable by a summation formula would not in general recommend the method. There is, however, one case—that of the compound survivorship annuity involving three lives—in which the special interest that has always been taken in the function may be considered a sufficient apology for a result which is both complicated and limited in its range of practical applicability; that case it is proposed to investigate in this note.

The Institute of Actuaries and the Faculty of Actuaries are at present jointly engaged on an investigation into the mortality experience of Life Assurance Companies, which will include an examination of the rates prevailing amongst Annuity Nominees. Nevertheless it is thought that any other investigation throwing light on this important subject may not be without interest.

I should be most obliged if you would be kind enough, to give me your opinion on the following point.

You know the Austrian Scheme for compensation for accidents of Labour and the allowances it provides, particularly in case of death of the Workman.