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).

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 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.

As the members of the Institute are doubtless aware, government in the United States differs in at least one important particular from that in Great Britain. In the former country all legislation must conform to the requirements of a written Constitution, and such conformity or non-conformity is decided in each case as it arises, without appeal, by a Supreme Court. In the latter country, on the contrary, the validity or otherwise of any Act of Parliament is decided by unwritten traditions and evolutions developed by the growth and experience of centuries. It is not my object or province to discuss the relative advantages and disadvantages of the two systems; I merely state the fact which must be clearly kept in view in order to understand the unique position of life insurance in the United States as regards governmental intervention.