The question whether the number of mixed lives at any age in the ultimate column of a select table can be subdivided into the number of lives still select and the number of damaged lives is a point of considerable interest in the practical use of mortality tables. And it was in connexion with a difference of opinion on this problem that the late Dr. Sprague made his last contribution to actuarial literature. Moreover, this was one of the few discussions in which he was apparently unable to carry conviction that his views were sound.

The scheme of National Health Insurance, apart from its general interest to the student of social questions, presents many technical features of special interest to the actuary, and it has been suggested that the completion of the first valuations of approved societies, i.e., the societies administering the monetary benefits of the system, affords an opportunity for discussion of the scientific problems to which these features give rise. With the Government Actuary's consent, I therefore submit in the following paper an examination of some of the more important points of actuarial interest which have emerged in the course of the valuation work. Before approaching the main theme of the paper, however, I have described briefly certain factors, such as the principal alterations made in the financial structure of the scheme by the Act of 1918, a knowledge of which is essential to an understanding of the later part of the paper. These preliminary remarks are placed in Part I, the main subject being dealt with in Part II.