Custom ordains that the incoming President shall open his term of office with an Address. This, it is surprising to discover, has not always been our practice. In fact, the first specific Presidential Address was not delivered until 1880 when Bailey initiated a series of Addresses unbroken since that date. Both you and the President are, however, more fortunate than our predecessors for, between 1880 and 1890, the President was expected—or, it may be, permitted—to deliver an allocution at the beginning of each Session falling within his term of office. Thus, Sprague, the last President who held office for more than the now conventional period of two years—subject always, of course, to re-election—holds the record of having delivered no fewer than four Addresses, all exhibiting, in matters actuarial and managerial, his redoubtable sagacity and authority.

As an organization increases in size, so must its management increasingly depend on statistical measurement of performance and statistical presentation of fact. The nature and range of the statistics will be governed largely by the functions of the organization concerned but, if the staff is of more than modest size, personnel statistics will certainly be among them.

Little space in the Journal has been devoted in the past specifically to graduation tests, and nowhere have the tests generally applied been concisely set out and fully discussed. The only papers during the last forty years on the subject have been by Seal and Daw; both these papers were submitted and discussed during the war years, with the result that many actuaries were unable to be present and state their views; indeed, many of us did not even know of them until the numbers of the Journal in question were published, and an opportunity to study them did not arise until after the war.

After the publication of the volume of statistics of the data derived from the Continuous Mortality Investigation 1924–29, experiments were made by the author in fitting the curves developed by Perks in 1931 (J.I.A. LXIII, 12) to various sections of the data. The experiments were later extended to include the data for the Light and Heavy tables and the experience for the period 1924–38. Although these experiments are now mainly of historical interest they represent useful material for research in testing and otherwise and, together with the results of some other published and unpublished graduations, they form the background of this paper.

The question of the effect of duplicate policies on the variance of the number of deaths in a mortality experience based on policies (not lives) has been discussed in two recent papers (Seal [1947] and Beard and Perks [1949]). The second of these papers shows that this variance depends on the sampling process envisaged and gives formulae for the variance under four such processes. It is the purpose of this paper to consider some practical aspects of the treatment of duplicates in a mortality experience.