The improvement in vitality is a subject of interest alike to the actuary and to the public statistician. It formed one of the topics for discussion at the Fourth International Congress of Actuaries held in New York in 1903, and papers were submitted by actuaries of different countries dealing with the subject mainly from the point of view of population statistics. The results of most direct interest to us were embodied in a paper by Mr. S. G. Warner On the Improvement in Longevity in the Nineteenth Century. They were based on the summarised returns of the Registrar-General's Reports for England and Wales for the years 1875 and 1900; and, while admitting the defects inherent in the data, Mr. Warner held that the statistics showed “a distinct decrease in the rate of “mortality as the century progresses; a decrease, on the whole, “so steady and symmetrical that it might fairly be looked on as a “settled and permanent tendency.