The report on the mortality experience of life annuitants during the period 1900-1920 published in 1923 by the Institute of Actuaries and the Faculty of Actuaries, and the report issued in the present year on the “Mortality experience of Government life annuitants, 1900-1920”, have brought into prominence the necessity of considering in our calculations the probability of future improvements in vitality. The special intention of the present notes is to examine the methods by which this subject has been treated in the two reports, which will be referred to as the 1923 report and the 1924 report. It will be convenient to consider the subject specially in relation to female lives, and more particularly in relation to the ultimate mortality after 5 years of such lives.