The necessity for a reliable investigation into the mortality experienced by life tenants under reversions has long been felt.

So far as I am aware, the only published experience is that given by Mr. Neil Campbell in a paper read before the Faculty of Actuaries in 1902 (T.F.A., vol. i, p. 79), although doubtless individual offices have at various times examined the mortality in respect of their own purchases. The investigation by Mr. Campbell was of considerable service in indicating the trend of the mortality, but was unfortunately of limited value inasmuch as it was based upon only 226 lives producing 2,097 years of exposure to risk.

The history of life insurance presents some curious changes in the character of the factors which have from time to time taken precedence as matters of anxiety to those responsible for the successful conduct of the business. In the early days it was anticipated that it was the rate of mortality which would give the greatest possibility of variation, and which was most likely to undermine the foundation of the structure. In time, however, this bogey was laid by the heels. Then, in the final years of last century the fall in the rate of interest was a matter of great concern in view of the persistent fall which had occurred over a long period, the danger being that the rate earned on accumulated funds would fall below that necessary to maintain solvency.

ALL the methods of group valuation submitted to the Institute in the last decade require the calculation of the second sum of the quantities valued, whether in the form of multiplications by —4½, —3½, … 3½, 4½, i.e., the second sum about the centre, or the more convenient second sum about the end. The object of this paper is to show that the α, β method can be transformed so as to avoid this difficulty.