In the paper which I submitted to the Institute on 28 April 1944 I discussed the most equitable method of treating appreciation or depreciation in the assets of an office distributing its surplus by means of a uniform reversionary bonus. I believe that the conclusions reached were correct within the limits set, but consideration of the discussion convinced me that these limits were too narrow, since they involved the treatment of the problem of appreciation or depreciation without reference to the other factors affecting equity in bonus distribution and excluded any solution based on the use of a system of distribution of profits other than a uniform reversionary bonus. I felt that the methods used in the paper might produce results of interest if applied to the general problem of securing equity when the conditions experienced differ from those assumed in calculating the premiums, and I was encouraged to proceed on these lines by the suggestion made by Mr H. E. Melville, speaking as Presidenti that the time was suitable for such an inquiry in view of the exceptionally wide fluctuations in the experience rates of interest over the past thirty years.