Some years ago I read before the Institute a paper bearing on this subject (see Journal, vol. xi., p. 90) in which I examined at considerable length the method of valuation which has been on various occasions so strongly advocated by Mr. Tucker, and which is denominated by him the “reinsurance method.” This term, however, appeared to me unsuitable, and I termed the method the “hypothetical method” of valuation; because the sums assured and the premiums are valued by means of a hypothetical table of the values of reversions and annuities, deduced by an inverse process from the premiums actually charged by the office. In that paper I compared Mr. Tucker's method with the net-premium method of valuation, and gave my reasons for believing the latter to be not only greatly superior to the former, but the method that should be generally employed. Subsequent consideration has however satisfied me that the net-premium method of valuation is also open to very serious objections, and that it is not applicable in all cases; and I propose on the present occasion, first to point out some of these objections, and then to consider briefly what method of valuation should be followed when the net-premium method is inapplicable. The subject however is a very wide one; and the present paper must be considered rather as a contribution to the discussion of a question that is all-important to those who have the responsibility of advising as to the liabilities of Life Insurance Companies, than as claiming to be itself a complete essay on the subject.