The subject of Annuities, in relation to the transactions of the Life Offices of this country, has seldom received definite consideration at the meetings of our Institute. An examination of the contents of the Text-Book and of the Index to the Journal furnishes abundant proof of the attention which has been given to the theory, but in regard to the practical working of annuity business, little has of late years been written. The most important contribution in the Journal, from the latter point of view, is that by Mr. G. H. Ryan (read before the Institute seventeen years ago) “On a Method for determining the Gain or Loss from Mortality in an Annuity Company.” Therein reference was made to another contribution by the same author, read before the Actuarial Society of Edinburgh during the Session 1884-5, and published in the first volume of the Transactions of that Society, “On the Several Mortality Tables Employed in the Valuation of Annuity Contracts.” Changes of the utmost importance have taken place during the period which has since elapsed, and it is proposed herein to deal with the cause and effect of such changes, and to gather therefrom some guidance for the future.