I do not think that any apology, is necessary for asking the members of the Institute of Actuaries to devote a meeting to a consideration of the subject of Sinking Fund Assurances. My paper—if paper it can be legitimately called—contains, I am afraid, little, if anything, that will be new to those actuaries who have had to consider the subject, and doubtless in itself demands a very ample apology for the temerity of its author in submitting it to the criticism of the Institute. I am not, however, without hope that the ensuing discussion may bring out some points of practical interest, and if this should be so, and more particularly if fuller consideration of the subject should lead to an arrangement on the lines indicated in the concluding paragraphs of my remarks, I think I may fairly ask that these results may be considered as to some extent a mitigation of my offence.