The value, to the practical actuary, of Makeham's formula for the law of mortality, as a means of facilitating the calculation of joint-life benefits, is well established. Considerable use, for instance, is undoubtedly made of the tables appended to the second volume of the Institute Text-Book, in questions of everyday occurrence involving the computation by the HM Tables of annuities on three or four lives. In like manner, where the employment of Carlisle annuities is desirable, the tables prepared in 1880 (see J.I.A., xxii, 191), by Messrs. George King and G. F. Hardy, afford a ready means of obtaining results which are at once consistent, and substantially in agreement with values derived directly from the parent table. With regard, however, to the calculation of contingent survivorship benefits, it seems worthy of consideration whether something may not be done to render expressions based upon Makeham's formula better adapted than they are, in the shape in which they are usually presented, to meet the exigencies of practical requirements.