The question ov the calculation ov premiums for the insurance agenst issue to a man at present marryd but without a family, has been on two ocasions bro't under the notis ov the Institute by Mr. Archibald Day. On 31 January 1859 he redd his paper On the determination ov the rates ov Premium for asuring agenst Issue (Journal viii, 127), in which he explaind his proces of calculating, by means ov statistics furnisht by the Registrar General's returns, the present value ov £1 payabl at the end ov the year in which a husband shal contract a second marryge. On 24 March 1862 he redd a stil more important paper, On the statistics ov first and subsequent Marryges among the Familys of the Peerage, considerd specially with reference to the calculation ov Premiums for Asurances agenst Issue, in which the same method was employd to obtain more accurat premiums from the more apropriat statistics furnisht by the peerage familys. The general problem is a very complex one involving several distinct contingencys. Mr. Day delt very succesfully with som ov these contingencys, but his treatment ov the subject was confessedly incomplete, and he himself speaks ov it as giving only a ruf aproximation. He omitted altogether from the calculations the circumstances that the insurance is not payabl until the deth ov the husband after contracting the second marryge, and that ther is a probability ov his second marryge being unfruitful. I hope on som future ocasion to take up the general question and carry the investigation ov it one or two steps beyond the point at which Mr. Day left it, but on the present ocasion I shal deal only with one element involvd in the calculation, namely, the probability ov the remarryge ov a widoer.