In December 1879 I read before the Institute a paper (J.I.A. xxii, 117) on the probability that there will hereafter be issue of a marriage hitherto childless. The statistics on which I based my conclusions, were those given by Dr. Matthews Duncan in his work, Fecundity, Fertility, and Sterility; and by Mr. Charles Ansell, Jr., in his Statistics of Families of the Upper and Professional Classes. But I was not altogether satisfied with the results I obtained; for, as I pointed out, the two sets of statistics differ from each other in some material respects, and I was unable to give any satisfactory explanation of the difference, or to say which set was the more trustworthy. For the purpose I had in view both sets had one great defect, namely, that they gave no information as to the number of childless marriages which corresponded to those that became fruitful at different intervals as stated in the tables. I have now, by means of a careful examination of the records of the British Peerage families, obtained a fresh set of statistics; and I purpose on the present occasion applying them to the solution of the same problem as I discussed in 1879.