At a recent meeting of the Institute, Mr. Sutton read an instructive paper on the method used by Milne in the construction of the Carlisle Table of Mortality, and the paper gave rise to an interesting discussion. I was surprised to find that it was the general opinion of members that Milne's description of his method is vague, and still more so to discover that more than one able investigator had expended much pains and ingenuity, unsuccessfully in my view, to unravel the mystery. Years ago I had studied Milne's explanations, and they seemed to me perfectly clear; and I had more or less tested his figures, and proved that they worked out correctly. So much was I satisfied, that it never occurred to me that the matter required further elucidation. But the remarks of Mr. Sutton in his paper, and of Mr. Manly in the-subsequent discussion, show that Milne has been very much misunderstood; or else that he has not only failed to explain his method, but that he has explained a method which he did not in the slightest degree adhere to, and that he thus has almost wilfully misled the student. Under these circumstances I may, perhaps, be pardoned if I give with some detail the results of my own researches,—which, since Mr. Sutton's paper was read, have been carried out to greater fulness—especially as I think that thereby may be vindicated the character of Milne for both lucidity and accuracy.