By this I do not mean what is usually called Newton's Table, but something which has a better right. First, however, I will speak of the table which, having Newton's certificate of accuracy, is (or was) usually called by his name.

Mr. Edleston, Fellow of Trinity College, in making researches for his biography of Newton, found out the author of the old table. His name was Mabbot, and he was manciple (mancipium) or caterer of King's College. Mabbot published his table in 1686, with the well-known attestation of Newton opposite to the titlepage. There seems to have been a special reason for procuring this certificate. The church lessors were beginning to open their eyes to the leniency of their terms, and Mabbot's tables were certainly intended both to urge them to raise their fines, &c., and to point out the proper way of doing it. Subsequent editions of these tables had attached to them the well-known letter which pointed out the advantage under which the tenant was living. As it was natural that the lessees should oppose the new scheme, and they would probably question its accuracy, it seems that Newton was applied to for the testimonial which, as is well known, he gave.

The series lx has been constructed, and from that series others are deduced to complete the Life Table, consisting now of six columns.

(1.) dx=lx−lx+1=number of deaths in the year of age following, out of lx alive at the age x. By taking x successively at 0, 1, 2, 3…to the last age in the Table, the numbers dying in every year of age are obtained.

I have a suspicion that Mr. Edmonds intends the fifteen pages on the “Law of Human Mortality,” which appear in the last Number of this Journal, to stand in place of an answer to my remarks “On an unfair suppression of due acknowledgment to the writings of Mr. Benjamin Gompertz,” printed in the July Number; for though no allusion is made to the charge, still less statement of it or answer to the evidence produced, there is one mention of me which looks so like a distortion of my paper, that I think the suspicion is justified. Mr. Edmonds says (p. 181), “Mr. De Morgan, in his office of self-constituted judge between Mr. Gompertz and me, overlooks this important error …” Now, though my paper does not deal with the truths or errors of either, but only with the question whether Mr. Edmonds's mention of Mr. Gompertz was suppressive; and though I never said, and certainly never thought, that there was or could be any question pending between Mr. Gompertz and Mr. Edmonds; and though I was not the judge, either self-constituted or otherwise, but only the promoter of an accusation of unfair suppression for others to judge of;—there is in the quotation that remote likeness to an account of my proceeding which often exists between that which cannot be answered and that which it is convenient to substitute for it.

An article published in this Journal last January (vol. viii., p. 316), proposed itself the problem of furnishing a test whether the degree of uniformity, or the reverse, observed in a table of statistics, required to be assigned to any other cause than the relative magnitude of the numbers of combinations which each figure in the table represented. The formulæ obtained in that article gave a general solution to the problem proposed, by giving an expression for the ratios of the numbers of such combinations which would be embraced under any figure in the table; and, consequently, expressing the relative frequency with which each number should be expected to occur from the mere consideration of counting the combinations represented by it.