It has been already stated (see footnote, p. 248) that, on the 20th April Professor Smyth brought before the Royal Society a new communication on the pyramids, the principal part of which consisted of a criticism upon the preceding observations, and a defence of his hypotheses regarding the Great Pyramid. His chief criticisms related to points already adverted to, and answered in footnotes, pp. 234, 248, etc. In addition, he expressed great dissatisfaction that the quotation from Sprenger, in Vyse's Work, quoted in footnote, p. 237, was not extended beyond the semicolon in the original, at which the quotation ends, and made to embrace the other or latter half of the sentence, viz., " ...; and that they appear to have repeated the traditions of the ancient Egyptians, mixed up with fabulous stories and incidents, certainly not of Mahometan invention."[276] But this latter half, or the traditions about the pyramid builders, Surid, Ben Shaluk, Ben Sermuni, etc., who lived "before the Flood," etc. etc., did assuredly not require to be quoted, as they had really nothing whatever to do with the object under discussion--viz., the opening of the sarcophagus under the Caliph Al Mamoon, and the accounts or history of the pyramids, as given by Arabian authors themselves. In the course of this communication to the Royal Society, Professor Smyth did not allude to or rescind the erroneous table and calculations from Sir Isaac Newton regarding the Sacred Cubit, printed and commented upon in some of the preceding pages (see _ante_, p. 244, etc.) But, at the end of the subsequent discussion he handed round, as a printed "Appendix" to his three volume work, a total withdrawal of this table, etc., and in this way so far confessed the justice of the exposition of his errors on this all-vital and testing point in his theory of the Sacred Cubit, as given in p. 243, etc., of the present essay. He attributes his errors to "an unfortunate misprinting of the calculated numbers;" and (though he does not at all specialise what numbers were thus misprinted) he gives from Sir Isaac Newton's Dissertation on the Sacred Cubit a new and more lengthened table instead of the old and erroneous table. For this purpose, instead of selecting as he did, without any attempted explanation in his old table, _only five_ of Sir Isaac Newton's estimations or "methods of approach," he now, in his new table, takes _seven_ of them to strike out new "means." The simple "mean" of all the seven quantities tabulated--as calculated, in the way followed, in his first published table--is 25.47 British inches; and the "mean" of all the seven means in the Table is 25.49 British inches. Unfortunately for Professor Smyth's theory of the Sacred Cubit being 25.025 British inches, either of these numbers makes the Sacred Cubit nearly half a British inch longer than his avowed standard of length--an overwhelming difference in any question relating to a _standard_ measure.