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132 coincidences in the Athenaeum," for 1860. There is a good deal in the work of mathematical interest.

Taylor's theories were enthusiastically supported and developed by his friend C. P. Smyth, astronomer royal for Scotland, and professor of practical astronomy in the University of Edinburgh, in his: Our Inheritance in the Great Pyramid, London, 1864, 4oopp.;second edition, 1874; third, 1877; fourth, 1880, 16 + 677pp. + 25 plates; ﬁfth, abridged, 1890. And in his: ''Life and Work at the Great Pyramid during the month: of January,. . ., and April, A. D. 1865. . .'', 3 vols., Edinburgh, 1867. De Morgan remarks (I. c., p. 292) that Smyth's "word on Egypt is paradox of a very high order, backed by a great quantity of useful labour. . . ."

In The Builder, vol. 24, 1866, p. 97, G. Thurnell has an article on "The geometrical formation of the great pyramid;" it is “proved" that the pyramid of Taylor, Smyth, and others is that of Herodotus (book ii, chapter 124) about 450 B. C. On pages 150-152 of this same volume of The Builder, E. L. Garbett contributes an excellent article on “pyramid geometry" clearly exhibiting unscientific deductions made from data of various workers. “Now, I cannot but ask, with this bird's eye view before us, where have we any evidence yet of the Egyptians embodying in these works any geometry, or any theoretic or liberal science at all." The article won applause from “A. X.” on pages 200-201. No very different attitude is maintained by R. A. Proctor, in his The Great Pyramid Observatory, Tomb, and Temple, London, 1883.

1855

, "Aegyptische Studien, III. Ueber die und den Symbolismus der Zahl 30 in den Hieroglyphen," 'Zeitschrift der Deutschen M orgenländischen Gesellschaft, Leipzig, vol. 9, 1855. pp. 492-499 + 1 plate.

1856

, "Ueber eine hieroglyphische Inschrift am Tempel von Edfu". . ., Akademie der Wissenschaften zu Berlin, Abhandlungen, aus dem Jahre 1855, Berlin, 1856, pp. 69-114 + 6 plates.

This deals with a great dedicatory inscription of about 100 B. C., where reference is made to a large number of four—sided ﬁelds. For each of these the lengths of the sides (which we may call, in order as we go around, a, b, c, d) and their areas are given; these areas may be determined by the formula 1½ (a + c)- M (b + d) = ¼ (ab + ad + be + ed), while the true value is ¼ [ab sin (ab) +