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Rh that it was a remarkable paradox, easily explicable; and that is all. After this evasion, Mr. James Smith is below the necessity of being told that he is unworthy of answer. His friends complain that I do nothing but chaff him. Absurd! I winnow him; and if nothing but chaff results, whose fault is that? I am usefully employed; for he is the type of a class which ought to be known, and which I have done much to make known.

Nothing came of this until July 1869, when I received a reprint of the above letter, with a comment, described as Appendix D of a work in course of publication on the geometry of the circle. The Athenæum journal received the same: but the Editor, in his private capacity, received the whole work, being 'The Geometry of the Circle and Mathematics as applied to Geometry by Mathematicians, shown to be a mockery, delusion, and a snare,' Liverpool, 8vo., 1869. Mr. J. S. here appears in deep fight with Prof. Whitworth, and Mr. Wilson, the author of the alleged amendment of Euclid. How these accomplished mathematicians could be inveigled into continued discussion is inexplicable. Mr. Whitworth began by complaining of Mr. Smith's attacks upon mathematicians, continued to correspond after he was convinced that J. S. proved an arc and its chord to be equal, and only retreated when J. S. charged him with believing in $3 1⁄8$, and refusing acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defence of his geometry from the assaults of the Athenæum. This the editor would not publish; so J. S. sent a copy to Mr. Wilson himself. Some correspondence ensued, but Mr. Wilson soon found out his man, and withdrew.

There is a little derision of the Athenæum and a merited punishment for 'that unscrupulous critic and contemptible mathematical twaddler, De Morgan.'

At p. 371 I mentioned Mr. Reddie, the author of Vis Inertiæ Victa and of Victoria tolo cœlo, which last is not an address to the whole heaven, either from a Roman Goddess or a British Queen, whatever a scholar may suppose. Between these Mr. Reddie has published 'The Mechanics of the Heavens,' 8vo., 1862: this I never saw until he sent it to me, with an invitation to notice it, he very well knowing what it would catch. His speculations do battle with common notions of mathematics and of mechanics, which, to use a feminine idiom, he blasphemes so you can't think! and I suspect that if you do not blaspheme them too, you can't think. He appeals to the 'truly scientific,' and would