NA rURE 



77 



THURSDAY, MARCH 22,, 1916. 



THE BUDGET OF PARADOXES. 



A Budget of Paradoxes. By A. de Morgan. 

 Second edition, edited by D. E. Smith. Two 

 .olumes. Vol. i. , pp. viii + 402; vol. ii., pp. 

 vSj. (Chicago and London : The Open Court 

 i'ublishing Co., 1915-) Price 305. net. 



THIS is not the first time the Open Court Co. 

 ' has deserved grateful thanks for under- 

 taking a reprint of a rare work, although they 

 will probably make no profit out of it. The editor, 

 well known as a writer on the history and teach- 

 ing of mathematics, has laid down for himself 

 an excellent plan^ namely, to preserve the text 

 intact, except where mistakes could be corrected 

 [ with certainty ; to indicate clearly the authorship 

 \ of every addition or alteration ; to add catchlines 

 ! to break up the text ; and to give notes for the 

 } information, not only of mathematicians, but of 

 [ those who treasure the " Budget " as a literary 

 I work of art, and who, even when well-read, may be 

 I puzzled by the numerous quotations and allusions 

 in which De Morgan delights. To produce an 

 annotated edition of this kind is a very difficult 

 task ; it would require another De Morgan to 

 perform it to perfection, and we thank Prof. Smith 

 for what he has done, without dwelling ungraci- 

 ously upon what he has omitted, or blundered in 

 "-ving to do. 



First of all we may say that the biographical 

 notes are abundant (too much so, st>me may 

 think) ; so far as they refer to mathematical 

 writers, they are generally appropriate, and so far 

 as we have tested, are accurate. To end up a 

 ten-line note on Rowan Hamilton with the sen- 

 tence " He also wrote on dynamics " irresistibly 

 reminds us of that other casual after-thought " and 

 the stars also " in Gen. i. 16. Here, as else- 

 where, the editor's humour is of the unconscious 

 ind; and one instance is so funny that we really 

 nnot pass it over. The Religious Tract Society 

 oee i. 194) censored a perfectly harmless passage 

 in one of Hannah More's tales which they were 

 j reprinting. On this De Morgan : " O fie ! Miss 

 I Hannah More ! and you a single lady too, and a 

 contemporary of the virtuous Bowdler ! " Edi- 

 torial comment : a note on Henrietta Maria 

 Bowdler, and not a word about the immortal 

 Thomas! Again, by confusing "Tom" Sheridan 

 with the elder Thomas S., the editor has found 

 one of the most wonderful mare's-nests on record 



In giving translations of quotations, etc., in the 

 xt Prof. Smith is sometimes painfully inaccur- 

 'e,^ and in other cases he is unsympathetic. As 

 n instance of what we mean, take i. 40, where 

 e read : " the answer is — 



" Rumpat et serpens iter institutum 

 — a line of Horace [Carm. iii. 27], which the 

 demons interpret as a direction to come athwart 

 the proceedings of the Institute by a sly trick." 

 If we are to have a translation here, the best 

 NO. 2421, VOL. 97] 



would be a mock-translation, such as "And let 

 the Old Serpent interrupt the proceedings of the 

 Institute," like De Morgan's "change dice into 

 coin " for mutat qtiadrata rotiindis, where the 

 editor gives no reference to the original context 

 (possibly to spare the feelings of a certain class 

 of millionaires). To return to the present case, 

 the editor's rendering is "Let the serpent also 

 break from its appointed path," which is incor- 

 rect, and neither suits the original context nor 

 the one to which De Morgan applies it. (And we 

 might have had, instead of this blunder, a brief 

 note on the Institiit national.) 



The list printed below 1 contains corrections of 

 errors we have found, which are serious enough 

 to be actually misleading; perhaps the Open Court 

 Co. might be willing to have them tested, and 

 then pasted as corrigenda in some at least of the 

 copies of this edition. 



Prof. Smith has adopted a system of what he 

 calls "slightly modernised spelling." If, in his 

 notes, he likes to print " equaled " (why not 

 "equald," like "herald" and "ribald," while we 

 are about it?) he has a perfect right to do so; but 

 we respectfully protest against his taking this 

 liberty with the text. And is dilletante a mis- 

 print, or an example of modernised spelling? 



To us, the one great failing of Prof. Smith, as an 

 editor, is that he has treated the " Budget " (natur- 

 ally enough, from his point of view) too much 

 as a chapter in the history of mathematics, or 

 rather of pseudo-mathematics. Really, it is a 

 study of a class of cranks (who are always with 

 us), and, as such, it is a section of the great 

 Book of Human Folly and Self-Conceit. Inci- 

 dentally, of course, it gives a portrait of the 

 author, who was a very remarkable man. No 

 mean mathematician, he was an excellent teacher 

 of his subject (we ourselves knew one of his 

 pupils); he was an expert in formal logic; an 

 antiquarian and humorist like \\"alter Scott, a 

 scholar and a wit like Sydney Smith. (His digres- 

 sion, ii. 22, suggested by the paradox of the 

 moon's rotation, is so like an essay by Sydney 

 Smith that if candidates in an examination on 

 English literature, were given a selected passage 

 from it, and asked to name its author, the intelli- 

 gent ones would be very likely to ascribe it to 

 S. S., that:imperishable ornament of the English 

 Church). Handicapped by that wretched name 

 Augustus, he made it one of the few exceptions 

 to a general rule^- Like Augustus among the 



1 In i. 4 Kleckerrnanno should be Keckermanno ; C/. means Claro, and 

 shouldhave been translated (the reference appears to be to Bartholomew K.) : 

 next p., veritate should be veritaii; gitamvis eo nomine non multuat 

 gratiae iniverit means "although he<K.) has not found much favour on 

 ihat score"; i. 7 " unproyoked " /. "unproved"; (i ) 13 /. " \fercfiant 

 Taylors'"; 73 (end) /. "the Moors that we see (amon? ourselves)"'; 104 

 /. prave (i\\f passage is from Phaedrus) ; 127 "work" /. "word"; 175, 

 "Tom Sheridan " means the only '^on of the playwright (R. B. S.). and there 

 are no chronological difficulties about the story, whether it be true or not ; 

 194 the reference is to Thomas Bowdler and his famous edition of Shakespeare ; 

 204 1 he book referred to is the " Trigonometry and Double Algebra"; 241 

 Fevilo m'ans Oliver Byrne {p. L 329) ; 299 SIow = Slough, and printing " Hr. 

 Heirschel at Slow " would have made things clearer; 302 for " qnib " 

 /. "squib." In ii. 2. /. "I had no need for that h^-pothesis " — t" render 

 aval's by "have" misrepresents Laplace; 4 (end) " sorest " is probaWy a. 

 misprint for " worst "; 15 (top) for "At least " /. " At last " ; 31 'L' should 

 be 'L(with ' foTth'' spr'ri/us as^er); the new editor has spoiled the joke, 

 such as it is; Tt.PaJisees, I. Penu'es; 136 f«.) "condemned " shrnid be 

 '■thought negligible"; 166 a crtt <&t'>»jV= " fancied himself obliged." and 

 gratuitetnent^ ' fj3itxi\loti%\y' '; 225 (end) the second " goals " should t-e 

 '• gaols " : and " sums ' (just above should be " sum." 



