ESSAYS 651 



of the history of each branch will be found in connection with the article which 

 deals with it," contains at least one more fearful blunder. " The medieval Ara- 

 bians," we read (p 882), "invented our system of numeration and developed 

 algebra." The origin of this blunder was probably the statement in Mr. W. W. 

 Rouse Ball's Short History of Mathematics (4th edition, London, 1908, p 186) 

 that men of science " had become acquainted with the Arabic system by the 

 middle of the thirteenth century." Two pages before this it is explicitly explained 

 by Mr. Ball that our numerals were used in India in the eighth or earlier centuries 

 and were introduced into Europe through the Arabs : the Arabs certainly did not 

 invent the system : they only gave it their name. The same account could easily 

 have been verified from the article Numeral in either the ninth or eleventh 

 edition of the Encyclopedia Britannica : the theory of the Greek origin of our 

 numerals could hardly be expected not to have escaped our author ; it had been 

 published only about four years before he wrote his article. 



The article Mathematics is brought to an end by half a column'of " Biblio- 

 graphy " (p. 883). In this short collection of books there are at least three mistakes 

 in spelling, not counting the spelling " Leibnitz," which is, I believe, due to the 

 editorial committee, but counting as mistakes the same spelling when the title of 

 a book is quoted in which there is the spelling " Leibniz." There are also two 

 faulty references. Among the books quoted on the history of mathematics, there 

 is a reference to Moritz Cantor's Geschichte. Nobody who knows anything of 

 modern historical research and who has read this book could possibly describe it 

 as " the one modern and complete source of information." This description is 

 made still more extraordinary by the fact that only the first edition of the book, 

 which has long been out of date, is mentioned. If, on the other hand, we are to 

 understand " modern " as referring to the period covered by the work in question, 

 a work which the author carried only up to 1758, and which others cont nued up 

 to 1799, can hardly be described as " modern." 



I will add a few words about other mathematical defects in the Encyclopedia 

 Britannica — most of the rest of which is so admirably written and edited. In the 

 ninth and tenth editions of the Encyclopedia Britannica, there was no biography 

 of Cauchy — one of the founders of the theory of functions of a complex variable — 

 although there are biographies of men like Poisson and Landen, who were of far 

 less importance mathematically and of no greater importance otherwise. Further, 

 in the tenth edition (1902, 31, 285), it was actually asserted that the third class of 

 Cantor's transfinite ordinal numbers begins with u", and the third and higher 

 classes are within what Cantor quite clearly defined as the second class. A 

 precisely analogous mistake would be to say that, amon< the finite integers, there 

 are some that are infinite. Now, it seemed to me that these two errors should 

 not be allowed to contaminate a source of knowledge, — which is what the Encyclo- 

 pedia Britannica may be for many, — and thus I wrote, about 1905, to the then 

 editor, Mr. Hugh Chisholm, pointing them out. Whether or no it was in conse- 

 quence of this letter— and it is hardly necessary to add that the errors are so 

 obvious to any competent mathematician that I can well believe that my letter 

 was superfluous— in the eleventh edition there was (1910, 5, 555) a biography of 

 Cauchy, and, though the author of the article Number reproduced much of his 

 article on the same subject in the tenth edition, among other alterations omitted 

 (cf. 191 1, 19, 850-51) the sentence criticised above— but, it may be added, he 

 ludicrously enough retained his "scheme of symbols" in which the fallacious 

 divisions into higher number-classes were marked out. 



