Sept. 12, 1889] 



NATURE 



459 



still worn on certain ceremonial occasions. Farish, who 

 was presiding, saXd, Dotntne opponcntium tertie,nonhabes 

 guod debes. Ubi sunt tui. . . . (with a long pause) Anglzce 

 hands? To whom with commendable promptness the 

 undergraduate replied, Dignissime domine moderator, sunt 

 inineo {Anglice) pocket. Another piece of scholastic Latin 

 quoted by Wordsworth is, Domine opponens non video 

 vim tuum argumentum." " 



In the last sentence " his scholastic Latin " would read 

 better than " scholastic Latin " : perhaps, however, this 

 alteration could not be made without violating historic 

 truth ; in which case it might be difficult (but we hope not 

 impossible) to substitute some other Latin sentence be- 

 longing undoubtedly to Farish, and anything hke as good 

 as his exquisite " Verte canefn exP It is recorded, to the 

 credit of Farish, that he resided and taught ; a rare in- 

 stance of virtue in a Professor of that period. Strange 

 abuses were prevalent in his time ; among them the 

 practice of " huddling " the disputations in the schools 

 may be mentioned. 



" By the Elizabethan code every student before being 

 admitted to a degree had to swear that he had performed 

 all the statutable exercises. The additional number thus 

 required to be performed were kept by what was called 

 huddling. To do this a regent took the moderator's seat, 

 one candidate then occupieak- the respondent's rostrum, 

 and another the opponent's. Recte statuit Newtonus, said 

 the respondent. Recte non statuit Newtonus, replied 

 the opponent. This was a disputation, and it was re- 

 peated a sufficient number of times to count for as many 

 disputations. The men then changed places, and the 

 same process was repeated, each maintaining the contrary 

 of his first assertion — an admirable practice, as De 

 Morgan observed, for those who were going to enter 

 political life. Jebb asserts that in his time (1772) a 

 candidate in this way could, as a respondent, read two 

 theses, propound six questions, and answer sixteen argu- 

 ments against them, all in five minutes." 



The above is extracted from the chapter devoted to the 

 exercises in the schools. This and the one on the mathe- 

 matical tripos (ix. and x.) are the two best chapters in 

 the book, and contain a large mass of interesting matter ; 

 but since the substance of both is reprinted from the 

 author's " Origin and History of the Mathematical 

 Tripos" (Cambridge, 1880), with which many of our 

 readers are doubtless acquainted, we refrain from making 

 any further quotations from either. We need only say 

 that together with chapter viii. (under the heading " The 

 Organization and Subjects of Education ") and chapter 

 xi. (" Outlines of the History of the University") they 

 constitute the second of the two well-defined portions 

 into which the present work is divided, and give a clear 

 though succinct account of the history of Cambridge and 

 of the principal object of study there, from the earliest 

 times to the date of the repeal of the Elizabethan statutes 

 (1858), with which the history is made to terminate. The 

 first seven chapters, which (see the preface) " are devoted 

 to an enumeration of the more eminent Cambridge 

 mathematicians, arranged chronologically," embrace the 

 same period of time. Their style is somewhat similar to 

 that of the author's " History of Mathematics " published 

 last year, but is still more concise. In them, with the 

 assistance affijrded by the introductory paragraphs prefixed 

 to each, we are enabled to trace the rise of mathematical 



. . 9 Ball, p. 106. 



science from the earliest times to the death of Newton (i. 

 to iv.), and its subsequent decadence in Cambridge (v. 

 and vi.), until we come to chapter vii., which is mainly 

 occupied with those mathematical reforms (initiated by 

 Robert Woodhouse, and carried out by Peacock, Her- 

 schel, Babbage, and others) which inaugurated the great 

 modern revival of learning in England, spoken of by Mr. 

 Ball in his concluding paragraph as the " new renais- 

 sance." The first portion of the work terminates with this 

 chapter, which also contains notices of some of the more 

 prominent mathematicians who graduated at Cambridge 

 since the time of the above-mentioned reformers, but not 

 later than the Tripos of 1859. Except in the ninth and 

 tenth chapters, the style is too condensed, and conciseness 

 is sometimes attained by the suppression of interesting 

 facts ; but this is not an unmixed evil, since the cost 

 of publication is thereby kept down, and we have every 

 reason to believe that those who are content to pay a 

 moderate price for a general view of the subject will find 

 in this little volume a very useful compendium of 

 Cambridge mathematical history. 



We ought to add that, in its externals, the book is all 

 that most attracts the fastidious purchaser. It is neatly 

 bound, in general correctly printed, in clear type, and on 

 good paper. The table of contents and index are also 

 good.i° 



'° In this note we append a few disjointed remarks for the sake of point- 

 ing out certain trivial errata, and small emendations, or what we believe to 

 be such : — 



P. 17, "belated traveller." A man who had travelled no farther than from 

 St. James's Park to Whitefriars (see " The Fortunes of Nigel," ch. xvi. and 

 xvii.) and who had remained in sanctuary there for some days, can hardly be 

 called a belated traveller because he asks for "a book— any sort of book — to 

 pass away the night withal," and we can discover no other reason. The 

 passage we allude to occurs in ch. xxiv. of Scott's novel, and in the version 

 from which we quote runs thus : — " She heard mith interest Lord Glenvar- 

 loch's regjiest to have a book — any sort oj book — to pass away the night 

 ivithal, and returned for answer, that she knew of no other books in the 

 house than her young mistress's {as she always denominated Mistress 

 I\ fart h a Trafibois ) Bible, which the owner would not lend ; and her Master's 

 Whetsione of Witte, being the second part of Arithtnetic, by Robert 

 Record, with the Cossike Practice and Rule of Equation ; which promising 

 volume Nigel declined to borrcnv." This is quoted both by De Morgan and 

 Mr. Ball, of whom the latter omits the italicized words, and the former those 

 only that are al o underlined. Both of them omit the comma between 

 "answer" and '"that"; and both spell "Bible" w.th a small "b," 

 " Master's " with a small '"m," and "Record" with a final "e." From 

 this we infer that both of them quoted from a version of Scott differing from 

 the one on our shelves in the above particulars, unless Mr. Ball copied his 

 quotation fiom De Morgan's. The fact that De Morgan makes no allusion 

 to a "belated traveller" seems to favour the former theory. Our author 

 deals with Recorde just as he has done with Scott : he takes a passage from 

 him, gives certain portions of it, and modernizes the spelling (see the quota- 

 tiuns from Kecorde on pp. 16-18, and compare them with those given in the 

 article by De Morgan, referred to in note ', which contains ail of them and 

 is easily procurable). The ghost of an old author has a right to complain of 

 the alteration of a single letter in his work, and to say " Interpretation will 

 misquote our i^ooks"(Hen. IV., Part I., act v., sc. 2). There ! we have com- 

 mitted the very offence we felt called upon to condemn, and have changed 

 Shakespeare's "1" into a "b." 



P. 31. For " circle of proportion" read " circles of proportion." 



P. 41. The first volume of Marie's " Histoire des Sciences math^matiques" 

 was published in 1883 : this date is changed into 1833 by an obvious mis- 

 print. 



P. 72. The correct title of Dr. Sloman's work (which lies open before us 

 as we write) is, "The claim" (not claims) "of Leibnitz to the invention of 

 the differential calculus." 



P. 91. Smith's " Compleat System of Opticks" was published in 1738 (not 

 1728). An advertisement dated ^'London, Apr. 25, 1738," speaks of it as 

 " Printing at Cavtbridge in Quarto, and will be published by the latter end 

 of May or the beginning oi J line " (we quote literally). 



P. 93. It is not easy to identify books whose tides are not given, but we 

 know of no text-book by Humphry Ditton "on the infinitesimal calculus" 

 of an earlier date than 1706, when his ''Institution of Fluxions "was pub- 

 lished. We therefore conclude that the date 1704 must be a rnisprint for 

 1706, and shall continue to think so until we actually see an edition dated 



On this page also, for "Robert Smith (1728)" read " Robert Smith (1738). 



P. 257. In the index, insert the reference " Commercium Epistolicum, 

 72"; for '"Creswell" read "Cresswell;" and in the third line of the 

 references to De Morgan, dele i8o. 



We have given the above list in compliance with the words, " I shall 

 thankfully accept notices of additions or corrections which may occur to any, 

 of my readers," with which Mr. Ball's preface terminates. 



