574 



SCIENCE 



[Vol. LVI, No. 1455 



very encouraging, there being some two score 

 British fliers, besides foreign aviators, notably 

 the Dutch airman, M. Fokker. A large num- 

 ber of short flights and some quite long flights 

 were made; yet on the whole the results of the 

 meeting were not of a sensational nature until 

 the last day of the meeting. The general con- 

 elusion is that British aviators do not fall 

 behind those of Grermany, and that it is possi- 

 ble to find suitable arenas in this country for 

 the practice and display of motorless flight. 

 The most notable achievement of the first day 

 of the contest was a thixty-seven-minute glide 

 by M. Fokker, but this -was surpassed by a 

 fine flight executed by Mr. F. P. Eayniham. 

 This aviator had already taken a place in the 

 front rank of British pilots in the recent air- 

 race round England: he added to his laurels 

 by remaining in the air in a motorless machine 

 for one hour and fifty-three minutes, thus 

 putting himself in the same category as the 

 German record-makers. Martens and Hentzen. 

 But on the last day, Saturday, two wor'ld- 

 reeords were nevertheless established. J. E. 

 Olley went up in a Fokker biplane, and re- 

 mained in the air with a passenger for forty- 

 nine minutes, while M. Maneyrolle, in a tandem 

 monoplane glider, succeeded in remaining in 

 the air for three hours twenty-two minutes, 

 thus winning the Daily Mail prize and beating 

 the previous record, that of Hentzen, by twelve 

 minutes. During the last ninety minutes of his 

 flight, M. Maneyrolle was accompanied by a 

 monoplane glider flown by Squadron-Leader 

 A. Gray, and it was night when the two ma- 

 chines landed within 100 yards of the point 

 from which they started. These competitions 

 on the South Downs will serve as an encour- 

 agement to motorless flight in this country, and 

 will help in the accumulation of knowledge and 

 experience on one of the most interesting de- 

 velopments in modern aeronautics. — Nature. 



SCIENTIFIC BOOKS 



The Theory of Functions of a Real Variable. 

 By E. W. HOBSON, ScD., LL.D., F.R.S., 

 Sadleirian Professor of Pure Mathematics 

 and Fellow of Christ's CoUege, in the Uni- 

 versity of Cambridge. Second edition, Vol. 



1. Cambridge at the University Press, 1921. 



Pp. xvi + 671. 



Because of the war and relativity, we are ajt 

 pi-esent in a period of increasing scepticism 

 towards so-called established principles and 

 facts. Many stUl believe, however, that mathe- 

 matical knowledge, at any rate, is beyond dis- 

 pute. For these there will be great disap- 

 poinitment in the pages of Hobson. The book 

 reads in places like unoonvincing philosophy, 

 and instead of statements made with full per- 

 sonal eonviotion, we find, at times, conflicting 

 opinions of "authorities" — beings supposed, by 

 some, to be unknown to mathematicians — and 

 inconclusive attempts at mediation. And yet 

 it is on the Theory of Functions of a Real 

 Variable that rigor in Mathematical Analysis 

 depends. The first edition appeared in the 

 course of Zermelo's work on Wohlordnung, 

 when mathematicians were just beginning to 

 get their bearings on certain controversial mat- 

 ters; after a lapse of foui'teen years, there is 

 the same indecision. Other writers on Real 

 Variables and Point Sets — for example, Haus- 

 doa-ft, Caratheodory and Hahn — ^adopt a single 

 point of view and proceed joyfully without 

 misgiving. Pi'ofessor Hobson wants to give a 

 comprehensive report — his book is the most 

 voluminous treatment of the subject — to in- 

 clude historical matter, and to be as fair as 

 possible, "no attempt has been made to give 

 dogmatic decisions between opposed opinions." 

 This wish to be fair makes Professor Hobson 

 exchange, at times, the role of mathematician 

 for that of reporter; it has the advantage, how- 

 ever, of making the reader independent of the 

 author — a significant advantage when we ob- 

 serve that even among mathematicians in- 

 stances are observable of opinions held not on 

 their merits but on the ground of personal and 

 nationalistic associations. 



The role of the mediator, however, is apt to 

 te a hard one, not only in industrial, but even 

 in mathematical affairs. For fear of being 

 one-sided, he may lose vivacity. Thus we 

 read on page 238 [author's italics], "In order 

 that a transfinite aggregate . . . may be capa- 

 ble of being ordered, a principle of order must 

 be explicitly or implicitly contained in the 



