576 



NATURE 



[May 6, 1922 



with technical students, who are only too apt to regard 

 mathematics as a game instead of an essential part 

 of their business. The book is, for the rest, well 

 proportioned and quite suitable for its purpose. 



(6) The subject known as " Elementary Algebra " 

 has been so metamorphosed in the past ten or twenty 

 years that its name ought to be changed. Graphs, 

 differentiation, integration, and nomography are not 

 algebra as understood by Salmon, Chrystal, or Weber. 

 A little trigonometry and as much geometry as is 

 required should be added and the whole called ele- 

 mentary mathematics. The breaking down of the 

 watertight compartments into which school mathe- 

 matics used to be divided is a development in the 

 right direction. 



The scheme of this book is interesting. The book- 

 work is only given in outline in the text or hinted 

 at in the introduction. It remains for the teacher 

 to fill in this framework according to his own lights. 

 And then the text-book gives him examples that are 

 both numerous and apposite. The scheme has much 

 to recommend it, and will be welcomed by teachers 

 who are accustomed to do their work thoroughly. 

 The authors need not apologise for introducing a 

 chapter on nomography, although this chapter will 

 be found difficult without a much fuller treatment. 



(7) It is a melancholy fact that examinations 

 dominate and thereby spoil much of the education 

 that they are intended to test and encourage. A 

 considerable part of the education in this country 

 has no higher purpose than the passing of a public 

 examination at some future date. Mr. Durell, who 

 is capable of much better things, says quite frankly 

 that he has compiled a cram book, and we can recom- 

 mend it for that purpose. The range is roughly that 

 of the Cambridge schedule. 



(8) The syllabuses for the Army entrance examina- 

 tions and those conducted by the Oxford and Cambridge 

 Joint Board have been assimilated, in the hope that 

 Army classes at public schools may thereby be dis- 

 continued. This is a little unfortunate for Mr. Fawdry, 

 whose " Co-ordinate Geometry " is written for Army 

 candidates. But the book should prove quite suitable 

 for the general classes into which the Army classes 

 may be merged. Mr. Fawdry has the humanity to 

 insert one or two historical notes (pp. 29 and 75). They 

 are slight, but it is wonderful how much interest they 

 add to the reading. We should like to see more of 

 them. 



(9) One of the difficulties of the teacher of modern 

 elementary geometry is thedevising of life-like examples. 

 He will solve this difficulty if he gets Mr. Scott's text- 

 book on practical geometry. The text-book is meant 

 for young draughtsmen, and is full of such things as 



NO. 2740, VOL. 109] 



draughtsmen have to draw. The only general criti- 

 cism we would make is that, while Mr. Scott gives 

 clear instructions, he never justifies them, and we 

 cannot believe that rule of thumb is a good rule even 

 for draughtsmen. Chap. 8, about which the author 

 is a little apologetic, is rather out of place. It con- 

 tains some methods of constructing a " true length," 

 when plan and elevation are given. The chapter is 

 good in itself, but it stands at a different level from 

 the rest of the book. The subject should be either 

 left out or treated more fully. Standing alone, it 

 will not be understood by the majority of readers. 



H. B. H. 



Studies in Symbiosis.^ 



Tier und Pflanze in intrazellularer Symbiose. By 

 Prof. P. Buchner. Pp. xi + 462+Tafel 2. (Berlin : 

 Gebriider Borntraeger, 1921.) 114 mk. 



THE third section of Dr. Buchner's book deals 

 with the highly controversial thesis that 

 symbiotic bacteria are the cause of luminosity in 

 many insects and marine animals. In this discus- 

 sion, the author's critical faculty is at fault. He 

 does not set out clearly the opposing lines of 

 evidence nor does he do full justice to the work of 

 Dubois, the protagonist of the " enzyme-theory " of 

 animal luminosity. 



Briefly, the issue is between the enzyme and the 

 bacterial modes of light production. According to 

 Dubois and Newton Harvey (whose work was 

 reviewed in Nature, October 6, p. 174), luminous 

 animals contain two substances, one of which, when 

 oxidised in the presence of the other, gives rise to Ught 

 of an extremely " efficient " kind. The firefly's light 

 is the standard — the most efficient light known, so 

 far as the amount of light in relation to the expenditure 

 of energy is concerned. One of these substances is a 

 heat-stable, dialysable, oxidisable light producer, the 

 other is not heat-stable, is non-dialysable, and is ap- 

 parently a proteid. These substances are obtained 

 by " dissolving " whole animals or their phosphorescent 

 mucus in water or alcohol and precipitating with 

 ammonium sulphate. No attempts appear to have 

 been made to test the solutions for the presence of 

 bacteria. An aqueous emulsion boiled in 20 per cent, 

 hydrochloric acid for three hours retains the power 

 of producing light when added to a cold-water emulsion. 

 In the former the heat-stable " luciferin " has been 

 separated from the unstable catalyst " lucif erase," 

 while both are present in the cold-water extract. 

 The presence of the activator is necessary for light 



1 Continued from p. 539. 



