September 13, 1917] 



NATURE 



a kno\vledg:e of pure chemistry this treatise will 

 prove an efficient guide to one of the most com- 

 plicated and technical branches of applied 

 chemistry. 



The introductory chapters deal with the history 

 of synthetic dyes and the nature of coal tar. It 

 is of interest to note how remarkably the nature 

 of tar varies with the temperature at which coal 

 is distilled. When produced at 400-500° C. the 

 tar is rich in volatile hydrocarbons, especially 

 paraffins, and is valueless for the colour maker. 

 At 900-1000° C. an optimum yield of aromatic 

 (benzenoid) compounds is obtained. Tar pro- 

 duced at the hig^her temperatures contains, 

 roughly, the following percentage amounts of im- 

 portant direct coal-tar products : — Benzene, 2 ; 

 toluene, 05; phenol, 06; naphthalene, 5-6; and 

 anthracene, 06. It is on these five substances, 

 together with two or three others obtained in even 

 smaller proportions, that the great synthetic colour 

 industry is based. 



Ten chapters are devoted to an explanation 

 of the chemical processes whereby the foregoing 

 direct coal-tar products are converted into inter- 

 mediate products, or "intermediates." Sufficient 

 theoretical matter is introduced into this section 

 to make the practical details readable and con- 

 nected. For example, the constitutions of 

 ■quinones and diazo-compounds are treated fully 

 because of their bearing on the structure of 

 organic dyes. 



The chapter on the application of dyes refers to 

 the dyer's classification of colouring matters into 

 acid, basic, mordant, direct cotton, vat, or sulphide 

 dyes. Concrete examples are given of each of 

 these groups of dyes with appropriate methods of 

 applying the colouring matters to the textile 

 fibres. 



A chapter on the colour and constitution of 

 dyes and coloured substances is followed by eleven 

 chapters devoted to the synthetic dyes classified 

 ■under their respective chromophores or charac- 

 teristic colour-bearing groups. 



One of the most informing of these sections is 

 the chapter on vat dyes. In this group we find 

 the oldest and newest colouring matters known to 

 dyers. Indigo and Tyrian purple were used by 

 the ancients, whereas the other indigoid dyes and 

 the anthraquinone vat and sulphurised vat dyes 

 liave all been discovered since the commencement 

 of the twentieth century. 



The last chapter describes the principal natural 

 dyes, a group of colouring matters which has 

 during the war regained a certain amount of its 

 former importance owing to the shortage of syn- 

 thetic dyes. 



The authors are fully alive to the national 

 Importance of establishing a British sphere of 

 Influence in dyes, and as an outward and visible 

 sign of this sentiment perhaps they might be per- 

 suaded to drop the inelegant expression "dye- 

 stuffs," obviously a literal translation of "Farl> 

 stoffe," in favour of such English terms as dyes, 

 colouring matters, • and dyewares. 



G. T. Morgan. 

 NO. 2498, VOL. 100] 



LUIGI CREMONA. 

 Opere Matematiche. ,Di Luigi Cremona. Tomo 



lerzo Pp. xxii+520. (Milano: Ulrico 



Hoeph, 1917.) Price Lire 30. 

 'T'HIS final volume of Cremona's collected mathe- 

 /• matical works contains thirty-six papers, 

 mcludmg the treatise on the general theory of 

 surfaces, the memoir on cubic surfaces, the tract 

 on reciprocal figures in graphical statics, and 

 various notes on birational transformations in 

 space. Prefixed thereto is a biographical notice by 

 Prof. E. Bertini, giving many interesting details 

 of Cremona's career. 



For many years Cremona was better known to 

 English readers than were the majority of foreign 

 mathematicians; and it is not difficult to give 

 reasons for the fact. So far as the geometry of 

 algebraic surfaces is concerned, he and Salmon 

 were kindred spirits ; and the latter gives numerous 

 references, in his "Solid Geometry," to Cremona's 

 investigations. 



Then the Clarendon Press published two ex- 

 cellent English translations of his "Elements of 

 Projective Geometry " and "Graphical Statics " at 

 a time when interest in these subjects had been 

 aroused by Henry Smith, Clerk Maxwell, and 

 others. Finally, Cremona's cast of mind and 

 style of composition could, and did, appeal suc- 

 cessfully to English mathematical taste. 



Perhaps Cremona's greatest achievements were 

 due to his superb qualities as a teacher and educa- 

 tionist. Though he lived until June 10, 1903, the 

 last of his mathematical papers appeared in 

 Proc. L.M.S. for 1884; and the reason was that 

 ► the Italian Government, recognising his value, 

 appointed him to posts of such importance as to 

 absorb all his energies. This is not the place 

 to estimate his services to the Italian system of 

 education ; but they were undoubtedly very great, 

 especially in such things as the courses given in 

 engineering. 



Cremona's ultimate rank as an original mathe- 

 matician will probably rest mainly on his dis- 

 coveries in the algebraical theory of birational 

 transformations; and it is not without justice 

 that the term " Cremona transformations " has 

 been adopted for the simplest class of them. 

 As developed by Nother and others, this theory 

 is of cardinal importance, both in analytical 

 geometry and in the theory of Abelian functions ; 

 and we may fairly say that Cremona was the 

 first to demonstrate its value and give brilliant 

 and orip^inal applications of it. As an exponent of 

 novel and comprehensive theories he displays 

 qualities of the very highest order. G. B, M. 



OUR BOOKSHELF. 

 Scientific Treatise on Smoke Abatement. By 

 H. Hamilton. Pp. xiiI+155. (Manchester: 

 Sherratt and Hughes, 1917.) Price 55. net. 

 It is a little unfortunate that the term " scientific " 

 should have been included in the title of this 

 book, seeing that the author is clearly more fami- 

 liar with the subject of mechanical engineering 



