392 



NATURE 



[September 30, 1909 



templated by the author, but his decease prevented 

 its production ; and the present work is to be re- 

 garded as a substitute. It is a translation of Heil 

 and Esch's " Handbuch der Gummiwarenfabrika- 

 tion," adapted for Enjjlish usage in respect of the 

 machinery generally employed in this country. 



Non-technical readers may be reminded that crude 

 rubber as imported contains a number of impurities — 

 water, woody tissue, sand, and other mineral matter. 

 Moreover, it is unvulcanised, and to fit it for diverse 

 uses various " filling " substances must be incor- 

 porated with it. The process of manufacture consists, 

 therefore, in the purification of the raw material ; 

 the mixing of this with ingredients which will impart 

 the required colour, durability, or other special 

 property to the article ; the fashioning of this plastic 

 mixture into tyre, tube, or whatever finished article 

 as desired; and lastly, the vulcanisation of the object 

 ■with sulphur, or chloride of sulphur, whereby the 

 rubber becomes non-adhesive, harder, and more 

 •durable. 



The authors give the plan and arrangement of a 

 factory for the carrying out of these operations in 

 what they consider to be the most advantageous 

 manner. They direct special attention to the necessity 

 for excluding dust in the making-up of rubber goods, 

 since leaky seams are liable to develop in goods if 

 particles of dust are allowed to settle on the edges 

 of the article during the joining process. Another 

 point to which they direct attention is the necessity, 

 after the rubber has been washed free from admixed 

 impurities, of drying it in a rational way. Far too 

 little regard is had to this important detail. The large 

 surface-area exposed favours atmospheric oxidation 

 of the moist, warm rubber, and the time of exposure 

 should therefore be as short as practicable. On the 

 ■other hand, if the material is imperfectly dried, goods 

 made from it are liable to rapid deterioration. To 

 ■dry it thoroughly, quickly, and safely is the desidera- 

 tum ; and the authors describe modern drying-rooms 

 and centrifugal plant adapted to this purpose. While 

 not recommending any one method as the best in 

 ■all circumstances, they discuss the general principles 

 involved, and plead for an intelligent application of 

 them. 



The necessity for avoiding undue "working" or 

 kneading of the dried rubber is also insisted upon. 

 Not only does it increase the expense, but the quality 

 suffers deterioration thereby. True, " rubber sub- 

 stance " is regarded as a mixture of polymerised 

 hydrocarbons, and too much kneading results in a 

 presumed depolymerisation of a portion of the 

 material, with consequent injury to the texture. 



A number of examples are given illustrating the 

 composition of " mixings " for making different 

 kinds of rubber articles; and the machinery for work- 

 ing and calendering the mixtures is described at 

 some length. 



As regards vulcanisation, it is a remarkable fact 

 that the processes still used are carried out essentially 

 in the same wSy as when first introduced, some 

 seventy years ago, by Goodyear, Hancock, and 

 Parkes. The details, of course, differ with the differ- 

 NO. 2083, VOL. 81] 



ent factories ; and the empirical methods evolved are 

 guarded as trade secrets. In fact, so perfectly has 

 long experience developed the rule-of-thumb indica- 

 tions that the authors think scientific investigation 

 can hardly result in any noteworthy revolution in the 

 methods of manufacture. It may be so; but this 

 is not quite the spirit in which progress is made. 

 A few years ago indigo-planters would have said 

 much the same thing.. 



Many illustrations accompany the text, which is 

 generally lucid, though occasionally with a leaning 

 to Teutonic stolidity. Except in this respect, the 

 translator has eliminated any lingual indication of 

 the origin of the book, which can be recommended 

 as a very practical and useful work. C. S. 



VECTOR ANALYSIS. 

 Vector Analysis: an Introduction to Vector-methods 

 and their Various Applications to Physics and Mathe- 

 matics. By Dr. J. G. Cofifin. Pp. xix + 248. (New 

 York : John Wiley and Sons ; London : Chapman 

 and Hall, Ltd., 1909.) Price lox. 6d. net. 



THIS " Introduction to Vector-methods and their 

 Various Applications to Physics and Mathe- 

 matics "is an exposition of the late Willard Gibbs' 

 vector analysis. The author in his preface warns us 

 that " no attempt at mathematical rigor is made " — 

 which perhaps explains the opening sentence of 

 chapter i. : " A vector is any quantity having direction 

 as well as magnitude." What of finite rotations? 

 Are thev not to be considered quantities having direc- 

 tion and magnitude? In an appendi.x the author 

 compares notations, not always quite accurately. He 

 believes Willard Gibbs' notation to be the simplest 

 and most symmetrical of any of the existing kinds. 

 Burali-Forti and Marcolongo, who believe they have 

 devised the perfect notation, object to Willard Gibbs's 

 " dot " in the scalar product, using a " cross " 

 instead. As regards the question of symmetry, the 

 truth is that the vector product is not symmetrical, 

 for in Gibbs's notation axb=— bxa. As a matter of 

 fact each vector analyst can always find sufficiently 

 self-pleasing arguments in favour of his pet notation. 



Notation apart, the book is well put together, and 

 lays stress on many important applications in 

 dynamics, elasticity, hydrodynamics, electricity, and 

 magnetism. The differential operator v> in its 

 Gibbsian phase, is developed in considerable detail. 

 But will non-Hamiltonian vector analysts never realise 

 how much they lose by working with what is not, after 

 all, the real Hamiltonian operator? By discarding the 

 associative law in vector products they lose the flexi- 

 bility of the real v. Pages of definitions would be 

 saved by a simple return to Hamilton and Tait; and 

 not only so, but the mind of the student would be freed 

 from the task of committing to memory the laws of the 

 equivalent operators as used by Gibbs, Heaviside, Gans, 

 Jahnke, Biicherer, Fiippl, Burali-Forti and Marco- 

 longo, &c. In the exercises at the end of chapter v. we 

 notice two mistakes. In exercise (4) we are told that 

 r.(axr) = 2a, where a is the length of the vector a. 

 In quaternions this is SvVap, But vVop = 2a, a 



