April 8, 1922] 



NATURE 



435 



intermediate liquefaction. But intermediate lique- 

 faction may be induced by pressure. If, therefore, the 

 process be effected under pressure, liquefaction will 

 occur and the substance will ultimately boil, although 

 on cooling the vapour may pass directly to the solid 

 state. The conditions under which distillation and 

 sublimation become identical operations were first 

 explained by James Thomson, though even now the 

 triple point pressures of only a few substances are 

 accurately known. Indeed, there is ample room for a 

 more extended investigation on the relation of this 

 factor to the other thermal constants of a body. The 

 author describes very shortly a few typical cases of 

 sublimation, such as iodine, sulphur, arsenious oxide, 

 and ammonium chloride, with illustrations of the plant 

 employed, and explains the principles involved in the 

 several instances. As these are not usually indicated 

 in text-books, the attention of teachers may well be 

 directed to them. 



The second section of the book, dealing with certain 

 technical and large-scale operations of distillation, 

 occupies about half the volume, and the examples 

 selected for description have been entrusted to chemists 

 with practical experience of their working. They 

 comprise : 



(i) Distillation of Acetone and «-Butyl Alcohol 

 on the Manufacturing Scale. By Dr. Joseph Reilly 

 and the Hon. F. R. Henley. 



(2) Distillation of Alcohol on the Manufacturing 

 Scale. By the Hon. F. R. Henley and Dr. Reilly. 



(3) Fractional Distillation as applied in the Petroleum 

 Industry. By James Kewley. 



(4) Fractional Distillation in the Coal-Tar Industry. 

 By Dr. T. Howard Buller. 



(5) The Distillation of Glycerine. By Lieut.-Col. 

 E. Briggs. 



(6) The Distillation of Essential Oils. By Thos. H. 

 Durrans. 



These, it will be seen, comprise all the main 

 technical processes with which British chemists, at 

 least, are concerned. 



Considerations of space preclude any detailed account 

 of these several sub-sections. The descriptions are 

 such as will appeal to the chemical engineer or works- 

 manager. They are concise, and deal mainly with the 

 practical aspects of the various processes, and the 

 illustrations — chiefly in the form of line-drawings — of 

 the plant employed, will commend themselves to those 

 actually interested in the different industries. There 

 is, as might be anticipated when several writers are 

 concerned with the application of the same physical 

 principles, a certain amount of repetition and over- 

 lapping. This is unavoidable, and is not to be depre- 

 cated even although these matters are adequately dealt 

 NO. 2736, VOL. 109] 



with in the theoretical section of the work. Their 

 restatement, in fact, is required in any adequate 

 account of their bearing upon the particular technical 

 process described. 



The book is remarkably free from typographical 

 errors, and we have noticed only a few mistakes — 

 mainly in the spelling of proper names : thus Speyer 

 (p. 29) should read Speyers, and Dufton (p. 138) is 

 erroneously printed Dutton. The work indeed is a 

 credit to all concerned in its production, and well 

 sustains the position it already holds as the chief 

 authority on the subject of distillation. In its present 

 extended form it affords an admirable illustration of the 

 benefits which follow the intelligent application of 

 physical principles to chemical processes on a manu- 

 facturing scale. 



Mathematical Analysis. 



(i) The Theory of Functions of a Real Variable and 

 the Theory of Fourier's Series. By Prof. E. W. 

 Hobson. Second edition, revised throughout and 

 enlarged. Vol. i. Pp. xvi + 671. (Cambridge: At 

 the University Press, 1921.) 45^. net. 



(2) Introduction to the Theory of Fourier's Series and 

 Integrals and the Mathematical Theory of the Con- 

 duction of Heat. By Prof. H. S. Carslaw. Second 

 edition, completely revised. Vol. i, Fourier's Series 

 and Integrals. Pp. xi + 323. (London: Macmillan 

 and Co., Ltd., 1921.) 30^. net. 



(3) A Treatise on the Integral Calculus, with Applica- 

 tions, Examples, and Problems. By J. Edwards. 

 Vol. I. Pp. xxi + 907. (London: Macmillan and 

 Co., Ltd., 1921.) 505. net. 



(i) '' I ''HE first edition of Prof. Hobson's treatise 

 A fell naturally into two parts. The first 

 five chapters were occupied with the theory of aggre- 

 gates, the general theory of functions, and the theory 

 of integration, while the last two dealt with the theory 

 of series, and in particular with Fourier's series. It 

 is the first five chapters which have developed into 

 the present volume. It was inevitable that a great 

 deal of the book would have to be rewritten, for the 

 theory has developed very rapidly ; there was a mass 

 of recent research to be incorporated, and much of 

 the older work has been definitely superseded. The 

 preparation of a new edition must have been a very 

 long and heavy piece of work, and Prof. Hobson is 

 to be congratulated on the progress he has made with 

 so formidable a task. 



There is a singular contrast between the two great 

 branches of the theory of functions. The complex 

 theory has always been popular. The power of its 

 weapons is obvious ; its methods have a striking, if 



