November 27, 1902] 



NA TURE 



77 



on the subject that has emanated from Sheffield, is no 

 exception to the rule, though certainly better adapted for 

 steel-works chemists than for students. 



The book is divided into thirteen parts — the first four, 

 containing 185 pages, being devoted to the chemical 

 analysis of iron and steel and their alloys ; and the 

 succeeding five, comprising 45 pages, to the analysis of 

 refractory materials, slags, fuel, boiler water and scales. 

 These are of the greatest value. In the preliminary 

 summaries placed at the beginning of each section, a 

 general view of the various methods is given which will 

 be found extremely useful in aiding the chemist to decide 

 on his course of action in any particular case. The 

 methods are described carefully and in sufficient detail, 

 without needless repetition and with a freedom from 

 error which cannot be too highly praised. Especially 

 interesting are the pages devoted to rapid analysis at the 

 furnace. Cases arise, for example, in the preparation of 

 armour plates when the percentage of a number of ele- 

 ments must be determined while the charge of fused metal 

 is still in the furnace. "It will be a matter for surprise to 

 many analysts that an expert operator was found to 

 occupy only eight and a quarter minutes in the estima- 

 tion of manganese, and that twelve minutes is considered 

 enough for the estimation of silicon. 



Part x., dealing with the analysis of the alloys of 

 copper and the " white metals," is little less satisfactory 

 than the preceding parts, but the remaining sections show 

 a distinct falling-off from the high standard reached in 

 the earlier pages. The micrographic analysis of steel is 

 not well described. The lack of detail and some mis- 

 leading statements prevent the article from being of use 

 to a beginner, and an experienced worker will find 

 nothing here to help him, except in the bibliography, 

 which, unfortunately, stops short in the beginning of the 

 year 189S ! The illustrations are poor, perhaps owing to 

 the fact that most of them are not photographs, but merely 

 hand sketches, and the absence of reproductions of the 

 structures to be observed under high magnifying powers is 

 noticeable. The weakest part of the book, however, is the 

 meagre and unpractical account given of pyrometry, which 

 is not written by either Mr. Brearley or Mr. Ibbotson. Only 

 the Le Chatelierthermocouple is described, and the modern 

 forms of pyrometers in which it is used, as well as other 

 types of instrument, are either ignored or barely men- 

 tioned. A clumsy and inconvenient method of recording 

 the indications of the thermocouple is described, a 

 method which was devised some years ago and aban- 

 doned everywhere, unless it is still in use in Sheffield, 

 within a few months of its introduction. In future 

 editions, this section should be either omitted or revised 

 and extended. 



At the end, there is a valuable bibliography of papers 

 •on steel-works analysis, which occupies 139 pages and 

 seems to be fairly exhaustive. It is compiled by Mr. 

 Brearley, and includes papers which appeared up to the 

 ■end of 1 901. 



The book, in spite of its uneven merit, can be confidently 

 recommended. The publishers have done their part of 

 the work well in all respects. The authors write readable 

 English, with a touch of the vigour on which Sheffield 

 ,prides itself, manifested, for example, in a certain contempt 

 lfor what they are pleased to call "hoary asseitions." 

 NO. 1726, VOL. 67] 



LECTURES ON CELESTIAL MECHANICS. 

 Die Mechanik des Himmels. Vorlesungen von Carl 

 Ludwig Charlier, o. Professor an der Universitat 

 Lund. Erster Band. Pp. viii + 488 ; mit zahl- 

 reichen Figuren. (Leipzig : Veit and Co., 1902.) 

 Price Mk. 18. 



THE number of text-books on the subject of celestial 

 mechanics is by no means so large but that an 

 addition ought to be warmly welcomed. More especially 

 is this the case when the author is one who has himself 

 made many valuable contributions to this difficult branch 

 of analysis. Prof. Charlier's original work is characterised 

 by great clearness and, as far as possible, simpliciiy. 

 These qualities are not wanting in the lectures which he 

 I has delivered in the University of Lund since the 

 autumn of 189S, and of which a first volume is now pub- 

 lished. One cause for some regret may perhaps be 

 mentioned. Prof. Charlier has shown, in several papers 

 which he has recently published, that he can write excel- 

 lent English. It is a pity, from our point of view, that 

 in the case of his lectures he has preferred to publish in 

 German, for there does not exist in our language a work 

 of the same scope. Let it be said, however, that the 

 German is exceptionally simple and should cause little 

 difficulty to a reader whose knowledge of the language is 

 slight. 



The scheme of the lectures is to give a simple ex- 

 position of the present position of researches in 

 celestial mechanics, so far as the motions studied 

 do not depend on the dimensions and figures of the 

 celestial bodies. In the selection of his subject- 

 matter, the author's aim has been two-fold, namely, 

 to lay stress on the results of the greatest astro- 

 nomical importance and to illustrate the clearness and 

 elegance characteristic of modern methods of analysis. 

 The numerical examples which have been introduced for 

 the sake of the former object might, perhaps, have been 

 augmented with advantage. Prof. Charlier freely ack- 

 nowledges the incompleteness of his work, and finds an 

 explanation in the transition period in which astronomy 

 stands and in which it is difficult to distinguish what is 

 essential from what is unessential. The excuse is un- 

 necessary, for it would be unfair to expect a systematic 

 treatise in what does not pretend to be more than a course 

 of lectures. And as such the book will be found in- 

 teresting and suggestive, because it forms an intro- 

 duction to recent developments of theory which have in 

 many cases been accessible only in the original memoirs 

 themselves. 



The scope of the work will be best understood by a 

 brief glace at its contents. This first volume contains 

 the results of a more general character in the problems 

 of two and three bodies. It is divided into seven sec- 

 tions. The first section contains preliminary theorems 

 in pure mathematics and mechanics which would pro- 

 bably be familiar to the class of English reader who 

 would attempt to use the book. At least, this is so in 

 the case of paragraphs dealing, for instance, with the 

 theory of determinants, the properties of functional de- 

 terminants, linear substitution and Lagrange's equations. 

 Yet it is useful to have such theorems actually at hand 

 for reference, especially in a book which is genuinely 



