78 



NA TURE 



[November 27, 1902 



elementary in the sense that no excessive demands are 

 made on the reader's knowledge at the outset. Here is 

 introduced the canonical form of equations which is 

 destined to play a predominant part in the sequel, and 

 earlier is a sketch of the theory of linear differential 

 equations with periodic coefficients as developed by 

 Hermite, Floquet and Poincare. 



In the second section, the partial differential equation 

 of Jacobi is discussed and Stackers important theorem 

 on the possibility of solving it by separating the variables 

 is given. This leads to the consideration of motions 

 determined by one degree of freedom, and in particular 

 of forms of motion termed "Libration" and "Limita- 

 tion," the latter being of the nature of Poincare's asym- 

 ptotic solutions. An account follows of conditionally 

 periodic motions, based on the researches of Staude. 



The third section treats of the motion of a particle 

 attracted by two fixed Newtonian centres of force. This 

 problem provides illustrations of the theory of the previous 

 section. Otherwise it is a little inconsistent with the 

 practical aim of the author, for its astronomical interest, 

 as was frankly admitted by Lagrange, is very slight. A 

 reference might here have been made to Prof. Green- 

 hill's paper on the stability of such forms of motion 

 (Proc. Lond. Math. Soc, vol. xxii.). 



The problem of two bodies is treated in some detail in 

 the fourth section, the Hamilton-Jacobi equation being 

 made the basis of the discussion. The case of a repul- 

 sive force is also discussed, and this leads to a digression 

 on the dynamical theory of the tails of comets. 



The most important results in the general problem of 

 three bodies are investigated in the fifth section. The 

 general integrals and the different forms which they 

 assume when expressed in different systems of co- 

 ordinates are discussed. The method of variation of 

 parameters is explained in conjunction with Jacobi's 

 canonical elements and also in connection with relative 

 coordinates. The chief results of Jacobi's classical 

 memoir on the elimination of the nodes and of Laplace's 

 theory of stability are given here. Finally, the equations 

 of the problem are reduced to the form expressing four 

 degrees of freedom. 



The rest of the book is devoted to the theory of per- 

 turbations. In the sixth section, Poincare's system of 

 canonical elements is introduced, the form of the de- 

 velopment of the disturbing function is described and a 

 very brief sketch of Laplace's coefficients is given. The 

 final section contains the theory of secular perturbations 

 of a planetary system, which is treated in some detail. 

 At the end of the volume will be found some useful 

 numerical tables. 



The second volume is promised for next year. It will 

 contain the theory of periodic orbits in the problem of 

 three bodies and researches on the convergence of 

 series. H. C. P. 



OUR BOOK SHELF. 

 Lexikon der Kohleiisloff- Vcrbindungen. By M. M. 



Richter. Pp. 2482. (Hamburg : Leopold Yoss, 1899.) 



Price, 39 parts, 1.S0 marks each. 

 NOTHING could illustrate more forcibly the rapid growth 

 of organic chemistry than the increased dimensions of 

 the new edition of Richter's " Tabellen der Kohlenstoff- 



NO. 1726, VOL. 67] 



Verbindungen," published in 1884, whichmow appears for 

 the first time under the title of " Lexicon." 



The first edition, the publisher tells us, accounted for 

 16,000 compounds ; in the present volume, which is 

 brought down to the first quarter of 1S99, 67,000 com- 

 pounds are described, so that in fifteen years organic 

 chemistry may be said to have multiplied more than four- 

 fold. It is not surprising to learn that the stupendous 

 labour of collecting and arranging this enormous mass 

 of material has taken ten years to complete. 



The lexicon contains all the known carbon compounds, 

 arranged in order of their molecular formula; on an in- 

 genious system, which is fully set forth in the introduc- 

 tion. The name and a few physical constants are given, 

 but the chief information is contained in the very full" 

 references to the original literature and to Beilstein's well- 

 known " Handbuch.'' Since the first edition of the book 

 appeared, the nomenclature of the Geneva Commission 

 has been introduced, and in many cases the new and the 

 old names appear side by side. 



There is also an index of the names of the different 

 compounds at the end of the volume. 



Where organic research is being pursued with the 

 almost feverish rapidity which is in.vogue, more especially 

 in the German laboratories, involving in the process the 

 production of many compounds, both old and new, it is 

 easy to understand the time and trouble which might 

 be expended in fixing the identity of these compounds. 

 One object of the lexicon is to lighten the labours of 

 the investigator in this direction. 



This becomes more imperative where the number of 

 isomerides is large, for it is not uncommon to meet with 

 50, 60, or even 100 substances with the same molecular 

 formula. For example, an experimenter who happened' 

 in the course of his research to obtain a compound of the 

 formula CjH^O,, would be confronted with a choice of 

 59 substances among compounds already known. By 

 reference to the lexicon, he would see from the 

 physical properties whether the compound had already 

 been prepared, or, failing this, he could at once refer to 

 the literature on the subject. 



Richter's "Tabellen" is sufficiently well known among 

 chemists and its utility long enough proved to ensure an. 

 excellent reception for the new edition and to render 

 superfluous any further description of its use or its- 

 merits. 



The author complains (and who does not) of the- 

 present system, or lack of system, of chemical nomen- 

 clature. 



Organic chemistry has, in fact, outgrown its mother- 

 tongue. It can no longer express itself clearly in the 

 language of its childhood. An attempt was made by the 

 Geneva Commission of 1892 to introduce reforms, and 

 some excellent proposals were made, and have since been 

 to some extent adopted on the continent. The author 

 adds, "it is and remains deplorable, the fact that the 

 resolutions arrived at at Geneva have no prospect of 

 being generally adopted." It is to be hoped that before 

 many more thousands have been added to the still 

 growing number of organic compounds, the confusion 

 which is rapidly impending through the want of a uni- 

 versally recognised system of nomenclature will be 

 averted by a complete and thorough revision, more 

 especially of the names of ring compounds. 



J. B. C. 



Ueber Harmonie und Complicaiio?i. By "Dr. Victor 

 Goldschmidt. Pp. 136; with 28 figures. (Berlin: 

 Julius Springer, 1901.) Price 4 marks. 

 Many attempts have been made to associate the forms 

 occurring in music with forms which manifest themselves 

 to senses other than that of hearing. If the term 

 "harmony" is used to include all such groupings and 

 arrangements as give us pleasure, then we have harmonies 



