NA TURE 



[May I, 1890 



tion and use of the microscope; especial attention being 

 given to forms of the instrument, like those devised by 

 Nachet and by the author of this work, for the special 

 purpose of studying crystallization and other physical and 

 chemical processes. 



The second division of the book treats of those phy- 

 sical properties of matter which are presented by all 

 bodies, whether in the solid, liquid, or gaseous state. 

 Such questions as the polarization and absorption of 

 light, the conduction of heat, and the electric and mag- 

 netic relations of various substances are here dealt with 

 by the author. 



The next division relates to the peculiar properties 

 presented by solids. Elasticity and plasticity are con- 

 sidered, and, under the latter head, the remarkable phe- 

 nomenon of the production of twinned structures in 

 crystals by mechanical means is fully discussed. Under 

 the head of cleavage we find a treatment of such pheno- 

 mena as the production of mathematical figures in certain 

 crystals by pressure, percussion, '«&c. ; while under the 

 heads of " Enantiotropie " and " Monotropie " are classi- 

 fied the consequences which follow from heteromorphism 

 among crystalline substances, and the tendency of the 

 heteromorphous forms to pass one into the other. 



The division dealing with liquids and their peculiar 

 properties contains discussions on fluidity, surface- 

 tension, diffusion, capillarity, and crystal-growth, with 

 the origin of structural anomalies. The problems of 

 solution and precipitation, with those of solidification 

 and fusion, are also treated of in this part of the treatise. 

 The second volume of the work commences with the 

 discussion of the properties of gases and their relations 

 to solids and liquids. This division of the subject, which 

 is very exhaustively treated, extends to 335 pages. 



The work concludes with critical remarks upon dif- 

 ferent molecular theories. The chapters dealing with the 

 theories of crystal structure, of allotropy, of heteromorph- 

 ism, and of isomerism, with several others, in the same 

 division of the book, are full of interest and suggestive- 

 ness. 



A supplement of about 150 pages is devoted to what 

 the author calls " crystal-analysis," or what is generally 

 known to geologists and mineralogists as " microchemical 

 analysis." Very minute particles of an unknown sub- 

 stance may often be determined by being treated with 

 appropriate reagents and studied under the microscope ; 

 in this way they are made to yield crystals of various 

 compounds which can be recognized by their charac- 

 teristic forms and habit. An admirable summary is given 

 by the author of the work of Boricky, Streng, Behrens, 

 Haushofer, and others, who have gradually perfected this 

 branch of research, and made the method one which is 

 of the very greatest service to the students of micro- 

 scopical mineralogy and petrography. 



While the physicist and chemist will find in this work 

 a perfect mine of interesting and ingenious experiments 

 {many of which are suited to class-demonstrations by 

 projection methods), the mineralogist and geologist will 

 hail the appearance of the book as one that completes 

 and supplements the well-known treatise of Vogelsang — 

 a work that has exercised the most important influence 

 on the development of petrological theory. 



In conclusion, it may be pointed out that, not only are 



the numerous observations of the author on crystallo- 

 genesis that are described in memoirs in GrotKs Zeit- 

 schrift included in the work before us, but many others 

 that have never before been published find a place in these 

 volumes. The work is very fully illustrated both with 

 woodcuts and coloured plates, and constitutes a complete 

 synopsis of all that is known on a number of questions 

 of great importance and interest to workers in many 

 different branches of science. 



BERTRAND ON ELECTRICITY. 

 Le^otis sier la Theorie Mathdmatique de L'Electricite, 

 profess^es au College de France. Par J. Bertrand. 

 (Paris : Gauthier-Villars.) 



THIS book contains lectures on electricity given by 

 M. Bertrand at the College de France. In his 

 preface the author states that he has confined himself to 

 the mathematical principles of the subject ; but this hardly 

 expresses the limitation he has imposed upon himself, 

 for a great many results which English students of elec- 

 tricity are accustomed to find in text-books on this sub- 

 ject are omitted from this work. A brief description of 

 the contents of the book will suffice to show this. The 

 first chapter contains an investigation of the attractions 

 of spheres and spherical surfaces when the law of attrac- 

 tion is inversely as the square of the distance ; the second 

 and third are devoted to the properties of the potential ; 

 the fourth contains an investigation of the conditions under 

 which the method of lines of force can be used ; the fifth, 

 which has the comprehensive title " Electricite Statique," 

 contains a short discussion of the electrical distribution 

 on two spheres which mutually influence each other, the 

 reciprocal theorems, and a discussion of the properties of 

 the Leyden jar so far as they can be discussed without 

 introducing the idea of specific inductive capacity ; the 

 sixth chapter contains some remarks upon magnets ; the 

 seventh treats of Ohm's law, and contains Kirchhoff's 

 equations for the distribution of currents amongst a net- 

 work of conductors, without, however, any applications 

 even to such an important case as that of Wheatstone's 

 bridge ; the eighth, ninth, and tenth chapters contain, 

 respectively, investigations of the magnetic forces pro- 

 duced by linear currents, the laws according to which 

 such currents act on each other, and simple applications 

 of these laws ; the eleventh chapter contains some ac- 

 count of the induction of currents, and, amongst other 

 things, some well-founded reasons for not deducing the 

 laws of induction from the principle of the conservation 

 of energy alone, but no hint is given of the possibility of 

 i regarding a system of currents as a dynamical system, 

 \ though the introduction of this idea by Maxwell has 

 i thrown new light over the whole subject and enabled ,; 

 many of the properties of currents to be recognized at 

 once as those belonging to any dynamical systems ; thie ^ 

 twelfth chapter contains some account of the application 

 j of the results of the previous chapters to dynamo-electric 

 machines ; and the thirteenth and last chapter discusses '• 

 units. 



There are two views which have been taken as to the 

 relation between the mathematics and the physics, which 

 ought to exist in a text-book on mathematical physics : ,^ 

 the one is, that it is the province of physics to supply the * 





