Febbuabt 11, 1910] 



SCIENCE 



223 



Chapters III. and IV. are devoted to an 

 extended discussion of the Zeeman effect and 

 of the propagation of light in a body com- 

 posed of molecules. In concluding, the au- 

 thor remarks on the inadequacy of the theory 

 in its present state, and cites the experiments 

 of Wood on sodium vapor, and those of 

 Humphreys and Mohler indicating the shift- 

 ing of spectral lines by pressure, as beyond 

 the power of the present theory to explain. 



In chapter V. optical phenomena in moving 

 bodies are considered. Fresnel's classical 

 work in this connection is reviewed, likewise 

 Stokes's theory of aberration with Planck's 

 well-known amendment. The theory of elec- 

 trons is applied to the deduction of Fresnel's 

 eoefScient. The Michelson-Morley experiment 

 is discussed, and its negative results explained 

 on the assumption of the Fitzgerald-Lorentz 

 shortening effect. The negative results of 

 Eayleigh and of Brace in looking for double 

 refraction due to the Fitzgerald-Lorentz short- 

 ening effect are explained on the author's the- 

 ory of corresponding states for a fixed and mov- 

 ing system. Abraham's results on the energy 

 of a moving electron are discussed. The ques- 

 tion of form of the moving electron is also con- 

 sidered; and the difficulty is brought out of 

 reconciling the rigid spherical electron of 

 Abraham, or the electron deformed by motion 

 into an ellipsoid having the original volume, 

 proposed by Bucherer and by Langevin, with 

 the experiments of Rayleigh and of Brace on 

 double refraction in moving bodies. The au- 

 thor's well-known electromagnetic equations 

 for a moving system are derived, and the in- 

 terpretation which has been given to his re- 

 sults by Einstein in the theory of relativity 

 is clearly brought out. 



Even the non-mathematical reader will not 

 find unusual difficulty in reading this book. 

 For the text itself is devoid of intricate mathe- 

 matical proofs. Those who are interested in 

 following through the analysis involved in the 

 demonstrations of the formulae employed in 

 the text are referred at the appropriate times 

 to the mathematical notes at the end of the 

 book. Throughout, the reader meets with the 

 usual clear methods of exposition so charac- 



teristic of all the author's writings. The book 

 is in English and published by the firm of 

 B. G. Teubner, Leipzig. 



A. P. Wills 



Taschenhuch filr Mathematiher und Physiher. 

 Unter Mitwirkung von Fr. Auerbach, O. 

 Knopf, H. Liebmann, E. Wolffing, u. A. 

 herausgegeben von Fellx Auerbach. 8vo, 

 pp. xliv -j - 450. Leipzig und Berlin, Teub- 

 ner. 1909. 6 Marks. 



While the chemists, astronomers, engineers 

 and other professional orders have long pos- 

 sessed pocket manuals for handy reference, a 

 similar convenience has not been provided for 

 mathematicians and physicists. The present 

 little volume supplies this want in a consid- 

 erable degree, and compresses into a small 

 space a remarkable mass of useful informa- 

 tion. The " Taschenhuch " will be issued an- 

 nually, with constant variation of subjects 

 treated so as to cover eventually as wide a 

 range as may be desirable. The first volume, 

 for 1909, has been delayed by circumstances 

 incident to a new undertaking, but future is- 

 sues are expected to appear early in each year. 

 A brief notice of Kelvin's work, accom- 

 panied by a portrait, opens the volume. There 

 follow a calendar for the year 1909, several 

 useful tables of astronomical, geographical 

 and other constants, and four-place tables of 

 logarithms, trigonometric and hyperbolic 

 functions, squares and Bessel functions. 

 These conclude the introduction, pages i-xliv. 

 The body of the manual is divided between 

 Mathematics, pages 1-160; Mechanics, pages 

 161-203; Physics, pages 204-350, and General 

 Chemistry, pages 351-369. Later come lists 

 of mathematical and physical journals and of 

 recent publications, a necrology, the roll of 

 teachers in the higher German institutions of 

 learning and a good index of the volume. 



Subjects reserved for treatment in later is- 

 sues are indicated in the text. Under Mathe- 

 matics are at present included the fundamen- 

 tals of arithmetic, theory of numbers, algebra, 

 determinants, theory of groups, infinite series, 

 differential and integral calculus, definite 

 integrals, differential equations, calculus of 



