NATURE 



457 



THURSDAY, MARCH i6, 1905. 



MODERN OPTICAL THEORY. 

 All Introduction to the Theory of Optics. By Prof. 

 A. Schuster, F.R.S. Pp. xv + 340. (London: 

 Edward .Arnold, 1904.) Price 155. net. 

 OROF. SCHUSTER has done excellent service 

 ^ to teachers and students alike by publishing 

 this book, which fills a very obvious gap. It is an 

 introduction to the theory, and purposely does not deal 

 with details of methods of measurement or instru- 

 mental appliances ; these are properly left to courses 

 of laboratory • instruction. .At the same time the 

 necessity for experiments and observations is every- 

 where present to the author's mind. The book is not 

 .1 mere mathematical treatise on simple harmonic 

 motion ; indeed, the analysis is generally easy, and 

 purely mathematical difficulties are avoided. Prof. 

 .Schuster writes as a physicist. The physical meaning 

 of the steps and processes employed is everywhere 

 insisted on, and the student is made to think through- 

 out. 



The stand]X)lnt of the author is best explained by 

 two short extracts from his preface. .After stating 

 that the elastic solid theory of optics as developed 

 in England by Green and Stokes has proved 

 insufficient, he continues, 



" Those who believe in the possibility of a mechani- 

 cal conception of the universe, and are not willing 

 to abandon the methods which from the time ot 

 (ialileo and Needham have led uniformly and ex- 

 clusively to success, must look with tlie gravest 

 concern on a growing school of scientific thought 

 which rests content with equations correctly repre- 

 senting numerical relationships between different 

 phenomena, even though no precise meaning can be 

 .iltached to the sj'mbols used." 



And again, 



" The equations which at present represent the 

 electromagnetic theory of light have rendered 

 excellent service, and we must look upon them as a 

 Iramework into which a more complete theory must 

 necessarily fit, but they cannot be accepted as 

 constituting in themselves a final theory of light. 



" The study of physics must be based on a 

 knowledge of mechanics, and the problem of light 

 will only be solved when we have discovered the 

 mechanical properties oi the ether. While we are 

 in ignorance on fundamental matters concerning the 

 origin of electric and magnetic strains and stresses, 

 it is necessary to introduce the theoretical study of 

 light by a careful treatment of wave propagation 

 through media the elastic properties of which are 

 known. A study of the theory of sound and of the 

 old elastic solid theory of light must precede there- 

 lore the introduction of the electromagnetic equations." 



The book proceeds on these lines ; the first part is 

 almost entirely kinematical ; the second part deals with 

 theories of light, starting first from an analysis o.' 

 the equations of motion of an elastic medium ; then 

 passing to those of the electromagnetic field, and 

 developing the two theories side by side as far as 

 possible. 



To turn now to some details. In the earlier 

 ch.qner^, in accordance with the views expressed in 

 NO. 1840, VOL. 7 1I 



the preface, the author deals with the properties of 

 vibrating mechanical systems, e.g., the air in a 

 closed space, or a stretched string. After some dis- 

 cussion as to periodic motion in general, the equation 

 of motion for an elastic body, propagating plane 

 waves of distortion, is found in an elementary 

 manner, and certain fundamental results are shown 

 to follow from its similarity to the equation for a 

 stretched string. Huyghens' principle of the super- 

 position of small motions is explained, and then the 

 reader, after a chapter on the nature of light, is 

 introduced to the principle of interference. 



The problems of diffraction are treated verv fully, 

 making use of the method of Fresnel's zones; the 

 method is modified by the author in a manner which 

 permits numerical results of a high order of accuracy 

 to be obtained without the introduction of Fresnel's 

 integrals. 



.After an interesting chapter on diffraction gratings 

 we come to one on the theory of optical instruments, 

 in which the resolving power of telescopes and 

 spectroscopes is carefully discussed. The theory of 

 the microscope does not find a place in Prof. 

 Schuster's book; perhaps it belongs rather to the 

 domain of geometrical optics. 



Fresnel's theory of double refraction is given very 

 fully, and it is based not on any unsound dynamical 

 reasoning, but on the ob.served experimental fact 

 that the velocities of wave propagation of a plane 

 wave moving through a crystal are given by the 

 axes of the section of a certain ellipsoid by the plane 

 of the wave; this is clearly the right way to deal 

 with this problem. When the laws of the propaga- 

 tion of light in a crystal are once determined the dis- 

 cussion of the rays and brushes due to the interfer- 

 ence of polarised light follows easily, and thus we are 

 led to Part II., which, a.s has been already said, deals 

 with theories of light. 



The equations of motion are found both on the 

 elastic solid and electromagnetic theory, and the 

 simpler phenomena are considered from both stand- 

 points. 



The weak points of the elastic solid theory, how- 

 ever, soon manifest themselves, and for the rest of 

 the book the equations of the electromagnetic theory 

 are mostly used; in dealing with dispersion 

 Sellmeyers' hypothesis of sympathetic vibrations is 

 applied to the electrons of a molecule, following 

 Drude, and the usual expression connecting the 

 refractive index and the frequency obtained ; the same 

 method is applied to explain the rotatorv effects of 

 sugar and other active substances, and in a most 

 interesting series of sections the Zeeman and other 

 allied effects are dealt with. In the last chapter 

 we have a discussion on the nature of light as the 

 resultant disturbance arising from the individual 

 vibrations of the molecules of the source. Enough 

 has probably been said to show the nature of the 

 book, but one characteristic should not be omitted. 

 Prof. Schuster has included short historical accounts 

 of the men who have made the science of physical 

 optics. .Among them we find the names of Young, 

 Fresnel, Cauchy, Stokes, and Maxwell; the interest 



X 



