700 Notices respecting JS'ew Books. 



The Analytical Theory of Light. By James Walker, M.A. 

 Cambridge ■University Press, 1904. 



The aim of this excellent treatise is " to give an account of 

 physical optics without having recourse to any hypothesis 

 respecting the nature of the influence that constitutes light or the 

 character of the medium in which it is propagated." In this 

 respect it resembles Lord Eayleigh's well-known article on Wave 

 Theory in the Encyclopaedia Britannica, and differs markedly from 

 Poincare's Theorie Mathematique cle la Lumiere, which builds on 

 elastic foundations, and from Drude's Optics, in which the 

 characteristic feature is the electron. It is well perhaps when our 

 imagination is being excited by whirls of charged corpuscles that 

 we should be recalled to what is essentially the original standpoint 

 of Presnel's theory. This is what Mr. Walker has done, and done 

 effectively and well. Nevertheless, although the notions under- 

 lying the electromagnetic theory of light have not been introduced 

 explicitly, the influence of this theory is shown in the particularizing 

 of two related quantities which the author calls the polarization- 

 vector and the light-vector. By use of these related vectors the 

 mathematical investigations are in many cases distinctly simplified. 

 It is obvious, indeed, that the author has taken full advantage of 

 the analytical methods which belong peculiarly to Maxwell's theory 

 without adopting the physical significance of the symbols used. 

 It might seem at first sight difficult to take account of the 

 phenomena of absorption and dispersion, without some distinct 

 understanding as to the nature of the dynamical link connecting 

 aether and matter. But a very general discussion of the facts of 

 absorption and dispersion suggests to the mathematician familiar 

 with workable functions that we have simply to introduce an 

 exponentially diminishing amplitude and a forced periodic 

 vibration ; and, behold, the deed is done. Similarly, when 

 Mr. Walker comes to treat of magnetically active media, he 

 obtains a sufficient basis for the mathematical representation by 

 introducing a suitable vector perpendicular to the magnetic force 

 and the polarization-vector. In a sense there may be no recourse 

 to an}^ ultimate hypothesis ; but the reader can hardly fail to see 

 the modern electromagnetic theory winking at him through the 

 lines and symbols of the fundamental equations. Nevertheless, 

 the author has to an interesting degree kept wondrously clear of 

 definite theoretical assumptions as to the inner nature of sethereal 

 and molecular processes. The treatment is instructive as showing 

 how far we can go in coordinating phenomena without committing 

 ourselves to a definite physical theory. In regard alike to the 

 experimental illustrations chosen to make the argument intelligible 

 as well as to the analytical methods employed, the book is thoroughly 

 up to date ; and all students of optical theory will welcome it as a 

 valuable addition to our scientific literature. 



