66 Scientific Intelligence. 



with the principal axis the same as that of the radius vector and 

 the angle in an ellipse. The law of Huyghens and Fresnel makes 

 the reciprocal of the wave-velocity stand in this relation. 



The law which our author has deduced has come up again and 

 again in the history of theoretical optics. Professor Stokes (Re- 

 port of the British Assoc, 1862, Part I, p. 269) and Lord Ray- 

 leigh (Phil. Mag., IV, xli, p. 525) have both raised the question, 

 whether Huyghens and Fresnel might not have been wrong,. and 

 it might not be the wave-velocity and not its reciprocal which is 

 represented by the radius vector in an ellipse. The difference is 

 not very great, for if we lay off on the radii vectores of an ellipse 

 distances inversely proportional to their lengths, the resultant 

 figure will have an oval form approaching that of an ellipse 

 when the eccentricity of the original ellipse is small. Rankine 

 appears to have thought that the difference might be neglected 

 (see Phil. Mag., IV, i, pp. 444, 445), at least he claims that his 

 theory leads to Fresnel's law, while really it would give the same 

 law which our author has found. (Concerning Rankine's " splen- 

 did failure," and the whole history of the subject, see Sir Win. 

 Thomson's Lectures on Molecular Dynamics at the Johns Hop- 

 kins University, Chap, xx.) Professor Stokes undertook experi- 

 ments to decide the question. His result, corroborated by Glaze- 

 brook, (P. R. S., xx, p. 443; Phil. Trans., clxxi, p. 421,) was that 

 Huyghens and Fresnel were right and that the other law was 

 wrong. 



• To return to our author, we have no doubt from the context 

 that he regards u, v,w, and n as relating to the ray and not to the 

 wave-normal. We suppose that that is the meaning of his re- 

 mark that the expression for the vibrations (quoted above) is to 

 be referred to the direction of the ray. It seems rather hard not 

 to allow a writer the privilege of defining his own terms. Vet 

 the reader will admit that when the vibrations have been expressed 

 in the above form an inexorable necessity fixes the significance of 

 the direction determined by u, v, 10, and leaves nothing in that 

 respect to the choice of the author. 



The historical sketches of the development of ideas in the theory 

 of optics, enriched by very numerous references, will be useful to 

 the student. An exception, however, must be made with respect 

 to the statements concerning the electro-magnetic theory of light. 

 We are told (p. 450) that the English theory founded by Maxwell 

 and represented by Glazebrook and Fitzgerald, makes the plane of 

 polarization coincide with the plane of vibration, while Lorentz, 

 on the basis of Helmholtz's equations comes to the conclusion that 

 these planes are at right angles. Since all these writers make the 

 electrical displacement perpendicular to the plane of polarization, 

 we can only attribute this statement to some confusion between the 

 electrical displacement and the magnetic force or 'displacement ' 

 at right angles to it. We are also told that Glazebrook's ' sur- 

 face-conditions ' which determine the intensity of reflected and 

 refracted light are different from those of Lorentz, — a singular 



