THEOBETISCHE OPTIK. 251 



(see p. 25) denotes the wave-length in vacuo of light of the period 

 considered, which we doubt not is the intention of the author, n must 

 be the wave-length in vacuo divided by the wave-length in the 

 crystal, i.e., the velocity of light in vacuo divided by the wave-velocity 

 in the crystal. With these definitions of u, v, w, and n, equation (13) 

 expresses a law which is different from Fresnel's. Applied to the 

 simple case of a uniaxial crystal, it makes the relation between the 

 wave- velocity of the extraordinary ray and the angle of the wave- 

 normal 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 (Report 

 of the British Assoc., 1862, part i, p. 269) and Lord Rayleigh (Phil. 

 Mag., (4), vol. 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., (4), vol. 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 "splendid failure," and the whole history of the subject, see 

 Sir Wm. Thomson's Lectures on Molecular Dynamics at the Johns 

 Hopkins University, chap, xx.) Professor Stokes undertook experi- 

 ments to decide the question. His result, corroborated by Glazebrook 

 (Pro. Roy. Soc., vol. xx, p. 443; Phil. Trans., vol. 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 remark 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. Yet 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, w, 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 



