Chemistry and Physics. 65 



We have sought -to test the proposed theory with respect to 

 that law of optics which seems most conspicuous in its definite 

 mathematical form, and in the rigor of the experimental verifica- 

 tions to which it has been subjected, as well as in the magnificent 

 developments to which it has given rise: the law of double refrac- 

 tion due to Huyghens and Fresnel, and geometrically illustrated 

 by the wave surface of the latter. We cannot find that the law 

 of Fresnel is proved at all in this treatise. We find on the con- 

 trary, that a law is deduced which is different from Fresnel's, and 

 inconsistent with it. We do not refer to anything relating to the 

 direction of vibration of the rays in a crystal, which is a point 

 not touched by the experimental verifications to which we have 

 alluded. We shall confine our comparison to those equations 

 from which the direction of vibration has been eliminated, and 

 which therefore represent relations subject to experimental con- 

 trol. For this purpose equation (13) on page 299 is suitable. It 

 reads 



" 2 y 2 to 2 



i + rs — zs + -» — zr* = °> 



n £ , n y , n 7 _ being the principal indices of refraction. This the au- 

 thor calls the equation of the wave-surface or surface of ray- 

 velocities. It has the form of the equation of Fresnel's wave-sur- 

 face, expressed in terms of the direction-cosines and reciprocal of 

 the radius vector, and if u, v, w are the direction-cosines of the 

 ray, and n the velocity of light in vacuo divided by the so-called 

 ray-velocity in the crystal, the equation will express Fresnel's law. 

 But it is impossible to give these meanings to u, v, w and n. 

 They are introduced into the discussion in the expression for the 

 vibrations (p. 295), viz: 



ar n ft n(ux + vy + wz)\ 



p = %{ cos 27T ( — i — y — i y 



' \T X J 



The form of this equation shows that u, v, w are proportional 

 to the direction-cosines of the vmve-normal, and as the relation 

 w 2 + v 2 + te 2 = l is afterwards used, they must be the direction- 

 cosines of the wave-normal. They cannot possibly denote the direc- 

 tion-cosines of the ray, except in the particular case in which the 

 ray and wave-normal coincide. Again, from the form of this 

 equation, X/n must be the wave-length in the crystal, and if A here 

 as elsewhere in the book (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 di- 

 vided 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-veloci- 

 ty of the extraordinary ray and the angle of the wave-normal 



Am. Jour. Sci.— Third Series, Vol. XXXI, No. 181, Jan., 1886. 

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