60 G. S. Hastings — Double Refraction in Iceland Spar. 



Art. V. — On the law of Double Refraction in Iceland Spar / 

 by Charles S. Hastings. 



The law of double refraction in uniaxial crystals, first dis- 

 covered by Huygliens, was supposed for a time to be defini- 

 tively established by Fresnel's deriving it from principles of 

 molecular mechanics. It was soon recognized, however, that 

 a fundamental hypothesis in his reasoning does not bear criti- 

 cal inspection ; namely, that the elastic forces brought into 

 play by distortions due to the passage of waves are the same 

 in kind as those produced by the displacement of a single par- 

 ticle. In short, Fresnel assumed that the velocity of a light 

 wave is independent of the direction of propagation and de- 

 pends only upon the direction of vibration. There have been 

 many notable efforts to get rid of this difficulty in the theory 

 of double refraction by a general treatment. Cauchy, Mac 

 Cullagh, Neumann and Green are those whose names are most 

 closely connected with the interesting history of investigation 

 in this field of mathematical physics. All of these investiga- 

 tions have the feature in common, that the natural interpreta- 

 tion of the equations makes the direction of vibration in plane 

 polarized light lie in the plane of polarization. To adapt the 

 solutions to the contrary assumption, which is almost certainly 

 the only one which can be reconciled to the known phenomena 

 of optics, requires the most artificial restrictions in the rela- 

 tions of the constants involved. By such forced interpreta- 

 tions of formulas having a large number of constants, it is 

 possible to derive a law for double refraction, even in Ice- 

 land spar, which does not differ from Huyghens's construc- 

 tion by an amount discoverable by observation ; but an agree- 

 ment between observation and theory extorted in this way can- 

 not be regarded as satisfactory. 



Intimately bound up with this question of double refrac- 

 tion is the question as to whether the differing velocities of 

 light in vacuum and in a dense medium are due to differing 

 densities or differing rigidities. Of these two views, equally 

 probable d priori, only the first can possibly be brought into 

 agreement with the observed phenomena of reflection. But 

 in the case of a velocity of propagation dependent on the di- 

 rection of wave-motion, which is the case of double refract- 

 ing media, the difficulty is to conceive of a density as dependent 

 upon direction. Rankine made the ingenious suggestion that 

 this difficulty might be avoided by assuming that the mole- 

 cules of a crystalline solid move in a frictionless fluid, and 

 thus that their effective masses might depend upon the direc- 

 tion of motion. The special interest of this view from our 



