FRESNEL ON DOUBLE REFRACTION. 239 



hypothesis, and prevented them from reading his treatise on 

 Light with the attention which it deserved. 



Amongst modern philosophers, Mr. Young is the first who 

 suspected the law of Huygens to be correct : it was by his ad- 

 vice that Dr. Wollaston verified it by numerous and precise 

 experiments. Scarcely was the result of these experiments known 

 in France, when Mains occupied himself with the same re- 

 searches, and found, as Dr. Wollaston had done, the law of 

 Huygens in perfect numerical accordance with all the measures 

 given by observation. M. de Laplace, considering double 

 refraction in the emission-point of view, made a skilful applica- 

 tion of the principle of least action to the calculation of the ex- 

 traordinary refraction. He found that the motion of the lumi- 

 nous molecules undergoing this refraction might be explained 

 by supposing them to be repelled by a force perpendicular to 

 the axis of the crystal^ and proportionate to the square of the 

 sine of the angle which the extraordinary ray makes with this 

 axis : whence it follows that the difference between the squares 

 of the velocities of the ordinary and extraordinary rays is pro- 

 portional to the square of the same sine. 



This result is only the translation of Huygens's law into the 

 language of the emission system. The calculations of M. Laplace 

 have not thrown any light on the theoretical question ; for they 

 do not show why the repulsive force emanating from the axis 

 should vary as the square of the sine of the inclination of the 

 extraordinary ray to this axis ; and it is extremely difiicult to 

 justify this hypothesis by mechanical considerations. 



In fact, the same polarized ray undergoes the ordinary or ex- 

 traordinary refraction in a rhomboid of calcareous spar, according 

 as its plane of polarization is parallel or perpendicular to the 

 principal section of the crystal ; it must be then the lateral 

 fronts of the beam, or the parallel faces of the luminous mole- 

 cules composing it, which alone determine, by the difference of 

 their properties or physical relations, the nature of the refraction ; 

 two of these fronts must be subject to the repulsive influence of 

 the axis, and the two others insensible to it. We must suppose 

 also the same absence of action on the anterior and posterior 

 faces of the luminous molecules, since on simply turning the ray 

 round itself, and without changing the direction of these latter 

 faces, we withdraw it from the repulsive power of the axis. But 

 the lateral faces of the luminous molecules are not less exposed 

 to the repulsive force emanating from the axis and acting per- 



