Astronomical and Nautical Collections, 185 



other rays differs in general very little from this. And if we 

 compare the thickness of the plate with the difference of the 

 paths thus formed, we may compute from it the difference of 

 the velocities of the ordinary and extraordinary rays. 



With this apparatus, Mr. Arago and myself made an ex- 

 periment on a plate of rock crystal parallel to the axis ; and 

 the result of our measurements gave us the same difference 

 in the velocities of the ordinary and extraordinary rays 

 as Mr. BioT had found by direct observation of the diver- 

 gence of their rays in prisms of the crystal. Mr. Biot's 

 method is equally accurate with ours, when it is required 

 to determine the refraction of crystals which have great 

 powers of separation, such as carbonate of lime, rock 

 crystal, and sulfate of lime : but the method furnished 

 by diffraction is far preferable for substances in which the 

 difference is less sensible : for if we take a pretty thick 

 plate, we can determine the difference of the velocities of the 

 two kinds of rays with a degree of accuracy almost unlimited ; 

 and it is not even necessary that the plate should have any 

 considerable thickness, in order that a very high degree of 

 accuracy may be attained : for it is easy to perceive a differ- 

 ence of one-fifth of an undulation, that is, of four millionths of 

 an inch, in the lengths of the two paths. The same experi- 

 ment might be applied equally well to the purpose of veri- 

 fying, in the most delicate manner, the law of Huygens, as re- 

 lating to rays passing very nearly in the direction of the axis. 



The agreement, thus obtained, between our results and 

 those of Mr. Biot, is sufficient to show the multiplicity of 

 relations which the principle of interference establishes be- 

 tween those phenomena of optics, which appear at first sight 

 to be the most diversified in their nature. 



We have supposed the rays of light to be polarised in 

 the same manner in these crystalline plates as in the thickest 

 crystals, that is to say, that the rays which are transmitted 

 by the ordinary refraction are polarised in the principal 

 section, and the others in a direction perpendicular to it. 

 This hypothesis, deduced from the most direct analogy, ought 

 not to be abandoned, unless it were found to be in positive 

 contradiction with the phenomena j and, in following the 



