128 Astronomical and Nautical Collections. 



tions, than the hypothesis of emission, it has already enabled 

 us to adapt our calculations much more correctly to the 

 phenomena ; and this is one of the least equivocal proofs of 

 the truth of any system. When a hypothesis is true, it 

 must lead us to numerical relations between facts the most 

 different in their appearances: while a false hypothesis, on 

 the contrary, may represent very accurately the class of 

 phenomena from which it has been deduced, in the same 

 way that an empirical formula may represent a limited 

 number of results that have afforded it ; but it can never 

 trace the secret relations which connect these phenomena 

 with others of a totally different class. 



It was in this manner, for example, that Mr. Biot in- 

 vestigated, with as much sagacity as perseverance, the laws 

 of the beautiful phenomena of colours which Mr. Arago 

 had discovered in crystallized plates, and found that the 

 tints exhibited by them followed, with regard to their thick- 

 nesses, laws similar to those of the coloured rings already 

 known ; that is to say, that the thicknesses of two crystal- 

 lized plates of the same nature, which exhibited any given 

 tints, were in the same proportion as two plates of air, 

 which afforded similar tints in the production of coloured 

 rings. This relation, indicated by analogy, without any 

 regard to a particular theory, was without doubt very re- 

 markable and very important ; but Dr. Young advanced 

 much further, by means of the law of interferences, which is 

 an immediate consequence of the system of undulations. 

 He discovered a much more intimate relation between these 

 two classes of phenomena ; that is, that the difference of the 

 lengths of the paths of the rays ordinarily and extraor- 

 dinarily refracted, in the crystallized plate, is precisely 

 equal to the difference of the paths described by the rays re- 

 flected at the first and second surface of the plate of air that 

 exhibits the same tint as the crystal : and the phenomena, 

 instead of a simple analogy, are reduced to the predicament 

 of identity. 



I might add that the laws, so complicated in appearance, 

 of the phenomena of diffraction, which liad escaped all at- 

 tempts to detect them with the assistance of experiments, as 

 combined with the theory of emission, are perfectly con- 



