COLOURS OF CRYSTALLINE PLATES. 133 



section of the crystals ; and that the results differ from those pro- 

 duced by thick crystals only in this, that the two pencils are 

 superposed.* The light resulting from the union of these oppositely 

 polarized pencils has, in certain cases, the properties ascribed to it 

 in the theory of M. Biot ; but these properties are immediate and 

 necessary consequences of the laws of interference of polarized 

 light, and of the theory of transversal vibrations. 



Let us now inquire what account the wave-theory furnishes 

 of the same phenomena. A ray of light on entering a crystalline 

 plate is divided into two, or, in the language of the wave-theory, 

 a series of waves incident upon the crystal is resolved into two 

 within it, which traverse it in different directions and with different 

 velocities. One of these sets of waves, therefore, will lag behind 

 the other, and they will be in different phases of vibration at 

 emergence. When the plate is thin, the emergent waves are 

 superposed ; and as the retardation will then amount only to a few 

 undulations and parts of an undulation, it would appear that we 

 have here all the conditions necessary for their interference, and 

 the consequent production of colour. Such was the sagacious 

 conjecture of Young. And indeed, shortly after the publication 

 of the first researches of M. Biot on the laws of the tints for 

 different thicknesses, it was observed by Young that these tints 

 corresponded accurately to the interval of retardation of the two 

 pencils ; so that they were manifestly due to interference, f This 

 correspondence is now made out in the fullest manner. It is an 

 easy consequence of Fresnel's theory of double refraction, that the 

 interval of retardation of the two pencils, in traversing a crystal- 

 line plate, is nearly proportional to the length of their path within 

 the crystal multiplied by the product of the sines of the angles 

 which their directions make with the two optic axes ; and as this has 

 been found to be the general measure of the tint, it follows that 

 the forms of the isochromatic curves the lemniscates and the 

 circles, are all necessary consequences of the wave-theory. 



* See Report made to the Academy of Sciences, in 1821, on the memoir of Freanel 

 relative to the colours of crystallized plates, Annalea de Chimie, torn. xvii. Indeed, a 

 more obvious objection to M. Biot's theory may be drawn from the fact which he has 

 himself observed ; namely, that the phenomena of colour may be produced by crottmg 

 two thick plates of nearly the same thickness, although the thickness in each was 

 sufficient to furnish two images sensibly separated, and therefore having a Jljctd 

 polarization. 



f Quarterly Rn'icic, vol. xi. 



