128 Mr. Ihrschel on the Action of [Feb. 



III. On the Causes of these Phenomena, 



The developement of colour along the axis of double refrac- 

 tion is at first sight analogous to the production of the secondary- 

 tints along the axis of rock crystal, discovered by M. Arago, and 

 recently explained by M. Biot, in a masterly memoir communi- 

 cated to the Academy of Sciences, on the hypothesis of a force 

 inherent in its molecules independent of their state of aggrega- 

 tion, by which they communicate a rotation in an invariable 

 direction to the axes of polarisation of the luminous rays. And 

 this analogy is partially supported by the fact, that the tint deve- 

 loped along the axis descends in the scale of colour as the 

 thickness increases. 



A more scrupulous examination, however, will show, that its 

 origin must not be sought in any cause of this nature, for (not to 

 mention the impossibility of explaining the phenomena of the 

 virtual poles by this hypothesis) if we place the principal section 

 of the crystal in the azimuth zero, the extraordinary image will 

 be found to vanish completely for every angle of incidence, and 

 whatever be the thickness of the plate. I may add too that I 

 have in my possession a crystal of quartz, which exhibits with 

 tolerable distinctness in some parts the phenomena of two axes, 

 and the appearances produced by the interference of the secon- 

 dary tints in this specimen ; while they agree completely with 

 M. Biot's explanation, differ entirely from those which form the 

 subject of this paper. 



In either are the phenomena above described explicable on any 

 supposition of a peculiar action of the crystal on the differently- 

 coloured rays, analogous to its ordinary or extraordinary disper- 

 sive power, by which the periods of alternate polarisation of the 

 molecules of some colours, should be lengthened, and of others 

 contracted, so as to disturb that exact proportionality to their 

 periods of easy reflection, and transmission, which M. Biot has 

 proved to be a necessary condition for the production of the 

 tints of Newton's scale. It is true, such laws of action may be 

 imagined, and I shall presently show must really exist ; in all 

 crystals probably to a small extent, but in two instances at least, 

 to a surprising degree. But this alone will avail us nothing. To 

 show this, and at the same time obtain a general analytical 

 expression for the tint developed af any inclination, and for 

 every hypothesis of the action of the crystal on the differently 

 coloured molecules, let us denote by c the length of a complete 

 period of easy transmission and reflection, or the extent of one 

 pulse, on the undulatory hypothesis in vacuo, and at a perpendi- 

 cular incidence for any homogeneous ray, and let C denote its 

 colour and proportional intensity, or illuminating power, in the 

 prismatic spectrum. Then will the formula representing a beam 

 of white ligbt intromitted into the crystal, be 



C + C' + C' + &c. 

 from one end of the s]^ectrum to the other. 



