III. On the Plane and Angle of Polarization of Light Reflected at the surface of a 

 Crystal. By The Rev. P. KELLAND, A.M., F.R.SS. L. $ E., late Fellow of 

 Queen's College, Cambridge ; Professor of Mathematics, fyc. in the University 

 of Edinburgh. 



(Read 7th December 1840.) 



THE present Memoir is, to a certain extent, a continuation of one which the 

 author presented to the Society in December 1838, and which has since been 

 published in the thirteenth volume of the Transactions. Other motives, however, 

 than the desire of completing the subject, have influenced him in producing the 

 following analysis. A very important point in the hypothetical conditions which 

 FRESNEL assumed to hold with respect to polarized light, has, of late, been warmly 

 combated, in various quarters. FRESNEL supposed that light polarized in a given 

 plane consists of vibrations of such a nature that the motion is perpendicular to 

 that plane. NEUMANN and other writers contend that the very opposite is the 

 fact. We hope to be able to offer evidence of some little weight in favour of the 

 former view ; at the same time we do not pretend to shew the actual impossibi- 

 lity of the truth of the latter. 



Our limits will admit only of a very slight sketch of the history of the theory 

 of Reflexion. In connection with the experimental discovery of the laws of crys- 

 talline reflexion, we have only to mention the names of BREWSTER and SEEBECK, 

 and to refer to their papers.* 



Dr T. YOUNG gave formulae which represent the intensity of light reflected 

 directly at a non-crystallized surface.f This demonstration was amended by 

 POISSON.^ Next, FRESNEL gave his attention to the problem in two memoirs 

 which appear in the Annales de Chimie.f His solution is based on the folio wing 

 hypotheses :-!. The vibrations of polarized light are transversal and perpendi- 

 cular to the plane of polarization. 2. The density of the ether within a refracting 

 medium is greater than that without. 3. The law of vis vita holds good. 4. The 

 resolved parts of the motion without the crystal are the same, parallel to the 

 common surface of separation, as those within. The first of these hypotheses is, 

 in part, different from that of YOUNG, || and has been attacked by BLANCHET, 



* Brewsterj Ph. Tr. 1819, p. 145. Report of Brit. Ass. vol. vi., Trans, of Sect. p. 13. Seebeck, 

 Annalen der Physik, vol. xxi. pp. 309, 289, vol. xxii. p. 126, and vol. xl. p. 462. 

 t Encyc. Brit. art. Chromatics. 



\ See Annales de Chimie, vol. xvii. p. 189, and 1815. 

 Vol. xvii. pp. 191, 312; also vol. xlvi. p. 225. 

 || Whewell, Hist, of the Ind. Sc. vol. ii. p. 417. 

 VOL. XV. PART I. L 



