Notes on some Points in the Theory of Light. 203 



we assume that each molecule describes an ellipse, the axes of 

 which are parallel to those of x and y\ that is to say, if we 

 make 



= p cos 0, TJ = q sin 0, 



(3) 



2ir , ^ . 



= y (* - ), 



and consequently, 



A =^) (sin 26 sin - 2 sin 2 cos 0), 

 ATJ = - q (sin 20 cos $ + 2 sin 2 sin 0), 



where = -^-, we shall find, by substituting these values in the 

 A 



equations (2), which must hold good independently of 0, 



s 2 = A' + C'k, s z = B' - ^-, (4) 



K 



S/sin 26 - 2k SA sin 2 = 0, 



o 

 S# sin 20 + 7- SA sin 2 = 0, 



Jv 



Tlie equations (2) are precisely the same as those which have teen employed 

 hy Mr. Tovey and by Professor Powell, the latter of whom, in his lately published 

 work, entitled, "A General and Elementary View of the Undulatory Theory, as ap- 

 plied to the Dispersion of Light, and other Subjects," has dwelt at great length on 

 the theory of elliptic polarization which they have been supposed to afford, and 

 which he regards as a most important accession to the Science of Light. Professor 

 Powell has also made some communications on the subject to the British Asso- 

 ciation, and has written two Papers about it in the Philosophical Transactions 

 (1838, p. 253 : and 1840, p. 157), besides several others in the Philosophical Ma- 

 gazine. He, however, always attributed this theory of elliptic polarization to 

 * Mr. Tovey, until his attention was directed, by a letter from M. Cauchy, to some 

 investigations of the latter which he had not previously seen (Phil. Mag. VOL. xix. 

 p. 374). Mr. Tovey set out with the principles of M. Cauchy, and therefore 

 naturally struck into the same track, in pursuit of the same object, apparently 

 quite unconscious that anyone had preceded him. It was, indeed, an obvious 

 reflection, that these principles, when generalized to the utmost, ought to include, 

 not only the laws of elliptic polarization, but (as really has been thought by M. 

 Cauchy and his followers) of dispersion and absorption, and, in short, of all the 

 phenomena of optics. 



