149 



we assume that each moleciiie describes an eUipse, the axes 

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



make 



^=:jocos(/), rjzzf^sin^, 



- __ (5/ _ ^), 



and consequently 



A| = p (sin 2B sin ^ — 2 sin ^0 cos <f), 

 Ar)— — g (sin 29 cos ^ + 2 sin W sin 0), 



where 6 — ^^, we shall find, by substituting these values in 

 A 



the equations (2), which must hold good independently of <p, 



«2-a' + c'/(-, 6-2 zzb'-^, (4) 



S/sin 29 - 2AS/« sin =0 = 0, 



2 

 2^ sin 26 + T S/« sin -0 = 0, 



wherein A- = - expresses the ratio of the semiaxes of the el- 



P 

 liptic vibration, and 



A' = 2^J|2/sin % B' z= |t, S5- sin W, 



0=:-^, S/* sin 20. 

 47r' 



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 Magazine. 

 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 investiga- 

 tions 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 

 any one had preceded him. It was, indeed, an obvious reflection, that these prin- 

 ciples, when generalised to the utmost, ought to include, not only the laws of 

 elliptic polarization, but (as really has been thought by M. Cauchy and his fol- 

 lowers) of dispersion and absorption, and, in short, of all the phenomena of optics. 



