119 



we assume tlmt each niolecuje describes an ellipse, the axes 

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

 make 



and consequently 



A^ = p (sin '29 sin ^ — 2 sin '0 cos ^), 

 ^^—-q (sin '26 cos ^ + 2 sin W sin </>), 



where 6 - ""4^, we shall find, by substituting these values in 



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



s-'-a' + c'/c, s-'-yi'-j, (*) 



^/sin 20 - 2/:SA sin -Q = 0, 



2 

 ^g sin 20 + T SA sin "^9 - 0, 



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



P 

 liptic vibration, and 



a' = 2^U/si" % B' = ^, S- sin ^0, 

 c' =: :^ SA sin 20. 



cialion, 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 h.s fol- 

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



