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XXIX. Researches in the Undulatory Theory of Light, con- 

 tinued ; on the Elliptical Polarization jn-oduced hy Qiiartz. 

 Part I. By J. Tovey, Esq. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



AT the conclus^ion of my paper on the Cause of the Ellip- 

 tical Polarization of Light, (L. and E. Phil. Mag., vol. 

 xii. p. 10,) I stated that I intended to apply my formulae to 

 the case of this phenomenon produced by quartz crystal. 

 The fulfilment of this intention has been long delayed ; but 

 I now proceed to the subject. 



In the first place it is needful to put the last four of the 

 expressions (3.), of the paper referred to, into a more con- 

 venient form, thus : by the rules of trigonometry, 

 1 — cos ^" A .r = vers ^ A ^ , 



and 



cos {kAx—b) — cos 6 = — cos b vers k A/' + sin b sm k A x, 

 cos {k Ax + b) — cosb = — cos b vers k Ax ~ sin b sin kAx, 

 sin (k A x—b) + sin Z» = + sin b vers k A x + cos & sin /: A ^, 

 sin {kAx + b) — sin Z> = — sin b vers kAx + cos Z> sin A' A x ; 



hence if we put 



m X.'\i{r) AyAzyetskAx = (T , ,^^. 



m 2.'^ (>•) Ay Az s'm k Ax = v' , ^ '' 



the expressions referred to will become 



— (T cos 6 + 0-' sin 5 = Sg, 



— 0- cos b — 0-' sin Z» = s'oj (\\ \ 

 <r' cos 6 + cr sin 5 = 53, 



<t' cos b — <T sin b = s'.^. 

 Now the third and fourth p( the equations (-i.)* give 

 $1 s\ = S3 s'a ; hence s, s, = cr'^ cos® b'—a- sin" b, and therefore 



cos«=±^5^^. (12.) 



The third of the equations (4.), and the value of s'g in (11.) 



g've p = ^ ^-r. (13.) 



' 0-' cos b — <T sm b 



Let cos b and —cos b denote the two values of cos 6 given 

 by (12.) ; these values will afibrd, by (13.), two correspond- 

 ing values of g, which denote by §j and g,, • ^^w either pair 

 of these values satisfies the conditions of the problem ; hence 



• The equations numbered from (1.) to (9.) inclusive, are in the former 

 paper. 



