o22 Mr. Tovey on the Elliptical Polarizatioii 



plcme of polarization is turned by the passage of the light 

 through the crystal. It is well known that different varieties 

 of quartz turn the plane of polarization in different directions, 

 the crystals being called right-handed or left-handed accord- 

 ingly. 



We now proceed to investigate the forms assumed, within 

 the crystal, by the surfaces of waves diverging from any given 

 point of it. Suppose the coordinates .r, ?/, z, to originate at 

 the (riven point, which denote by O ; from O conceive a line 

 O X, to be drawn parallel to the axis of the crystal, and let 

 the axes of x, y, z, be denoted by O x, O y, O z. Take O x^. 

 Ox, Oy, in the same plane, and suppose the molecules to be 

 so arranged that the system of coordinates may be turned on 

 the axis Ox, without affecting the values of the sums (16.) ; 

 then, by art. 4, vol. ix. p. 421, B^ will vanish, as we have 

 supposed, and the values of v^', v^-, will be expressed, ap- 

 proximately, by the equations (18.). Hence we may take 

 A, - Ag /-/ — p, sin b . B, k^ , 





The equations (12.) and (13.) give 



^'~ (t' cos b-a- sin y (29.) 



s, 



' ^ 0-' cos b + a- sin b ' 

 and therefore, since s, sj = o"'^ cos" i — tr"^ sin- b, (pres. vol. 

 page 169,) we find 



P>P. = - % ■■ (30.) 



hence, by supposing s, nearly equal to s/, we have 



PjP2 = — 1, nearly; (31.) 



which, by (28.) gives 



v^ — v^ = A, — A/, nearly. (32.) 



If we were to leave out of each of the equations (28.) the 

 two last terms, which are comparatively very small, these 

 equations would coincide with (3.) of article 6, vol. ix. p.422; 

 whence it follows that the investigation comprised in the ar- 

 ticles 6 — 12, of that paper, would apply to the present case, 

 and, consequently, the forms of the surfaces of diverging, or 

 converging, waves are nearly the same in quartz as in an or- 

 dinary mineral crystal. This is confirmed by experiment. 



It has been shown, in the investigation just referred to, 

 that the waves diverging from the point O will consist of two 



