170 Professor Powell on certain points 



For elliptically polarized light, on the hypothesis of sym- 

 metrical distribution, we can follow out results analogous to 

 those above obtained. We should have instead of the form 



(21.), 



n'^h = ?« S [p2sin-^]; (57.) 



and instead of (25.), 



71^ h = m 2 [p' 2 sin'^ 6], (58.) 



which is identical with the former, whence we have p = p' ; 

 also, 



71' = ^- 2 [p 2 sin2 6]. (59.) 



The formula (27.) is thus reduced to 



sin b - § (60.) 



Thus (although with altered values) the formula for elliptic 

 polarizatio7i is a solution of the original equation equally in 

 the form (10.) (11.), and when reduced to the form {55.) 

 (56.) by the hypothesis o^ sy7n7netrical distrihUio7i. In other 

 words, of the equations, in the form (10.) (11.), the formula for 

 elliptic polarization is the only solution: in the form {55.) 

 (56.) the formulas for elliptic vibrations or i-ectilinear in- 

 differently are solutions. 



(8.) Thus it follows, that if we suppose the setherial mole- 

 cules imsymmetrically distributed, then elliptic polarizatio7i 

 alo7ie is the result, ^tlier so constituted can7iot adi7iit recti- 

 linear vibralio7is. Light, therefore, entering such a portion of 

 a-ther necessarily becomes elliptically polarized. 



If we suppose the molecules symmetrically distributed, this 

 is compatible with either elliptic or rectilinear vibrations in- 

 differently. Either therefore will be propagated according 

 to the condition of the intromitted ray. 



Thus elliptic polarization is traced to its cause in the simple 

 consideration that the vibrations which constitute it are neces- 

 sarily produced when waves are propagated through any 

 portion of aether in which a symmetrical arrangement of the 

 molecules does not subsist. 



The investigation conducted by Mr. Tovey's method*, is di- 

 rected to showing by the equations (4.) of his paper, that when 

 the sums involving the odd powers of the differences are 7iot 

 evanescent, the quantities b and p (the ratio of the semiaxes of 

 the ellipse) are defenni7iaie ; or, in other words, the expressions 

 must belong to ellipses, or in a medium so constituted as to 

 make those sums finite, elliptical polarization will result. When 



• L. & E. Phil. Mag. and Journal of Science, vol. xii, p. 10. 



