500 Mr. R. H. M. Bosanquet on the 



If the light thus polarized, with known values of (/>, be exa- 

 mined with a glass-bundle polarimeter, it is possible to express 

 experimentally the inclinations of the glass bundle in terms of cf>, 

 where cos 2<j) is the numerical measure of the polarization. This 

 is Rubenson's method. The change of sign corresponds con- 

 veniently with the expression " positive " or " negative " pola- 

 rization. 



Now Brewster's measure of polarization is R, defined by the 

 relation R = 0-45° (Ed. Trans, xxiii. 233, Phil. Trans. 1830, 

 136) . Hence the polarization indicated by R is cos 2(45°+ R), 

 or, disregarding sign, sin 2R; so that R = 45° represents com- 

 plete polarization, R — common light. If the polarization 

 were negative, it would be represented by negative values of R. 



Brewster's normal value of the maximum zenith polarization 

 is about 30° ; and he notices that the horizontal polarization at 

 right angles to the sun (minimum maximorum) is somewhat 

 less. 1 have not been able to find out how he got from the 

 observations the constants he employs in either case ; but they 

 represent the observations very fairly. We are now able to enter 

 on the method employed by Brewster for the construction of his 

 maps. It is explained, both in the text in Keith Johnston and 

 in the Philosophical Magazine, 1847, vol. xxxi. p. 451, where 

 a slightly different version is given ; so there is no room for 

 doubt that the procedure about to be described was that actually 

 employed. 



First was considered the section of the sky in the plane of zenith, 

 sun, observer, the normal positions being as given above, and 

 the maximum polarization being about 30°. This distribution 

 was represented by the expression 33J° sin D sin D', where 

 D, D' were the angular distances from the two neutral points. 



In the zenith (where D=D'=^- 18° 30') this gives 30J o nearly. 



The law of variation was not in any way determined; but the 

 expression gives the required value in the zenith, and vanishes 

 at the neutral points. 



Having regard to sign, this expression represents the distri- 

 bution of polarization in the plane of sun, zenith, and observer 

 sufficiently well, except that we shall see reason to believe that 

 the polarization must vanish at the sun and antisolar point. 

 But it is necessary to make the convention that D, D' shall be 

 taken negative when reckoned in the direction opposite to the 

 zenith. The following figure shows more clearly what is meant ; 

 the dotted lines represent negative, the continuous line represents 

 positive polarization. 



