100 Dr Seebeck on the polarizing angles 



The index of refraction is the tangent of the angle of pola- 

 rization ; or according to his other mode of expressing it. 

 When the polarization is complete, the reflected ray forms a 

 right angle with the reflected ray. Dr Brewster arranges his 

 measurements in a table which contains the following: eighteen 

 substances, viz. air, water, Jluor-spar, obsidian, bird-lime, sul- 

 phate of lime, rock crystal, opal coloured glass, topaz, mother- 

 of-pearl, Iceland-spar, orange coloured glass, spindle ruby, 

 zircon, glass of antimony, sulphur, diamond, chromate of lead. 

 By comparing the observed with the calculated angles of po- 

 larization, he found that the difference varied from -f- 25' to 

 — 32', the sum of the eighteen positive differences being 85/ 

 and that of the negative ones 174/, which does not seem incon- 

 siderable when we consider that the observed property is the 

 mean of a number of observations. 



These differences are, nevertheless, not to be ascribed to ac- 

 cidental mistakes of observation, for the table contains six or 

 seven doubly refracting bodies ; and Dr Brewster has himself 

 shown in a later memoir in the Philosophical Transactions for 

 1819, that in this class of bodies the angle of polarization va- 

 ries with the inclination of the reflecting surface to the axis of 

 the crystal. These variations, indeed, are so considerable, that 

 they explain the cause of many more glaring differences than 

 those in the table referred to. 



With respect to a particular class of singly refracting sub- 

 stances, viz. the glasses, Dr Brewster found very considerable 

 deviations from the law of the tangents ; but he regards them 

 as only apparent exceptions, as he found that they were ow- 

 ing to chemical alterations on the surface, which changed the re- 

 fractive power of the surface without changing that of the re- 

 maining mass, so that the angle of polarization observed on the 

 surface cannot correspond to the refractive power of the mass. 



It is evident, therefore, that in such cases the angle of po- 

 larization should be measured on newly polished surfaces of 

 glass ; but Dr Brewster does not say that he has made any ex- 

 periments of this kind. 



Under these circumstances, it did not seem to me superflu- 

 ous to resume the inquiry, limiting it to singly refracting sub- 

 stances, and directing my attention particularly to the surfaces 



