Polarization of the Light of the Sky. 499 



consequently of Brewster's point, appears to be of extreme 

 difficulty. 



Brewster himself has occasionally seen a fourth neutral poiut 

 in the neighbourhood of the antisolar point; and there exist 

 isolated observations of other points. But for the present pur- 

 pose it will be sufficient to consider the three above named, as 

 they stand on quite a different ground as to evidence from the 

 others, and they are those on which Brewster founds his dis- 

 cussion. 



Brewster assumes for his normal positions : — sun in horizon ; 

 altitude of Arago (above horizon opposite sun) = altitude of 

 Babinet (above sun) = depression of Brewster (below sun) 

 = 18° 30'. Of course Brewster's point would not really be 

 visible under these circumstances ; but it is assumed that that 

 would be its position if it were visible, for the sake of obtaining 

 a normal configuration. I may here say that I have not been 

 able to find out how Brewster determined this value 18° 30'. 

 I attribute a certain weight to it, and to the assumption that 

 the points are symmetrically situated (under normal circum- 

 stances of course), as representing Brewster's opinion on points 

 of fact; but I cannot get the number, or the symmetry, out of 

 the observations. My impression is that he assumed the sym- 

 metiy, which no doubt exists, at all events as a rough approxi- 

 mation, and then took some sort of mean of all the observations. 

 For the present I retain Brewster's numbers, as they afford a con- 

 venient presentation of the principal point at issue, and are, in 

 all probability, subject to the assumptions made, not very wide 

 of the truth. 



Measure of polarization. — Brewster employs a peculiar mea- 

 sure of the polarization of partially polarized light, founded on 

 a hypothesis which, I suppose, few now remember*. Referring 

 to Phil. Trans, vol. cxx. p. 76, we see that Brewster's <f> is what 

 I shall call " the polarimeter angle." 



We may remark that if a ray of polarized light is decomposed 

 by a doubly refracting quarter-wave plate cut parallel to the 

 axis, into elliptically polarized light, then, if </> be the angle be- 

 tween the principal section of the plate and the plane of polariza- 

 tion, the intensities of the components of the principal vibrations, 

 according to Malus's law, will be A 2 sin c/> 2 and A 2 cos 2 $ ; and 

 if we put 



,., . . . Difference of principal intensities 



r olanzation= — 5 — — ^ — ~ — = — r-r— t-. > 



Sum of principal intensities 



we have 



t> i • cos 2 cf> — sin 2 (f> , 



Polarization = — g-r ^r = cos *9» 



cos^cp -f surtp 



* Phil. Trans. 1830, pp. 69, 133. 

 2 K2 



