84: Mr. J. 0. McConnel on the 



horizon (except exactly in the line AB) is more or less 

 polarized in a horizontal plane. Hence the resultant of all 

 this subsidiary light is slightly polarized in a horizontal plane. 

 The case is not very different when AB is inclined somewhat 

 downwards. As to the strength of this residual polarization 

 I shall have something to say later. 



Since the imperfection of the polarization at the maximum 

 point is due to light reaching the particles from the earth and 

 sky, yve ought to find a great effect produced, as Loi'd 

 Eayleigh has suggested, by the presence of snow on the ground. 

 Again, at high altitudes above sea-level, owing to the dark- 

 ness of the sky, the polarization should be more perfect. 

 During the past year, having been resident for the most 

 part at tolerably high altitudes, I have taken a good many 

 measures of the maximum polarization with the object of 

 examining these two points. Though the measures are 

 rough, they are, I feel sure, free from large error. This is 

 more than I can say for any other measures of the kind 

 that I have come across, as I shall now explain. 



Criticism of Brewster's and E.ubenson's Measures. 



The most extensive series of measurements on record are 

 those of Brewster and Eubenson. Both used a pile of thin 

 glass plates, tilted at such an angle as to depolarize the sky 

 light, and tested the depolarization with a Savart polariscope. 

 Brewster * seems to have relied on the formula : — 



Ratio of principal intensities after passing through plates 



= cos^"(fc—t') X ratio before entering, where n is the 



number of plates, and tc' are the angles of incidence 



and refraction. 



This can be readily derived from Fresnel's expressions for 



the refraction of polarized light, but it only applies to the 



portion of light that is refracted directly through the plates. 



Besides this there are other portions, twice reflected, four 



times reflected, &c. which ultimately get through the plates. 



* Phil. Mag. Aug. & Sept. 1865. Brewster does not fully describe in 

 these two papers how he calculated the polarization from the readings 

 of his polarimeter. He refers to other articles which I have not had 

 the opportunity of looking up. But a little further on he quotes a 

 formula equivalent to the above (with a misprint of ?i for 27i) without 

 any reservation. Besides he obtained values of the polarization which 

 are quite extravagant. He uses the measure R where tan^ (45° — R) = ratio 

 of principal intensities, which I call r. At mid-day on June 10th, 1841, 

 at St. Andrews, he found R = 30^° j whence r='07. While to judge 

 from Rubenson's observations, which I have analj'sed below, it seems in 

 the highest degree unlikely that r was really less than •20, 



