OF ARTS AND SCIENCES : SEPTEMBER 13, 1871. 



331 



the determination of elevations. He showed that, after apply- 

 ing all the known corrections, a residual error remained, owing 

 to which observations made in winter sometimes gave results 

 a hundred feet lower than those made in summer. 



Remarks on this communication were made by the President, 

 and Messrs. L. Agassiz, B. Peirce, and T. M. Brewer. 



Professor E. C. Pickering showed a new application of Fres- 

 n el's formula of Reflection. 



If i and r are the angles of incidence and refraction, and A and 

 B the magnitudes of the two reflected beams polarized at right angles, 



we have A 



sin 2 (i — r) 



andB = 



_ tan 2 (i — r) 



If in these we make the 



' sin 2 (i -f- r) " tan 2 (i -\-r ) 



index of refraction = 1 -f-dn or very nearly unity, we obtain by dififer- 



dii 1 2 cM 2 



entiating and reducing A =— (1-|- tang 2 /) and B = — (1-j-tang 2 /) . 



Substituting in these formu- 

 las different values of i we com- 

 pute the accompanying table. 

 The first column gives i, the 

 second A or more strictly 

 1 



(1 + tang 2 /) = 



The 



I! 



A + B 

 00.0 

 6.2 

 26.0 

 60.0 

 94.5 

 100.0 

 94.1 

 60 

 26.0 

 6.2 

 1.2 



A — B 



100, or 



third column gives B or the 

 amount of light polarized in 

 the plane of incidence ; the 



fourth h (A -J- B) the total light reflected, and the fifth 



the degree of polarization in percentages. It will be noticed that 

 at 45° the polarization is complete. Now the light of the sky may 

 be accounted for, if we suppose the sunlight specularly reflected by 

 very minute surfaces of air or aqueous vapor, the index of refraction 

 in this case being very near unity. Our table then shows that the 

 light should increase from the antisolar point towards the sun, becoming 

 very great near the latter. At a distance of 10° the angle of inci- 

 180 -10° 



dence would be 



85°, and the light over 17,000 times as 



great as opposite the sun. Again, the polarization would attain its 

 maximum 90° from the sun. These phenomena are quite in accord- 

 ance with the observed facts. 



