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XVI. Measurements of the Polarization of the Light reflected by 

 the Sky and by one or more Plates of Glass. By Professor 

 Edward C. Pickering, Boston, U.S.* 



r |^HE following observations, which will be published in full 

 -*- in the l Proceedings of the American Academy of Arts and 

 Sciences/ were conducted to test FresnePs formula for the re- 

 flection of light. He showed that, if the light was polarized 

 in the plane of incidence, the amount reflected would be 



sin ( i ' 7* I 



A= . ,. -r. while if polarized in a plane perpendicular to it 



sm 2 (z-fr) 



for* ^ in , ., y* \ 



the proportion would be B = — ~ t, i and r representing 



the angles of incidence and refraction respectively. Natural 

 light may be regarded as composed of two equal beams polarized 

 at right angles, hence the amount reflected 



L v ' z Vsm 2 (i + r) tan 2 (i + r) J 



a formula which may be applied to any special case by substitu- 

 ting proper values for i and r. The value of A evidently in- 

 creases as i varies from 0° to 90°. That of B, on the other 

 hand, diminishes from 0° until z-f-r = 90°, when it equals 0; or 

 at this angle, which is that of total polarization, all of the ray B 

 is transmitted, all the reflected beam being polarized in the plane 

 of incidence. When 2 = 90°, A=l, B = l ; hence all the light is 



reflected. When i = 0°, A, B, and R equal / J ; hence the 



reflected light increases with n, being zero when n = l, and 100 

 per cent, when n=. oo. Many familiar phenomena are thus 

 readily accounted for — for instance, the brightness of the dia- 

 mond, the covering power of white lead as a paint, and the bril- 

 liancy of wet or varnished stones and woods. 



A curious case presents itself when n=l +dn, or differs from 

 unity only by an infinitesimal amount. A then becomes equal 

 to ^fo 2 (1 + tan 2 z) 2 , and B to Jrfn* (1 - tan 9 *) 8 . When i = 0, 

 A, B, and B equal \dn^ ; and this quantity is accordingly taken 

 as the unit in Table I. The first column gives various values of 

 the angle of incidence, the second and third the corresponding- 

 values of A and B, the fourth the amount of light reflected, and 

 the fifth the degree of polarization. The other columns will be 

 explained hereafter. This Table is evidently applicable to all 

 cases where the media bounding the surface have nearly the same 

 index of refraction, whether its absolute amount is great or small. 



* Communicated by the Author. 



