the Light reflected by the Sky and by Plates of Glass. 133 



and through the top of this passes the end of a second ~Y, 

 through the end of which the polarimeter slides. Three of these 

 tubes are graduated to show the azimuth and altitude of the 

 polarimeter tube, and the amount it is turned round its own 

 axis. 



The working of the instrument is as follows. If the NicoPs 

 prism be removed and the light unpolarized,the two images of the 

 aperture at the end will be equally brilliant. If now the NicoPs 

 prism be replaced and turned, the images will vary in brightness, 

 alternately disappearing at intervals of 90°. If the light is po- 

 larized, one image will in general be brighter than the other; 

 but by turning the NicoPs prism, certain positions will always 

 be found in which the two images will be equal. The percentage 

 of polarization is then readily determined from the angle through 

 which the prism has been turned. To determine the law which 

 connects these two, let the plane of polarization be vertical, and 

 the line of junction of the two images parallel to it. Then call 

 A and B the brightness of the two images respectively, in which 



A— B 



case the polarization p = -r — ^. If the prism be turned through 



an angle v, one image will have a brightness A sin 2 v, the other 

 B cos 2 v ; and if they are equal, A sin 2 v = B cos 2 v ; hence 



cos 2 v — sin 2 v _ 



p = — = — : — ^- 2 — = cos 2v. 

 cos^v-f snrv 



The amount of polarization is then very simply found by turning 

 the Nicol until the images are equal, then reading the angle, 

 doubling it, and taking the cosine. Evidently there are four 

 positions of equality of the image ; and in the following experi- 

 ments all four were observed, reading to tenths of a degree, and 

 the mean taken. 



The results may be reduced by a Table of natural cosines, 

 first multiplying the angle by 2. Evidently, when the light 

 is unpolarized, the angle will be 45° ; when totally polarized, 0°. 

 When the line of junction is inclined to the plane of polariza- 

 tion by an angle w, the observed polarization p'=p cos 2w. 

 This suggests a means of determining the direction of the plane 

 of polarization. Make two observations of the amount of polar- 

 ization, turning the polarimeter 45°. Then call p, p' } p ]l the 

 true and the observed polarization in the two cases, and w the 

 unknown angle between the line of junction in its first position 

 and the plane of polarization. Having given p' and p n , we 

 wish to determine p and w. Evidently p'=p cos 2w, and 

 p"=p cos 2 (45° — vj) =p sin 2w. Taking their quotient gives 



tan2w= -j-. and the sum of their squares gives p = s/p H -\-p m . 



