OP ARTS AND SCIENCES. 11 



To avoid the defects of the above instrument, the following arrange- 

 ment has been employed. A brass tube, A B, Fig. 3, about a foot 

 long, is closed at one end by a double image prism, B; and at the 

 other by a rectangular aperture. A, of such a width that its two 

 images, as in the Arago polariscope, shall be in contact, but not over- 

 lapping. To the prism is attached a Nicol's prism, free to turn, and 

 carrying an index, moving over a graduated circle, which shows how 

 far it has been rotated. The tube is then mounted, so that it can be 

 set at any altitude or azimuth, or rotated around its own axis, and three 

 graduated circles serve to measure these quantities. In the instrument 

 as actually constructed (Fig. 4), the whole is supported on an upright, 

 which terminates below in a large screw, C, by which it may be 

 attached to a post or tree, when used out of doors. A tube slips over 

 this, which carries a cross-piece forming a T, ^^^ through the top of 

 this passes the end of a second T, 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 around its own axis. 



The working of the instrument is as follows. Tf the Nicol's prism 

 is removed, and the light unpolarized, the two images of the apertui'e 

 at the end will be equally brilliant. If now the Nicol's prism is 

 replaced and turned, the images will vary in brightness, alternately 

 disappearing at intervals of 90°. If the light is polarized, one image 

 will in general be brighter thau the other ; but by turnmg the Nicol's 

 prism, certain positions will always be found in which the two images 

 will be equal. The peicentage of polarization is then readily deter- 

 mined from the angle through which the prism has been turned. To 

 determine the law which connects these two, let the plane of polariza- 

 tion 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 case the polarization p = -^ „. If the prism is turned 



through an angle v, one image will have a brightness A sin" v, the 

 other B cos^ v ; and if they are equal, A sin^ v = B cos"-^ v, hence p 



COS y "-^ sin* y 

 = — r, — ; — r-;y— r= COS 2 V, The amouut of polarization is then very 

 cos^ V + sin- V 1 J 



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 experiments all 



four were observed, reading to tenths of a degree, and the mean taken. 



To make the reduction. Table IX. is employed, in which the columns 



headed JO give the percentage of polarization corresponding to the angle a. 



