132 Prof. E. C. Pickering on the Polarization of 



horizontally. The percentage of polarization will therefore equal 

 cos 2 a — sin 2 a 



= cos 2a 5 from which the polarization correspond- 

 cos* a + sin* a 



ing to any given angle is readily determined. 



The result of such a comparison is given in Table III. Four 

 series of observations were taken, from which curves were con- 

 structed as in fig. 8, with angles of incidence as abscissae, and 

 percentages of polarization as ordinates. A curve was next 

 drawn, coinciding with them as nearly as possible ; and its ordi- 

 nates are given in Table III. column 3; the angles of incidence 

 are given in the first column, and the theoretical polarization in 

 the second column of the same Table. Column 4 gives the dif- 

 ferences ; and from it we see that, while the agreement is very 

 close between 0° and 60°, above this point a marked variation 

 is perceptible. This deviation will be further discussed in con- 

 nexion with fig. 8. 



Table III. — Table for Arago ? s Polarimeter. 



i. 



Theoretical. 



Empirical. 



Difference. 



o 







00 



00 







20 



51 



5 



-0-1 



30 



11-4 



130 



1-6 



40 



21 8 



23 5 



17 



50 



351 



370 



1-9 



55 



420 



430 



10 



60 



48-9 



490 



1 



65 



541 



575 



3-4 



70 



563 



635 



7-2 



75 



55-8 



67-0 



112 



80 



52-6 



720 



19-4 



To avoid the defects of the above instrument, the following 

 arrangement 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 overlapping. To the prism is attached a 

 NicoFs 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 round 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 up- 

 right, 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 "|"; 



