ON THE POLARISATION OF THE ATMOSPHERE. 



233 



receiving the light at very small angles of incidence. This instrument, shown in 

 the annexed figure, consists of two tubes of the same length, one of which, EFHG, 



Fig. 5. 



moves within the other ABDC. One plate of glass, EL, longer than AB, moves 

 round a joint at E the end of the tube EFHG, resting upon C the end of the tube 

 ABDC, so that when this tube EFGH is pushed in, the plate EL forms a greater 

 angle with the axis of the tube, and when it is pulled out a smaller angle. 



Now, if AB = EF, BF will be = AE, the tangent of the angle ACE, AC being 

 radius, or of the angle of incidence of rays that fall upon EL parallel to the axis 

 of the tube. The degrees of rotation, R, therefore, of the planes of polarisation 

 produced by the refraction of the plate EL at different inclinations to the axis of 

 the tube may be calculated from the formulae — r 



R = ^ - 45°, and 

 Cot. p = cos^. (i — i') ', 



i being the angle of incidence, and i' the angle of refraction. The values of R, 

 the measures of the degrees of polarisation, being laid down on the tube EF, we 

 have a polarimeter which gives us direct measures of the polarisation of atmo- 

 spherical, or any other kind of polarisation, when it does not exceed the maximum 

 polarisation produced by the refraction of one plate. In this instrument the zero 

 of the scale is at F, and B is the index. 



In place of one plate, EL, we may use two, three, or more plates, and thus 

 obtain a measure of all degrees of polarisation. If ?i is the number of plates, the 

 value of R will be as follows: — 



■R = p- 45°, 



Cot. <p = cos" {i — i'). 



In the instrument which I constructed the radius AC was 1-13 inch, or 



33-9 

 ~30" 



inch, 



and the scale on FB was laid down from the following table, the index of refrac- 

 tion of the plate EL being 1-51. 



Angles of Incidence i. 



Angles of Refraction t'. 



Rotation R. 



Length of Tangent. 



0° 







0° 0' 



0' 





30 







19 20 



1 



0'655 inches 



40 



34 



25 31 



2 



0-968 



47 



46 



29 22 



3 



1-244 



63 



17 



32 4 



4 



1-515 



57 



39 



34 1 



5 



1-784 



61 



25 



35 3 



6 



2-074 



