512 Mr. R. H. M. Bosanquet on the 



states this as a fact, it is clearly only an inference. If he had 

 been led to connect the evanescence of the neutral angle with 

 perfect polarization in a direction normal to the sun, he would 

 hardly have said so. As a general rule, the zenith maximum 

 polarization is about 30°, and the horizon maximum less, the 

 zenith neutral angle small, and the horizon neutral angle about 

 20°. These data define pretty nearly the relative stages. 



To gain some light on the general relation between the max- 

 imum polarization normal to beam and the neutral angle, I 

 formed a pair of corresponding values, by taking from Brewster's 

 observations eight sets of pairs of values, of four or five pairs 

 each, all from good-days' observations. The polarizations taken 

 were the horizon maxima. Although observed in a direction at 

 right angles to the neutral pointy yet being about the same 

 altitude (for Brewster generally observed the neutral point im- 

 mediately after it rose), in the mean of still days the air might 

 be expected to be in the same condition in the two places. The 

 resulting pair of values was : — 



Maximum polarization Altitude of Arago's point 



in horizon. above antisolar point. 



25° 20° 20' 



The observations of Arago's Point are far superior to those 

 of the other points, the observations of the latter being much 

 more difficult ; I therefore confined myself to the former. 



It was then natural to try and formulate the general relation 

 between the polarization and the neutral angle, bearing in 

 mind the terminal conditions, and requiring a somewhat close 

 agreement with the above normal value. After numerous trials 

 I hit upon the formula 



sin a = tan (45°— R), 



where a is the neutral angle, and 45°— R the polarimeter angle 

 for normal emission. 



This satisfies the terminal conditions, making a = when 

 R=45° (Stage I.), and « = 90° when R = (end of Stage II.) ; 

 and for R = 25° we have a = 21° 20', which is just a degree from 

 the value 20° 20' of the observations. 



To give some idea of the character of the observations the ■ 

 following Table is subjoined ; it contains the eight means em- 

 ployed above, each number being the mean of such observa- 

 tions on one day as have seemed to me to have been taken 

 under comparable circumstances. 



