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



affecting the values in zenith and horizon at right angles to sun, 

 or the evanescence at neutral points. The formula now becomes 



R = (33i -3i°sin^)ysinT . sin (<9-18§°). sin (0-r-18i°), 



which represents all Brewster's results, as well as the necessary 

 conditions inferred from the consideration of the experiments. 



n is here some large number which cannot be determined 

 without more evidence. The object is to get a factor which is 

 very nearly unity except for evanescent values of Q. 



For the sake of comparison, the following sketch (figs. III. 

 & IV.) is drawn on the same arrangement as Brewster's maps, 

 showing the general course which the lines of equal polarization 

 must take under these circumstances. Continuous lines repre- 

 sent the course of given values of positive polarization, dotted 

 lines of negative. 



The interval between the continuous and dotted lines represents 

 the neutral region, in which the neutral points lie. 



The projections of III. and IV. are the same as Brewster's I. 

 and II. above given. 



I have said that the symmetry requires the evanescence of the 

 polarization at the sun and antisolar point ; and I have repre- 

 sented this consideration in the above empirical formula by the 

 factor \/sifl 0, where n is a large indeterminate number. I 

 have also pointed out that Tyndall's experiments contain no 

 evidence of this phenomenon. There are, however, several 

 observations of the sky which I cannot attribute to any thing 

 else. About the antisolar point, I do not consider that the 

 observations are of any value, as, strictly speaking, the direct 

 rays of the sun can never fully reach the antisolar point when 

 it is observed ; but a neutral region immediately surrounding 

 the sun has been observed on several occasions. Babinet 

 observed it as a neutral point below the sun; Rubenson ob- 

 served it above. Babinet's account is very clear (Comptes Ren- 

 dus, 1846, No. 2, p. 233). Karsten, in Fortschritte der Physik, 

 ii. (1846) p. 187, gives an account in which the neutral region close 

 to the sun is explained as being Brewster's point ; the existence 

 of negative polarization below it disproves this. 



Nothing has been said hitherto as to the variation of stage 

 corresponding to the variation of the zenith-distance of the 

 observed point in the sky. We have no polarimeter measures, 

 in Tyndall's experiments, of the variation of the polarization of 

 light normally emitted with the variation of the neutral angle. 

 In the observations of the sky, however, we have some material, 

 though not very direct, bearing on this point. Observations of 

 the distance of the neutral points from sun and antisolar point, 

 at varying altitudes, occur in Brewster, and also observations of 



