R. 



Zenith maximum 



o 



/ 



29 



50 



29 







28 







29 







27 



30 



25 







22 



30 



27 







Polarization of the Light of the Sky. 513 



R. Altitude of Arago above 



Horizon maximum. antisolar point. 



o 

 28 



50 



29 







20 



30 



27 







25 



30 



22 



30 



19 



30 



27 



30 



o 



21 



/ 

 



19 







]9 



20 



20 30 



21 



40 



20 







20 







21 







Considering the roughness of the methods of observation, and 

 the considerable irregularities, the deviation of one degree from 

 the result will not affect the representation of the general course 

 of the observations. I might extract any quantity of the ob- 

 servations ; but it seems better to leave them to be referred to 

 by any one interested in the subject. I do not believe that it 

 is possible to represent their general course, as far as this point 

 is concerned, better than by the above formula. More nume- 

 rous and better observations may be hoped for at some future 

 time ; with what we have I do not think we can get any fur- 

 ther. 



The observation of the polarization of normally emitted light 

 with the polarimeter, simultaneously with the observation of the 

 neutral angle, in experiments such as Tyndall's on smoke, will 

 furnish results the comparison of which with the above formula, 

 or with any subsequent formula or explanation, will be of 

 interest. 



Recurring to the transformation of Brewster's formula, and 

 putting R for the maximum normal polarization and « for the 

 neutral angle corresponding to the stage of any portion of the 

 sky observed, we have, applying the above formula, R =45° — 

 tan -1 sin a; and substituting this value for the zenith-constant, 

 we get, for any inclination 9, 



tj 45°— tan -1 sin a B/ -r— s . , t s - ,* . \ 



R = s Vsin0 • sm(0— a) sm (0 + a). 



cos 2 * v ' v 



I do not mean to say that this extended formula rests on any 

 detailed evidence; but it represents the general course of the 

 values, and indicates the direction in which observations are 

 required, or, perhaps, rather experiments. 



I have already adverted to the observations of Rubenson as 

 supplying values of the variation of maximum polarization from 

 zenith to horizon. The rough rule I deduced from some of his 

 sets is, expressed in Brewster's measure, subtract from the maxi- 

 mum zenith polarization one twelfth of the zenith-distance. 



Phil. Mag. S. 4. No. 334. Suppl. Vol. 50. 2 L 



