452 Sir David Brewster on the Polarization 



Lemniscates, as in biaxal crystals, and consequently the po- 

 larization in the horizon greater than in die zenith, which is 

 contrary to observation. I have therefore added a correction, 

 depending on the zenith distance and azimuth, which makes 

 the formula coincide better with observation, namely, 



R = 33|-°(sin D sin D')— 6° 34' (sin Z sin A) ; 



Z being the zenith distance, and A the angle of azimuth. 



Assuming, therefore, that the distance of the neutral points 

 from the sun and from the antisolar point is 18° 30', when the 

 sun is in the horizon, and that the atmosphere is perfectly pure 

 and uniformly transparent, the lines of equal polarization will 

 have the forms and the degrees of polarization represented by 

 the formula. The direction of the polarization follows the 

 same law as in biaxal crystals, the lines without bands or colour 

 corresponding with the black hyperbolic branches in the pola- 

 rized rings produced by these crystals, being distinctly seen 

 with the polariscope. 



VII. On the Construction of the Map of the Lines of equal 

 Polarization. 



Had the map been on a greater or a less scale than it is, it 

 might have been desirable to appropriate a single curve to 

 every single degree, or to every two degrees of rotation or 

 polarization. On the present scale, the curves would have 

 been too numerous and close had there been one to each 

 degree; and with only one to each two degrees, they would 

 have been too distant, in so far as that the form of the curves 

 round the neutral points would not have been sufficiently seen. 

 I therefore adopted such a number of curves, viz. 18|, as 

 enabled me to get the curves. No. 2, continuous round each 

 neutral point. Hence the formula became 



N = 20-5 (sin D sin D')— 3-9 sin Z sin A, 



or in the plane passing through the sun and the zenith, in 

 which Z and A become zero, 



N=25-5 (sin D sin D'). 



In the zenith itself we have N = 18*45, and at P, P' we 

 have N = 0. 



The curves thus obtained do not represent values of N in 

 degrees of rotation, but in numbers, each of which is equal to 

 l°-626. Hence R = N 1°'626, and the distance between each 

 curve is 1°*626. The following table contains the rotations or 

 degrees of polarization, indicated by each of the curves num- 

 bered from ^ to 18*45 in the map : — 



