2G Mr. R. H. M. Bosanquet on a new Form of Polariscope, 



Distribution of direction of planes of polarization about a neutral point 

 lying above sun or antisolar point. The sun or antisolar point is indicated 

 by the dot at the bottom of the figure. 



Outline of the theory of the distribution of polarization in the 

 neighbourhood of a neutral point. 



If two equal polarizations be superposed whose directions 

 make with each other any angle, the resulting direction of 

 polarization lies along the bisector of the angle between them. 



Let A be the common amplitude of the two vibrations, 0, <£ 

 their directions estimated from any initial position, 7 the angle 

 between them; then 6 — < p= zr y. 



Let X be the intensity of the components along the initial 

 line. Then X 2 = A 2 (cos 2 + cos 2 </>). It is required to find 

 the positions for which X has maximum and minimum values. 



X dX=0 = A 2 (cos 6 sin 6 d 6 + cos<f> sin <f>d (f>); 

 and 



dd-d<j> = 0, 

 whence 



sin 2 6=— sin 2$, 



o=-4>, 



or #=7r — </>, whence — ^-=^; 



and the required positions are the internal and external bi- 

 sectors of the angle between the given polarizations. It is 

 evident that the internal bisector corresponds to the maximum, 

 the external to the minimum value. 



If, then, a constant hori- 



