Doubly Refracting Plates and Elliptic Analyzers 17 



Any definite elliptically polarized light is, therefore, repre- 

 sented by a definite point on a Poincare Sphere. Its ellipticity is 

 determined by the latitude of the point, and its azimuth by the 

 longitude. Points on the same circle of longitude represent light 

 of the same azimuth but varying ellipticity. Points on the circle 

 of zero longitude represent light of zero azimuth. Points on the 

 same circle of latitude represent light of the same ellipticity but 

 varying azimuth. Points on the equator represent plane polar- 

 ized light. Ellipticities equal but opposite in sign are represented 

 by latitudes equal but opposite in sign. 



If a given latitude, I, on the sphere, be said to correspond to a 

 given ellipticity, e, when c=-tg l / 2 l, and a given longitude, //;, to 

 correspond to a given azimuth, 6, when 111 = 2$, any elliptically 

 polarized light is represented by the point on the Poincare Sphere 

 of corresponding latitude and longitude. The effect of a doubly 

 refracting plate may then be stated as follows : 



A doubly refracting plate turns the Poincare Sphere about an 

 axis in its equator whose longitude corresponds to the azimuth 

 of the plate, through an angle equal to the order of the plate ex- 

 pressed in degrees. 



A plate with rotary power, on the other hand, evidently turns 

 the Poincare Sphere about its pole as an axis. 



Since a series of rotations is itself a rotation, the effect of any 

 number of doubly refracting plates is evidently equivalent to the 

 effect of a single doubly refracting plate and a plate with rotary 

 power. 



A sphere constructed to show these relations has proven a 

 great convenience in tracing the effects of doubly refracting 

 plates, and in checking the results of the various formulae. The 

 sphere is mounted, free to rotate about an axis in its equatorial 

 plane, the axis in turn being movable in longitude. The sphere 

 is provided with three circles : a circle of latitude, a circle of 

 longitude and a circle to measure the rotation about its axis. 

 The latitude circle is graduated directly in ellipticity instead of 

 degrees. The longitude circle is graduated in double degrees, 

 to read azimuths directly. The circle for measuring rotation is 

 graduated directly in orders of doubly refracting plates. To ob- 



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