1884.] homogeneous polarized light seen in a uniaxal crystal. 85 



But -jn — function of 6, h, and is the same for all points on the 

 do 



line OP and on an oval of intensity h. 



. • . r . OS = constant. 

 Hence the area of triangle OSP is constant. 

 Therefore we have 



Proposition XIX. All normals to ovals of intensity k drawn at 

 points on a straight line through the origin touch a rectangular 

 hyperbola. 



Cor. The tendency of normals at a distance is to become co- 

 incident with OP, for the hyperbolic curve has its asymptote 

 along OP. 



Thus again we see the curves are circular at distance from 

 origin. 



Proposition XX. The form of the curves near the point curves is 

 elliptic, and the centre of such ellipses is very nearly at the 

 point curve. 



This follows from the equation without difficulty. 



Proposition XXI. Ovals of the second and higher orders have 

 points of inflexion if the ovals are sufficiently near to the circle 

 of intensity k = 0. 



Consider an oval of the second order which is near to a circle 

 of intensity h = 0. 



The portion of the curve near A being very nearly of a circular 



