Double Refraction of Quartz. 87 



At a distance from the center the black brushes are seen. If the 

 combination be turned so that the right-handed slice is nearest to 

 the polarizing plate, the spirals are turned in the opposite direc- 

 tion. This is one of the most beautiful phenomena of optics. 

 The slices from whose appearance the figure was drawn are each 

 0,16 inch thick. 



I shall now proceed to explain the mode of calculating these 

 phenomena on assumed laws of the nature of light in the two 

 rays of crystals. 



In fig-. 14, let AB, CD, be two parallel rays of the same 

 pencil incident on a plate of calc spar cut perpendicular to its 

 axis, of which one furnishes the ordinary ray BE, and the 

 other the extraordinary ray DE, which afterwards pass in the 

 same direction EF. (The extraordinary ray of AB, and the 

 ordinary ray of CD are not to be considered here, as they do 

 not emerge at E : but each of them will interfere with some 

 other ray). The paths are found by this construction. Draw 

 GK a tangent to a circle whose radius is GHxh (preserving 

 Biot's notation) ; draw LN a tangent to the ellipse whose seini- 

 axes are EM x a, EM x h. The velocity and direction of the 

 ray will be represented by the radius joining the point of in- 

 cidence with the point of contact, the velocity in air being 

 represented by GH, EM. Hence the path of the ordinary raj 

 (measured by the path in air which it would have described in 

 the same time) exceeds that of the extraordinary by 



Putting d for the angle of incidence, and T for the thickness 



of the plate, this is found (after all reductions) 

 T 



= -r [y/l — b 1 sm-0—*Jl — a : sin-flj. 



When 6 is small, this is nearly = T x ^=^ x P. Call this e. 



