Double Refraction of Quartz. 105 



Therefore in the bright or dark rings =^ will be greater than *, or 



\ 



f + 7T, or yj, + 2 7r, &c. by an angle a. which is always included between 

 and 90°, and which has its maximum at a part which, when « is less than 

 90°, is found by looking a little to the negative side of the perpendicular 

 and parallel to the plane of reflexion (thus, if the crystal be right handed, 

 we must look to the left of the upper part, and the points of the square 

 appearance will be found in that place). When a is greater than 90°, the 

 maximum value of the tangent takes place for points found by looking a 

 little to the positive side of the perpendicular and parallel: but the tangent 

 is then negative (for tan a which enters as a multiplier is negative). Con- 

 sequently the maximum contraction of the circle is found by looking to the 

 positive side, and the points of the squares wiU be found by looking to the 

 negative side. Whichever therefore be the direction in which the analyzing 

 plate is turned, the circles will be changed into the form represented in 

 fig. 15 (the crystal being supposed right handed). This remarkable conclu- 

 sion agrees perfectly with the facts of observation. 



2. If k is very small, the expression for tan w may become negative, 

 which shews that «, will suddenly exceed 90°, and after having continued 

 so during the change of <p through an arc of various extent (according to 

 the value of a) will suddenly become less than 90°. This shews that the 

 form of the bright and dark rings will be that of fig. 2, except that in- 

 stead of absolute interruption of the rings by the eight radii, they will pass 

 very highly inclined through those radii. The rings of quartz become so 

 faint at a distance from the center that I have not been able to observe 

 whether this is or is not supported by fact. 



3. We have already noticed that when a = 90° + ~ there is a dark 



A" 



spot at the center. Now for any given value of e, it appears (from the 

 Vol. IV. Part I. O 



