COLOEJS IN PEEFECTLY TRANSPARENT MEDIA. 193 



In crystals of the orthorhombic system, the three ellipsoids will 

 have their axes parallel to the rectangular crystallographic axes. If 

 we take these directions for the axes of coordinates, E, F, G, E', F', G', 

 e, f, g will vanish and equation (13) will reduce to 



a 



If the coordinate axes are so placed that 



a > b > c, 



the optic axes will lie in the X-Z plane, making equal angles with 

 the axis of Z, which may be determined by the equation 



- b - c ~ P *(E - C) - 4-7T 2 (B' - cry 



To get a rough idea of the manner in which varies with the period, 

 we may regard A, B, C, A', B', C' as constant in this equation. 



But since the lengths of the axes of the ellipsoid (a, b, etc.) vary 

 with the period, it may easily happen that the order of the axes 

 with respect to magnitude is not the same for all colors. In that 

 case, the optic axes for certain colors will lie in one of the principal 

 planes, and for other colors in another. For the color at which the 

 change takes place, the two optic axes will coincide. The differential 



coefficient -J- becomes infinitely great as the optic axes approach 



coincidence. 



In crystals of the monoclinic system, each of the three ellipsoids 

 will have an axis perpendicular to the plane of symmetry. We may 

 choose this direction for the axis of X. Then F, G, F', G', /, g, will 

 vanish and equation (13) will reduce to 



a 



P 2 



The angle made by one of the axes of the ellipsoid (a, 6, etc.) in 

 the plane of symmetry with the axis of Y and measured toward the 

 axis of Z, is determined by the equation 



tan 20- 6 



" ~ ~ 



To get a rough idea of the dispersion of the axes of the ellipsoid 

 (a, b, etc.) in the plane of symmetry, we may regard B, C, E, B', C', E', 

 as constant in this equation, and suppose the axis of Y so placed as 

 to make E vanish. 



It is evident that in this system the plane of the optic axes will be 

 fixed, or will rotate about one of the lines which bisect the angles 

 made by the optic axes, according as the mean axis of the ellipsoid 



G. II. N 



