Dispersion of Colors in perfectly transparent Media. 273 
we may regard equation (9) as the equation of an ellipsoid, the 
radii vectores of which represent in direction and magnitude the 
amplitudes of systems of waves having the same kinetic energy 
due to the irregular part of the flux. These ellipsoids, which 
we may distinguish as the ellipsoids (A, B, ete.) and (A’, B’, 
etc ), as well as the ellipsoid before described, which we may 
call the ellipsoid (a, 5, etc.), must be independent in their form 
and their orientation of the directions of the axes of codrdinates, 
being determined entirely by the nature of the medium an 
period of oscillation. They must therefore possess the same 
kind of symmetry as the internal structure of the medium 
__If the medium is symmetrical about a certain axis, each 
ellipsoid must have an axis parallel to that. If the medium is 
symmetrical with respect to a certain plane, each ellipsoid must 
ave an axis at right angles to that plane. If the medium after 
a revolution of less than 180° about a certain axis is then equiv- 
alent to the medium in its first position, or symmetrical with it 
with respect to a plane at right angles to that axis, each ellipsoid 
must have an axis of revolution parallel to that axis. These 
relations must be the same for light of all colors, and also for 
all temperatures of the medium. 
15. From these principles, we may infer the optical charac- 
teristics of the different crystallographic systems. — : 
n crystals of the isometric system, as in amorphous bodies, 
the three ellipsoids reduce to spheres. Such media are opti- 
cally isotropic, at least so far as any properties are concerned 
which come within the scope of this paper 
In crystals of the tetragonal or hexagonal systems, the three 
ellipsoids will have axes of rotation parallel to the principal 
crystallographic axis. Since the ellipsoid (a, }, etc.) has but 
one circular section, there will be but one optic axis, which 
will have a fixed direction. : 
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 codrdinates, 
E, F, G, K’, F’, G’, e, #9 will vanish and equation (13) will 
reduce to 
aa’ +b? +ey? 
v= ene 
pi 
_ Ifthe codrdinate axes are so placed that 
a e, 
the optic axes will lie in the X-Z plane, making equal angles 
¢ with the axis of Z, which may be determined by the equa- 
tion 
tan” gee (A—B)—47° (A’—B) 
”~b—e p* (B—C)—47’ (B’—C’) 
