274 J. W. Gibbs—Double Refraction, ete. 
To get a rough idea of the manner in which g 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, 4, ete.) 
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 ° becomes infinitely 
great as the optic axes approach coincidence. : 
In crystals of the monoclinic system, each of the three ellip- 
soids will have an axis perpendicular to the plane of symmetry. 
Then F, G, 
We may choose this direction for the axis of X. 
F’, G’, fg, will vanish and equation (18) will reduce to 
yr te tof tey?+epy 
The angle @ made by one of the axes of the ellipsoid (a, 4, etc.) 
in the plane of symmetry with the axis of Y and measured 
toward the axis of Z is determined by the equation 
: *E—47? E’ 
tan 26= 
of the two optic axes will be unequal. The same crystal, 
however, with light of different colors, or at different tempera- 
tures, may afford an example of each case. 
In crystals of the triclinic system, since the ellipsoids (A, B, 
etc.) and (A’, B’, etc.) are determined by considerations of a 
different nature, and there are no relations of symmetry to 
cause a coincidence in the directions of their axes, there will 
not in general be any such coincidence. Therefore the three 
axes of the ellipsoid (a, 6, ete.), that is, the two lines which 
bisect the angles of the optic axes and their common norma}, 
will vary in position with the color of the light. 
16. It appears from this foregoing discussion that by the 
electromagnetic theory of light we may not only account for 
the dispersion of colors (including the dispersion of the lines 
