IDENTIFICATION OF FERTILIZER MATERIALS. 9 
the optical character of a biaxial crystal can be determined when 
only one hyperbola appears in the field. The phenomena are similar 
to those presented when both hyperbolae appear. 
OPTIC AXIAL ANGLES. 
In the interference figure of sections cut normal to the acute 
bisectrix and rotated into the 45° position, the distance between the 
hyperboles, i. e. ; between the two dark spots, represents the angle 
between the two optic axes. The observed angle, 2E, however, is 
not identical with the actual angle, 2V. The symbol 2H is some- 
times used to represent the angle when it is measured in an oil. The 
distance between the points of emergence of the axes, in the 45° 
position, can be measured by a micrometer eyepiece. Let this dis- 
tance be 2d. Then 
SinE =jy 
E is half the axial angle in air, d is half the distance between the 
points of emergence of the optic axes as measured with the eyepiece 
micrometer, and C is a constant which must be determined for each 
lens combination. It may be determined by using a mica plate, 
whose axial angle is known, as an object and substituting in the 
formula. If n is the mean index of refraction of the mineral, then 
SinE 
SmV=-^- 
2V can thus be readily found. In a large number of cases the simple 
designation of the angle as " large" or "small" will serve all purposes; 
and this relative size may be observed by a glance at the interference 
figure. 
DISPERSION. 
Here p is used to indicate red light, and u violet light. Observa- 
tions are made on the interference figures. 
In the orthorhombic system the dispersion is least, p < v or p > v, 
for the color within the circle which is nearest the bisectrix and which 
touches the concave side of the hyperbola when the crystal is in the 
45° position. The colors are symmetrical to the bisectrix. 
In the monoclinic system there are three kinds of dispersion, 
inclined, horizontal, and crossed. In inclined dispersion the colors 
are arranged symmetrically to the line joining the loci of the hyper- 
bolae, but are not symmetrical in the other direction. One locus is 
oval shaped, larger, and less intense; and the other is round, intense, 
and smaller. In horizontal dispersion, the colors are not arranged 
symmetrically to the line joining the loci of the hyporbolse. They 
are symmetrical, however, to a line at right angles to this line. In 
crossed dispersion there is only a point of symmetry. 
