16 Transactions of the Royal Microscojyical Society, 
stage is arranged parallel to one set of lines, and the analyzer over 
the eye-piece crossed so as to give rise to a naturally dark field. 
The object is then introduced and rotated until it is in such a 
position that it does not in any way depolarize the light. The 
polarizer and analyzer are then removed, and the microscope so 
adjusted that the lines of the grating are seen in good focus through 
the crystal. If both systems of lines are doubled, as in the case of 
the olivine of the Kittersgriin meteorite, shown by Fig. 11, the 
crystal must have two optic axes, inclined to one another at a 
considerable angle. If, however, only one system is doubled, as in 
Fig. 10, it may be a two-axed crystal, cut obliquely only to one 
focal axis; but if on examining a number of different crystals, 
scattered in various positions through the thin section of rock, only 
one system of lines is invariably doubled, the mineral must either 
have only one optic axis or two which are inclined to one another 
at a small angle, two of the three indices of refraction being very 
nearly equal. 
A little care is sometimes necessary in order to see the lines 
well separated. Frequently they lie in different planes, so that 
they cannot be seen in focus at the same time, especially if too 
high a magnifying power is used. On the contrary, the horizontal 
separation may be so small that they cannot be seen separately, 
unless a high power is employed. The extent of this separation 
varies directly as the intensity of double refraction, and as the 
thickness of the section, but also, as previously named, depends on 
the direction in which it is cut. With a i object-glass and a 
powerful eye-piece, there is no difficulty in seeing that one set of 
lines is divided by calcite, even when it is only 40 V 0 of an inch 
thick, since its double refraction is so strong, but a much greater 
thickness of some minerals would be necessary. Care must be 
taken not to confound this true separation with any duplication of 
the lines due to accidental reflexions, which are distinguished by 
varying with slight movements of the object. 
If any individual crystal be so cut that its optical characters 
cannot be determined by means of this visible horizontal separation 
of the lines, it must necessarily be cut in such a direction as to 
enable us to determine them by means of the focal character of the 
images, the one method being the most applicable just when the 
other breaks down. 
As a practical example, I will describe what I observed in a 
section of lava from Vesuvius about of an inch thick. It 
contains a few scattered crystals of what I believed to be olivine. 
In some cases neither system of lines was sensibly divided, but 
both images were bifocal, and I obtained for the three indices 
about I • 77, I • 72, and 1-64. In some examples only one system 
of lines was divided, but in others both, one being separated by 
