sorby: optical characters of minerals. 
9 
focus parallel, and at the other perpendicular to the axis. If 
the section be strictly parallel to the axis the focal point of 
the ordinary image is nearly half-way between these two foci 
of the extraordinary ray, and coincides, in horizontal position 
with the point at which the two elongated bands intersect. 
There is thus no lateral displacement of the images. If, 
however, the section be not parallel to the axis they are dis- 
placed laterally, this character being a very delicate test of 
the accuracy with which the section' has been made. In fact, 
in all cases, if the two opposite surfaces are parallel, the 
character and position of the images at once indicate the 
exact relation between the optic axes and the planes of the 
plate, whether they be natural or artificial. 
On viewing the rectangular grating through a section cut 
more or less nearly parallel to the principal axis, no lines 
whatever can be seen by means of the extraordinary ray, 
unless one system is nearly parallel to the axis. At one focal 
point one system of lines is seen, and at the other focal point the 
other system, so that the image due to the extraordinary ray 
may be said to be bifocal. On rotating the grating, the lines 
are seen to become broader, then obscure, and finally invisible. 
Unlike the image due to the ordinary ray, the bifocal image 
has thus a special focal axis, and the lines can never be seen 
in sharp focus if they are not either parallel or perpendicular 
to this axis. 
On the whole, then, we have three focal points, one for 
the ordinary, and two for the extraordinary ray; and by 
observing these we obtain three different indices of refraction, 
one being that of the ordinary ray /x ; and, provided that the 
section is closely parallel to the axis, the index derived from 
the lines parallel to the axis in the extraordinary image 
is the true index (p ) of the extraordinary ray, whilst the third 
1 a 2 . 
index is of the very abnormally high apparent value ^ 
