The President's Address, II. C. Sorby, F.E.8., P.G.S. 9 
truly unifocal and the other bifocal, unless the section is nearly 
perpendicular to the optic axis ; and crystals having two optic 
axes give two images, both of which are bifocal, unless the section 
is nearly parallel to four different planes much inclined to the 
plane of the optic axes. The separation of the focal points in bifocal 
images varies directly as the intensity of the double refraction and 
the thickness of the specimen ; and if the double refraction he 
weak and the section too thin, the bifocal character of the image 
may not be recognizable with an object-glass of too low power. 
Sometimes, however, as in orpiment, the difference in the focal 
distances amounts to more than one-fifth its thickness. As a 
general rule, all the more important facts may be observed quali- 
tatively, no matter what may be the direction of the section, 
though it may not be suitable for determining the true value of the 
indices. The natural planes of crystals belonging to all those 
systems in which the axes are rectangular, are, however, often in 
the proper direction ; and, unless their surfaces be very irregular, 
perfectly satisfactory results may be obtained by mounting the 
specimens on glass and fixing over them a thin glass cover with 
Canada balsam, or by using oil of cassia or some other liquid of 
nearly the same refractive power as the specimen under examina- 
tion, if it be desirable not to use balsam. 
Applying this method to the study of various minerals, the 
difference between them is found to be very great. We can, 
usually, at once see whether they give a single unifocal image or 
one or two bifocal images, and form a very good opinion respecting 
the intensity of the double refraction, and easily determine whether 
it is positive or negative. There can never be any question as to 
the index of the ordinary ray since the observed index is always 
true, and in many cases the index or indices of the extraordinary 
ray can also be determined. All these facts combined furnish data 
so characteristic of the individual minerals, that it would usually 
be difficult to find two approximately similar. In any case we have 
data which may often be of the greatest assistance in identifying 
the different species. Of course this method cannot be employed 
if the specimens are opaque, or have such a fibrous or laminar 
structure as to prevent our distinctly seeing the lines of the 
grating; but the presence of a vast numher of fluid cavities and 
minute crystals or granules may not signify much. 
The above sketch of some of the leading principles involved in 
this method of research would be very inadequate if on the present 
occasion it were desirable to fully explain its application to the 
study of crystals sufficiently large to be cut in a proper direction, 
and to make it possible to determine the indices with considerable 
accuracy. It will, however, I hope, be enough to indicate what 
we might expect to be able to learn by applying the method to the 
