The T resident's Address, H. C. Sorhy, F.R.8., P.G.S. 7 
an angle of divergence greater or less than that depending on the 
index of refraction, according to the direction of the section, and to 
whether the double refraction is negative or positive. Thus, for 
example, in the case of calcite cut perpendicular to the axis, the light 
diverges equally aJl around the axis, less than normally, and there- 
fore the focal point of objects seen through the section is made 
abnormally short, and the apparent index abnormally small, being, 
in fact, Only 1 • 332, whereas the true index of the extraordinary 
ray is 1*480, and of the ordinary 1 * 658. 
Crystals like orpiment or aragonite, which have two optic axes 
and three different indices, have no ordinary ray, and no perma- 
nently unifocal image, but two bifocal images polarized in opposite 
planes. We may thus have four different apparent indices. In 
the case of orpiment the image of a small circular hole is drawn out 
at two different foci into two crosses, as shown by Fig. 5. Each 
cross is produced by the combination of two bands of light polarized 
in opposite planes, each due to an extraordinary ray, analogous to 
the single extraordinary ray of calcite. In the case of aragonite, 
cut perpendicular to the principal axis, the arms of the crosses are 
nearly equal, but spread out in the manner shown by Fig. 6. 
This spreading out varies according as the aperture of the object- 
glass is large or very small. If the section is in a plane somewhat 
oblique to the principal axis, one bar of the cross is distorted into 
an irregular circle, and one arm of the other bar is spread out into 
a sort of crescent. 
A remarkable peculiarity of crystals which thus give two well- 
pronounced bifocal images, is that though they may be perfectly 
transparent, and distant objects distinctly visible through them 
with the naked eye, the systems of lines at right angles to each 
other are perfectly invisible with the microscope, except at par- 
ticular azimuths. I was extremely surprised at this fact when 
first I observed it, and could not understand the reason of this 
apparently strange peculiarity. 
When the section is cut parallel to the principal and to one of 
the secondary axes, we obtain a cross with unequal arms at four 
different foci ; and when cut parallel to the principal, and along the 
diagonal of the secondary axes, one image has the bifocal character 
very strongly developed, and the other is almost or quite unifocal, 
but can be shown to be also due to an extraordinary ray, by causing 
the light to pass obliquely. 
If we wish to ascertain the real value of the indices, we must 
hear in mind the following facts : The image due to the light 
passing through substances not possessing double refraction, or to 
the ordinary ray of crystals belonging to the rhombohedral and 
dimetric systems, has no special focal axes, and the apparent 
index is the true index, no matter what may be the direction of the 
