The President's Address, H. C. Sorhj, F.R.8., P.G.S. 5 
mineral which has no double refraction, he placed on the stage of 
the microscope, with its surfaces perpendicular to the line of vision, 
the two systems of lines can still be seen at the same focus, no 
matter what may be the azimuth of the lines to the axes of the 
crystal. The image may thus be said to be unifocal, and to have 
no special focal axis. The index of refraction, determined as above 
explained, is that of an ordinary ray. On the contrary, if the 
mineral possesses double refraction, the phenomena seen by means 
of the extraordinary ray may be totally different, and as though a 
cylindrical lens had been placed in front of the object-glass. In 
order to he able to examine separately the two rays polarized in 
opposite planes, a NicoFs prism must be used over the eye-piece, 
arranged at such an azimuth as to transmit one or other ray alone. 
The ordinary ray has just the same properties, and is strictly 
unifocal, no matter what may be the direction of the section of the 
crystal ; but the characters of the extraordinary ray differ greatly, 
according as the section is cut perpendicular, oblique, or parallel to 
the principal axis. I cannot 'refer to a better example than calcite. 
On examining the image of the circular hole and of the grating 
through a section parallel to the axis, the plane of polarization of 
the Nicol being arranged perpendicular to the axis of the crystal, 
so that only the extraordinary ray is transmitted, it will be found 
that at two difierent foci the circular hole is elongated in opposite 
planes, and that both sets of lines are invisible, unless they are 
nearly parallel and perpendicular to the axis, and that there are 
two focal points, separated from one another by an interval some- 
what more than one-eighth of the thickness of the section, at each of 
which only one system can be seen at once. The image is thus 
truly bifocal, and has a definite focal axis, and the lines are dis- 
tinctly visible only when parallel or perpendicular to this axis. 
When determined in the manner already explained, the index of 
refraction for the lines parallel to the principal axis of the crystal 
is the true index of the extraordinary ray, whereas that for the 
lines perpendicular to this axis is only an ajp]parent index, and is 
equal to the square of the index of the ordinary ray, divided by 
that of the extraordinary. 
The striking difference between a unifocal and a bifocal image 
becomes at once intelligible if, instead of a grating, we examine 
through the mineral the image of a small circular hole, as Fig. 1. 
In the unifocal image this is seen undistorted, well defined all 
round at one definite focus ; whereas in the bifocal image there is 
no focal point whatever at which the hole can be seen of its true 
size and shape. There is one focal point for the two opposite sides 
of its circumference which are parallel to the focal axis, and at 
this focus the circle is drawn out parallel to that axis into a long 
hand, and there is another focal point for those parts of the circum- 
