6 Transactions of the Boyal Microscopical Society. 
ference which are perpendicular to the axis, and the image, is then 
drawn out in a direction perpendicular to that of the former image, 
as shown by Figs. 2a and 2h. At an intermediate focal adjustment 
we see merely a large circle without any definition. It therefore 
follows that the series of black points forming a line would be 
similarly drawn out at the two foci into lines, and if these over- 
lapped, as they would if the line were at that particular azimuth, 
we should appear to have a well-defined black line, whereas at 
other azimuths this line would be spread out into a band, and so 
diluted with white light, as to be practically invisible. In a 
section parallel to the axis the images of the small hole are directly 
superimposed, hut if we examine it through a section parallel to 
the cleavage they are widely separated in the plane of the principal 
axis, as shown by Fig. 4, and appear to lie at different levels. That 
due to the ordinary ray remains in the centre of the field, and is 
not in any way distorted, whereas that due to the extraordinary ray 
is thrown out of the centre from the line of axis, and is both dis- 
torted and fringed with colour. This image is very decidedly 
bifocal, hut one system of lines is much obscured by coloured 
fringes, unless we illuminate with the approximately monochromatic 
light transmitted by red glass. When the section is cut in planes 
more and more inclined to the axis, the bifocal image becomes 
more and more nearly unifocal, and when the section is per- 
pendicular to the axis it is unifocal, hut can be distinguished from 
that due to the ordinary ray by causing the light to pass obliquely. 
We then see two images with both sets of lines, at perfect focus, 
directly superimposed at two very widely separated levels, as 
though there were two sets of lines ruled on opposite sides of a 
glass plate. One gives the true index of refraction of the ordinary 
ray, and the other an apparent index, which is equal to the square 
of the true index of the extraordinary ray, divided by the true 
index of the ordinary. On examining the small circular hole it is 
seen undistorted, in perfect focus, at two widely separated foci, 
surrounded with a large nebulous circle, due to the other image 
seen out of focus, as shown by Fig. 3. 
All these phenomena are totally unlike what can be seen with 
the naked eye in looking directly through sections cut either 
parallel or perpendicular to the axis. A white or black spot placed 
close to the specimen is then not even divided into two. The 
phenomena seen with the microscope depend entirely on the power 
of the object-glass to collect divergent rays. In the case of sub- 
stances having no double refraction, this divergence merely obeys 
the laws of ordinary refraction, and enables us to measure the 
index in the manner already explained ; but, in the case of the 
extraordinary ray, the light is bent from the normal line unequally 
and in opposite directions, and may thus enter the object-glass at 
