12 Transactions of the Royal Microscopical Society. 
As an illustration of the use of this method, I give the par- 
ticulars in the case of a section of the pitchstone of Arran which 
is about -gV of an inch in thickness. The space between the 
glasses was 2 • 54 ; the apparent thickness of the upper balsam • 12, 
and of the lower • 22. The total displacement of the focus was * 89, 
from which must be deducted *19 for the balsam. Hence the 
2*03 
mean apparent index is ^ = 1*526. This corrected for 
Zi * Uo — / u 
the effects of the aperture of the object-glass would be about 1 * 52. 
One image was very decidedly bifocal, and the other very nearly 
unifocal, as though the crystal had two optic axes, but two of 
the three indices nearly equal. In all these characters this mineral 
corresponds most closely with adularia, so that its general com- 
position cannot differ much from that variety of felspar. The 
only question is whether the double refraction be not positive, 
instead of negative, which it does really seem to be. 
The only serious objection to this direct method of comparison 
is the chance of error in measuring the thickness of the balsam 
used in mounting, and when this is relatively great, it is better to 
adopt one or other of the following systems, in which the thickness 
of the balsam may be entirely neglected. 
It can easily be shown that if parallel plates of two transparent 
substances be of exactly the same thickness, their apparent thick- 
ness {t and i!') as measured through themselves, varies inversely as 
their indices of refraction (//< and f). If then the index of one 
of them ( yLt) be known, that of the other can easily be calculated, 
thus 
t 
These relations enable us to ascertain the approximate value of the 
indices of refraction of minerals in very thin sections without any 
special preparation, by making only a few simple measurements. 
Fig. 8 shows the section of the edge of a thin plate of rock 
covered with a thin glass which projects beyond it, the space 
between the two glasses being filled with hard Canada balsam (h), 
as shaded. Now in this case, if we measure the apparent thick- 
ness of any mineral near the edge, by focussing first to its upper 
and then to its lower surface, and also observe the difference in the 
focal position of the lines of the grating, as seen through the 
mineral and through the balsam alone, we can at once calculate 
the index of refraction. A moment’s reflection will show that 
the thickness of the balsam over and above the thin slice need not 
be taken into account, since the displacement in the focal length 
only corresponds to a thickness of balsam equal to that of the 
mineral, whatever it may be. The only source of material error 
