338 The American Geologist. j un c, i89i 
mineral. The only minerals that I think of where the double 
refraction, i. e. difference of refraction, is so great that it is 
plainly perceptible without using both nicols are the carbonates 
(for which it is characteristic), and talc and sericite, where it may 
be complicated with pleochroism. 
The double refraction is of course indicated by the highest of 
Newton's colors that the mineral gives. If there is any quantity 
of the mineral in the section, and of a known mineral, as quartz, 
with which to compare it, the double refraction can be determined 
to about ten per cent, of accuracy. For the retardation corre- 
sponding to the highest color on Newton's scale given by the 
unknown mineral, is to the retardation corresponding to the high- 
est color given by the known, as the double refraction of the 
former is to that of the latter (/. e. , .009 for quartz). 
The classification by double refraction is rather arbitrary. I 
have tried to have as few minerals as ma}' be on the border lines, 
and to have the groups broad enough so that one can really de- 
termine in which a given mineral belongs. Yet here, too, it is 
generally best, if b} T its double refraction you think that it belongs 
in one group, to consider adjacent groups as also possible. 
Most minerals have an extension. — either perpendicular to the 
best cleavage, if there is but one, or if there is more than one, 
equally good or nearly so, in a zone, — parallel to their intersection. 
This direction of extension is generally easily recognized. It 
is almost always near the same direction of light vibration, 
whether that be the one corresponding to the greatest refraction 
(c) called -f-, or the other called — . In quadratic and hexagonal 
minerals the extension and an extinction will be in the same 
direction, and in rhombic and many pseudo-quadratic or hexagonal 
minerals it is practically so. Such are placed in the columns 
-4-ex. or —ex. as the case may be. Rarely the extension is in 
the direction of the mean index of refraction, so that the extinc- 
tion in that direction is sometimes direction of greatest index 
of refraction sometimes of least. Then it comes in the column 
+ex. 0. 
If the extinction lies always within 45° of, but not always 
coinciding with, the -f- extinction, it is put down as -)-ex. not 0, 
and similarly with —ex. not 0, and +ex. not 0. After each 
mineral- is given the extinction angle, if any, then b the middle 
index of refraction, then as a numerator 2V and denominator t — a. 
