REFRACTIVE INDICES. 
99 
or (2) by noting* the azimuths of the planes of polarization of the maxima 
and minima of the boundary curves of total reflection, in which case the 
plane of polarization of the value /3', which is to be discarded, is normal to 
the plane of incidence, while that of the correct /3 is inclined to the plane of 
incidence. Special cases, where the section is cut nearly normal to an optic 
axis, often give rise to intricate relations which are of theoretical interest 
but practically never occur in actual work. 
Viola and Cornu have shown how it is possible to determine by calcula- 
tion and also by a graphical method the positions of the principal ellipsoidal 
axes and of the optic axes relative to the crystal plate under examination ; 
in short, to ascertain practically all of the optical constants of the crystal 
from the observations on the single polished plate by means of the total 
refractometer. The following graphical method, which is apparently new, 
illustrates the principles on which their methods are based. f In the stereo- 
graphic projection, Fig. 62, let the directions Z'A, Z'B, Z'C, be the observed 
azimuths of the maxima and minima of the boundary curves which corre- 
spond to the three principal refractive indices. These are then the lines of 
intersection of the principal planes of the triaxial ellipsoid with the crystal 
surface on which the measurements were made and which is the plane of 
projection in the figure. Draw Z'a, Z'b, Z'c normal to Z'A, Z'B, Z'C; then 
the three principal ellipsoidal axes must be contained in these planes Z'a, 
Z'b, Z'c; and their positions are readily found by determining graphically 
those great circles YZ, YX, and XZ, whose intercepts between the radii Z'b 
and Z'c, Z'b and Z'a, Z'a, and Z'c, respectively, are 90. From the figure 
*C. Viola, Accad. d. Line. Rend., I, 279, 1899; Zeitschr. Krist., 36, 345, 1902; A. Cornu. C. R.. Ill, 125. 
463, 1901; Bull. Soc. Min., 25, 7, 1902. 
fCompare P. Pockets, Kristalloptilc, 130-131, 1906; also Duparc and Pearcc. Traits' de Technique Min- 
eralogique et Pe'trographique, 390-391. 1907. 
