i6o 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
line through H parallel with the plane of vibration Y'Z' (Fig. 91). The 
intersection F of this great circle with the polar circle of H is then the desired 
direction. The point can also be found, as Professor Becke has shown 
recently,* by noting that it is at the intersection of the straight line HFY' 
(Fig. 92) and the circle BDE polar to //.f This direction of vibration F is 
not, however, contained in the plane Y'Z' (Fig. 91), the extinguishing plane 
of the upper nicol; in this case the point // can not be perfectly dark, if the 
above reasoning be correct. If the extinguishing plane of the nicol were 
Z'X' instead of Y'Z 1 1 the point C would be the direction of vibration for 
a dark point H, while G would be the equivalent point determined by the 
method of Professor Becke. 
FIG. 93. 
FIG. 94. 
According to the writer's method of construction the directions of vibra- 
tion of any dark point of the interference figure, as viewed through the upper 
nicol, must lie in the extinguishing plane of the upper nicol. The directions 
found by Professor Becke's method are not in general contained in this plane 
and appear, therefore, to be incorrectly located. Objection has been made 
by Professor BeckeJ to the writer's method because the lines D and C are 
not 90 apart, while the points F and G are precisely so. In answer to this 
it may be stated that in any direction within a crystal plate (as // in the 
uniaxial crystal plate of Fig. 93, Z being the optic axis) two waves are pos- 
sible whose directions of vibration D and C (Fig. 93) are strictly normal to 
each other and to the line of propagation //. In the interference figure, 
however, these directions are not observed along the line of propagation H, 
but as they appear in projection ; and in the plane of this projection the lines 
of vibration are not 90 apart. To assume, therefore, that the planes of 
polarization of the two possible waves as observed in the interference figure 
are tangent to the two lines parallel with YZ through // in stereographic 
*T. M. P. M . M, p93, 1909. 
tin this figurethe line K'//cuts the great circle RE at F, as Professor Becke has shown; the line //Pinter- 
eels the horizontal circle at /-; the angles J.M. A ' )". A'.Y are right angles; the angle CD is equal to K.L. 
the ang'.e between the lines of projection of the lines OF and OG (O being the center of the sphere of projec- 
tion) on the horizontal plane. In Fig. 93. the angle X'M is equal to the angle DI and also to the angle 
ZHX' or -4 of the spherical triangle 7.117.'. 
IT. M. P. M.. 28, J 93 . 1909. 
