OPTIC AXIAL ANGLE. 
159 
propagated along P', but still vibrating along OT in the original plane of 
vibration, will be destroyed by total reflection in the analyzer, just as is 
the wave OP. Since the entire field may be covered with waves similar to 
OP', whose directions of vibration are contained in the plane of vibration 
Y'Z', all the waves of the converging cone from the condenser and objective 
systems are extinguished by the analyzer, and the field appears dark between 
crossed nicols provided no birefracting crystal plate intervenes. The effect 
of the lens system of the microscope is, therefore, to change the directions 
of propagation of transmitted light-waves, but not seriously to affect the 
plane in which their vibrations take place.* Conversely, if Z' V (Fig. 90) 
be the extinguishing plane of the analyzer, and H any dark point in the field 
of the interference figure, the direction of vibration for this light-wave H 
FIG. 91. 
must be contained in the plane Z'Y' and also in the polar plane to H'; it is 
accordingly the direction D. If its direction of vibration be not in the plane 
Y'Z', it will not be totally extinguished in the upper nicol and the point H 
will not appear completely dark. Briefly stated, for any dark point H of 
the interference figure, the direction of vibration is the line of intersection, 
OD, of the extinguishing plane X'Z' of the upper nicol with the plane BE 
polar to H. This is the rule of construction given by the writer for finding 
the plane of vibration of any dark point in the interference figure. As noted 
above, the rotatory effects of the surfaces, both of the crystal plate itself and 
of the glass mounts and lenses, are disregarded in this connection. These 
effects are small, but still noticeable, and the method, in consequence, is only 
an approximate method. 
In Professor Becke's method, outlined above, the direction of vibration 
for a dark point P on the zero isogyre of the interference figure is found by 
drawing in stereographic projection the great circle which is tangent to a 
*That there is some effect on the planes of polarization of transmitted light- waves is at once evident, even 
without accurate measurements, from the lark of uniformity in illumination of the field when viewed under 
crossed nicols in convergent polarized light. A dark cross divides the field into quadrants which are per- 
ceptibly lighter than the bars of the cross. This cross is visible in every microscope and it not always due 
to faulty construction of the objectives nor to strains in the glass. The effect of inclined surfaces is also 
clearly shown on the margins of air-bubbles included in Canada balsam or glycerin or other liquid mounted 
between object-glass and cover-slip. Compare P Rinne. Centralblatt fur Miner.. 1000, 88-89; also G. 
Cesaro, Bull. Acad. roy. Belgique, Classe Sciences, 459, 1906. 
