ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
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possible principal sections at right angles. It is at right angles foftho 
optic axis and is the polarization plane of the extraordinary wave when 
the light is propagated at right angles to the axis. Thus tangents to the 
equator are all possible directions of vibration of the one wave — whether of 
the ordinary or extraordinary remains still undetermined. Now, possible 
polarization planes for the extraordinary wave are all planes at right 
angles to the principal sections, and of these there can be drawn an 
infinite number as great circles through a determined diameter of the 
equator of the sphere. If a diameter to the equator be drawn at right 
angles to a chosen meridional principal section, and a plane containing 
it be supposed to be turned through all possible angles about it, the 
plane in all positions during the rotation remains at right angles to 
the principal section, and therefore represents in all these positions a 
possible polarization plane of the extraordinary wave. 
Matters are simplified if, instead of the possible polarization planes 
of the extraordinary wave, we consider the possible directions of vibra- 
tion in these planes. These directions must, under all circumstances, 
be at right angles to a principal section, and must therefore be at right 
angles to the line of intersection of 
the plane of polarization of the extra- 
ordinary^wave with a principal section. 
On the surface of the sphere, there- 
fore, the tangents of the great circles 
which belong to possible polarization 
planes of the extraordinary wave, do 
not all correspond to the directions of 
vibration in these polarization planes, 
but only such tangents as stand at 
right angles to a principal section. 
In fig. 30 o o' denotes the optic 
axis with principal sections drawn 
through it which cut the sphere in 
meridians ; a a' is the diameter of the 
equatorial plane ; aba'b’ any possible 
polarization plane of the extraordinary 
wave ; s s' the only possible directions of vibration in this plane ; w u f 
a direction in this plane, which cannot be a direction of vibration. 
Now consider the case of a plate of a uniaxial crystal cut at right 
angles to the optic axis. When this is traversed by a plane light-wave 
in the direction of the optic axis there is no double refraction, and the 
light propagates itself with the velocity of the ordinary wave. Since 
the vibrations are at right angles to the optic axis, their direction lies 
in that plane of the crystal which exhibits the highest possible symmetry, 
viz. in the so-called basal plane of the rhombohedral, hexagonal, and 
tetragonal systems. All directions, then, in such a plane must be re- 
garded as optically similar, since light propagates itself at right angles 
to planes of this symmetry as ordinary light. In the case of a plate cut 
parallel or oblique to the optic axis, the ordinary wave polarized in the 
principal section behaves so far like ordinary light, that it always exhibits 
the same velocity as light propagated in the direction of the optic axis ; 
while the wave polarized at right angles to the principal section has a 
Fig. 30. 
o' 
