96 Prof. W. Voigt on the Behaviour of Pleochroltic 



the minor to the major axis of the vibration-ellipse as factors 

 may be neglected. The region within which the simplified 

 formulae are not applicable is in general extraordinarily 

 small. 



In this way an explanation is very easily obtained of the 

 dark pencils — first noticed by Brewster — which make their 

 appearance when a natural source of light of sufficient 

 dimensions is viewed through the crystal, without the use of 

 any polarizer. The distribution of intensity is such that the 

 hyperbolas mentioned in proposition (b) represent curves of 

 constant absorption. The ellipticity of the vibrations in the 

 plate need not in the case of this phenomenon — to the degree 

 of approximation considered — be taken into account. Ac- 

 cording to the strictly correct formulae the distribution of the 

 intensity is somewhat modified in the neighbourhood of the 

 singular axes. 



9. The ellipticity of the vibrations has, on the other hand, 

 a marked effect on the appearances presented when a single 

 polarizer is used — whether it be that natural light is allowed 

 to fall on the plate and is examined by means of an analyser, 

 or that plane polarized light is after transmission examined 

 by the unaided eye. Here an opportunity presents itself for 

 testing in a simple manner one of the most remarkable 

 consequences of theory. 



If the experiment be carried out in the manner indicated 

 with a plate of an ordinary or an active transparent crystal, 

 whereby two linear or two elliptic similar but crossed vibrations 

 of oppositely directed sense are propagated through the crystal, 

 then according to theory there should be no interference- 

 rings visible around the optic axis. Should, on the other 

 hand, the vibrations be propagated through a pleochroitic 

 crystal whereby the two elliptic vibrations have the same 

 sense of rotation, then theory demands the presence of such 

 rings. Experiment is completely in accord with this, and 

 thus proves the existence, hitherto not established, of these 

 pairs of waves with vibrations of the kind described. 



The existence of the rings is easily proved in many pleo- 

 chroitic crystals. Frequently it is possible to see them by 

 looking with the unaided eye through the crystal plate at the 

 sky when the light from the latter is strongly polarized; they 

 have in this case been known for some time, but only now 

 has a theoretical explanation been furnished. That the ex- 

 planation given above, which is based on the peculiar nature 

 of the vibrations in the waves traversing the plate, is the 

 correct one, follows especially from the changes which come 

 over the appearance presented when the plane of polarization 



