and Brushes" observed through a Spatli Hemitrope. 563 



quarter-wave mica-plate upon a crystal of Iceland-spar cut 

 perpendicular to the axis, so that the plane containing the 

 optic axes of the mica-plate makes an angle of 45° with the 

 vibration planes of the crossed nicols. 



The explanation of the phenomena of refraction has been 

 given in text-books on Optics*. There, the formation of 

 the three images and the polarization are all explained. The 

 disappearance of the outside images in certain positions, as 

 stated before, is connected with the orientation of the optic 

 axis of the intervening layer to that of the main crystal. 



The problem of the form of the rings and brushes through 

 a twin crystal has been treated mathematically, but the case 

 has always been considered where a twinning plane separates 

 two crystals, The problem of the two similar crystal wedges 

 separated by a thin twinned lamina inserted between them 

 in an inclined position appears not to have been solved, and 

 an investigation in this direction forms the subject-matter of 

 the present paper. 



3. Explanation of the Photographs. 



The crystal that was employed in the following experi- 

 ments was cut perpendicular to the axis, and the portions 

 free from the twinning layer showed the ordinary '■' rings 

 and brushes" peculiar to crystals cut in such a manner. 

 The angle which the twinning plane makes with the faces of 

 the crystal is determined by observing the marginal outline 

 of the plane as seen on looking through the edge of the 

 crystal. 



The Hemitrope, as examined with tourmaline tongs, shows 

 very beautiful distortions and changes in the usual circular 

 ring-system. It is difficult to photograph the successive 

 stages completely, and it is found that the changes repeat 

 themselves four times during a turn of the crystal through 

 2-7T, when the tourmalines are crossed, — the position for which 

 mo*t of the observations were made. The rings lose their 

 circular nature altogether, and they will be found to be 

 elliptic as if pressed up and down or sideways. Moreover, 

 the change due to the introduction of the thin twin plane is 

 most prominent near the central part of the system. These 

 changes at the centre mixing up with the crosses make the 

 central portion look rather cumbrous. 



Figs. 1 to 4 (PI. IX.) represent the changes for a rota- 

 tion of the crystal through 7r/2, when the analyser has its 



* Mascart, Traite d'Optique, vol. ii. p. 192. 

 2 2 



