136 Note on the Optical Characters of Ludlamite. 



side of the normal 01. Consequently the normal of the face 

 10 makes an angle of 22° 55' on one of the principal sec- 

 tions. A plate was accordingly ground from this crystal in a 

 direction as nearly perpendicular as was attainable to this prin- 

 cipal section ; and a second plate was formed from a cleavage 

 fragment of another crystal as nearly as possible perpendi- 

 cular in direction to that of the former plate and to the plane 

 of symmetry. 



Examined in oil, the optic axes were found to make an ap- 

 parent angle of 97° 50 / in the former plate and of 119° in the 

 latter. The first mean line is therefore inclined on the normal 

 of the face 1 at 22° 55', and on the normal of the face 01 

 at an angle 77° 38'; and the acute angle between the optic 

 axes within the crystal, as obtained by calculation, is 88° 54'. 



The dispersion of the optic axes for the different colours 

 appears to be inconsiderable. The striated structure of the 

 crystal from which the plate was cut perpendicular to the first 

 mean line somewhat obscured the tints close to the hyperbolas ; 

 but in both the eyes representing the optic axes a blue fringe on 

 the convex side of the hyperbola was discernible. In the other 

 plate this characteristic was more marked, as in it each hy- 

 perbola presented a blue fringe within the first ring on the 

 side nearest, and a red fringe on the side opposite, to the 

 second mean line. Consequently the mean lines for these 

 colours can be very little dispersed ; for their dispersion is not 

 recognizable in the plates experimented on ; but the optic axes 

 for the red rays present a slightly wider divergence in respect 

 of the first mean line than do those for blue light. 



The optical character is positive, as shown by the dilatation 

 of the rings in the former of the two plates when a plate of 

 quartz, cut perpendicular to the axis, is rotated on a line per- 

 pendicular to that which joins the optic axes in a Noremberg 

 polarization-apparatus. 



It may be worth while observing that the directions of the 

 principal sections in a small plate can be determined with ease 

 and with considerable accuracy by the method above described, 

 since, if the point of maximum obscuration is difficult to be 

 hit upon with precision, this determination can be much faci- 

 litated by a slight rotation of the analyzing prism to right or 

 left ; for then tints developed in the crystal assist in indicating 

 a slight inclination of its principal section to the plane! of po- 

 larization. Of course the relative directions of the principal 

 sections of the crystal, and of the trace (or edge) of one of its 

 faces perpendicular to the plane of symmetry, are readily de- 

 termined either by the revolution of the crystal on the rotating 

 stage till the trace of the plane is in contact with the wire of 



