THE MICROSCOPE BY MEANS OF THEIR OPTICAL CHARACTERS. 623 



(fig. 19), while the convex margin will exhibit lower colours. 

 If the crystal have the opposite character, the reverse will be 

 the case. The amount of the curvature of the isogyre in this 

 position gives some idea of the magnitude of the acute optic- 

 axial angle. If the isogyre be straight, the angle will be 90 

 {fig. 18), while if it forms a right angle coinciding with two arms 

 of the cross wires, it is 0. In this case the other branch of 

 the hyperbola coalesces with it, forming the cross characteristic 

 of a uniaxial crystal (fig. 21). 



A very rough approximation to the optic axial angle, which 

 may be employed for determinative purposes, may be obtained 

 by taking the angular distance 6 round the circumference of the 

 field between the darkest point in one end of a branch of the 

 hyperbola and the nearest cross wire, and doubling it (fig. 19). 

 The result is usually too high, especially for medium angles, in 

 which the error may amount to 10. F. Becke has shown how 

 a much more accurate result may be obtained,* and a still 

 more rigorous procedure is described by F. E. Wright. f 



These methods may be applied even when the section is not 

 exactly at right angles to the optic axis, if the point of emergence 

 of the latter appears in the directions-image (fig. 20). Such 

 sections may be recognised in the object-image by the compara- 

 tively low relative retardation. 



Sections showing a Black Cross ivhich breaks up on Rotation of 

 the Stage. Unless the section be at right angles to an acute 

 bisectrix, the character of the longitudinal direction of vibration 

 (see p. 620) will be that of the crystal, and this will always be the 

 case if the section shows high relative retardation compared with 

 most other sections of the same mineral with the same thickness. 

 The black crosses seen in sections of uniaxial crystals parallel to 

 the optic axis and of biaxial crystals at right angles to the 

 optic normal are distinguished by the rapidity with which 

 they break up and leave the field when the stage is rotated. 

 Where the optic axial angle is small, sections at right angles to 

 the obtuse bisectrix resemble those at right angles to the optic 

 normal. 



* Min. Petr. Mitt. {Tschermak), vol. xxiv., 1905, pp. 35-44; Min. 

 Mag., vol. xiv., 1907. p. 280. 



j American Journal of Science, Series IV., vol. xxiv., 1907, pp. 

 332-341. In the same paper other methods are discussed. 



