146 METHODS FOR PREPARING, EXAMINING, AND MEASURING 



by the use of the larger instruments. The use of the special eyepieces 

 arranged with artificial twins of calcite or quartz enables the observer to 

 determine the extinction angles of the crystals with as much accuracy as 

 can be done with any form of polariscope. 



From such observations, made with the aid of this form of microscope, 

 the following constants may be determined : 



(1) The plane angles of the crystals, in most cases the interfacial 

 angles, giving the data from which the axial ratios are computed in other 

 words, the morphological constants of the single crystals. 



(2) The relation of the parts of the composite crystals or twins to each 

 other, their angles, and the position of the twin plane, twin axis, compo- 

 sition plane, and other constants of the twin crystals. 



(3) The pleochroism of the crystals, the character of the colors of the 

 light vibrating parallel to the elasticity axes in the crystal. This is effected 

 by the use of the single polarizing prism below the stage. Bj 7 analyzing this 

 light with the microspectroscope the differences of tint and color may be 

 given quantitative values in wave lengths. 



(4) The position and relative values of the light elasticity axes in the 

 crystals, upon which depend the angles of extinction of the crystals, meas- 

 ured from certain crystallographic axes or planes or edges. In uniaxial 

 crystals (tetragonal and hexagonal systems) there are two such elasticity 

 axes the ordinary ray, designated as co, and the extraordinary ray, desig- 

 nated as f . Either one of these may be the axis of greater or less elasticity, 

 and according as the extraordinary ray is the axis of less elasticity or of 

 greater elasticity the crystal is called optically positive or optically negative. 

 In biaxial crystals (orthorhombic, monoclinic, and triclinic systems) there 

 are three elasticity axes at right angles to each other, and these are desig- 

 nated as a, the axis of greatest elasticity; b, the axis of mean elasticity; and c, 

 the axis of least elasticity. 



(5) The position and angle of inclination of the optic axes or lines of 

 single refraction through the crystals. These always lie in the plane of the 

 elasticity axes a and c and the angles between the optic axes are bisected 

 by the axes a and c. According as to whether c or a is the axis bisecting 

 the acute angle, the acute bisectrix, Bx n the crystal is called optically posi- 

 tive or negative. Thus if Bx a = c, the optical character is positive. The 

 apparent angle between the optic axes is determined by means of an eye- 

 piece micrometer in an observation of the interference figure, looking along 

 the acute bisectrix of the optic axes, and this angle is designated as 2E. 

 The character of the double refraction may be determined by this angle. 



When good crystals were available for examination the physical data 

 above enumerated could all be determined. Other data were recorded, 

 such as the morphological habit, the character of the heterogeneous aggre- 

 gates formed by the crystals, their relative dimensions, general color, etc. 

 The character of the material under investigation was determined by the 

 use of a Zeiss microspectroscope. As a general rule, the crystals were kept 

 under examination until they ceased to change or until they were destroyed 

 by bacterial decomposition. In this way the changes that the crystals went 



