563 



through, until it intersects tlie oonstrucied polar circle in the left 

 pai't of the figure. 



'This point of intersection is the stereographical projection of the 

 molecular plane, which corresponds with tlie spot in the right part 

 of fig. 2. The points in can be easily found from the points z by 

 an additional construction, in which a circle with a radius of 50 m.m. 

 is used ; the contractions of the original distances to C, — whicii 

 thus can be represented by m:. — are moreover for spots in the 

 neighbourhood of C only so slight, that without considerable error, 

 instead of m, the point z itself may be used ; but at greater distances 

 from C this of course is no longer allowable. The system of polar 

 circles and poles of reticular planes obtained in this way, will give 

 a direct review of the total zone-relation and of the indices of the 

 molecular planes; while the calculation of the angles between the 

 poles of those reticular planes and the plotting of gra|)hical con- 

 structions etc., can be made in the way usual in crystallonomy. It 

 is adviceable to keep the radius of the projection-circle in the left 

 part of fig. 2 equal to 2A (100 m.m.); then it is possible to execute 

 the diff'erent constructions by means of Wl'LFk's stereographical pro- 

 jection plat with a diameter of 20 cm. The indices of the poles of 

 the reticular planes are the same as the original ones of the spots 

 in the projection to the right of fig. 2. 



Finally we can express the different intensities of the spots in the 

 original figure, into the projection-figure of the corresponding molecular 

 planes to ihe left of fig. 2; in this way a further discussion of the 

 relations between the indices of the reticular planes and their 

 spectral-resolving power can be made, in the way indicated for the 

 first time by Bragg. 



§ 4. As an applicafion of the discussions given above, we will 

 consider here more in detail the RöNTOKN-patterns of the finhi/dritc. 

 The parameters of this mineral are: a : /; : c = 0.8932 : J : J. 0008; 

 from this it follows, that for a distance of iOO m.m. between the 

 plane of projection P and the viewpoint () of the projection, the 

 projected spots for Ihe faces SlOij, jOiJj and |UOj will be situated 

 at the distances : 



For a plate parallel to {100| : 



in the direction of the 6'-axis at 112.04 m.m. froni C 

 „ „ ., „ „ ^'-axis „ 111.95 „ „ „ 



For a plate parallel to jOiOj: 



in the direction of the (^'-axis at 100.08 m.m. from C 

 „ „ „ „ „ .'l-axis „ 89.32 



