280 Mr Haidinger on the Regular Composition 



certain their junction, since portions of the faces marked M 

 will then coincide in one continuous plane. When the re-en- 

 tering angles at n and o are likewise filled up, a six-sided prism 

 is produced, having four angles of 117° 13', and two of 125° 34'. 

 But it occurs often, that in the same manner in which one 

 individual is joined to the original one, in a plane of M, con- 

 tiguous to w, Fig. 6, in the same manner also one individual 

 is joined to the same parallel to the other face of M, contigu- 

 ous to the point r. The inclination of M on M' of the two 

 individuals added, is = 720 — (3 x 117° 13'+2 x 125° 34'), or 

 = 117° 13'. If all the individuals be continued beyond their 

 respective faces of composition, a figure will ensue like a star 

 with six radii, similar to Fig. 7. The angles formed at the 

 points w, produced by the faces M and M ', or M" and M n \ if 



6fl2tf°— -117° 13') 

 they should happen to meet, are = 180° + = 



188° 21', the supplement of which to 360° is 171° 39'. 



In order to show the application of these rules to nature, a 

 few examples may now be given, selected from the varieties 

 actually met with ; although even the figures employed in the 

 explanation of the theory are found more or less distinctly, 

 and usually with various additional faces, as Fig. 6, at Johann- 

 georgenstadt in Saxony, and Wanlockhead in Scotland ; Fig. 

 3, and Fig. 5 at Leadhills, &c. Fig. 8 is a twin-crystal, of 

 the di-prismatic lead-baryte, from Nertschinsk in Siberia. It 

 is one of those which give the idea of a six-sided prism acu- 

 minated by six planes, set on the lateral planes of the prism. 

 The two individuals are joined parallel to a face of M, as ap- 

 pears more distinctly in the projection Fig. 9, where the line 

 r z represents that plane. The face I and I meet at z, and 

 produce an angle of 11 7° 13', while the angle at r is — 720° — 

 3xH7°13'— 2xl21°23i'-125°34. No re-entering angles 

 appear, if the face of composition passes exactly through the 

 edges of combination between Pr and Pr -f- co . But if this be 

 not the case, such angles will become apparent, as in the figure 

 10. The difference of the angle z' from 120° is = 121°23|' 

 — 117 c 13=4°10£', that of the angle r' = i25°34'— 121°23J' 

 =4°10| / ; the angles themselves are equal to 184*10^', and 

 175°49J'. Usually these re-entering angles are easily ob- 



