80 



HABIT AND INTELLIGENCE. 



[chap. 



Boracite. 



Intermedi- 

 ate forms, 

 showing 

 the true 

 affinities 

 of the 

 rhombo- 

 hedral 

 system. 



The most remarkable instance of a species intermediate 

 between classes is that of boracite, which is geometrically 

 one of the cubic system, but has the optical properties of 

 a rhomboheclral crystal: its optic axis is parallel to one 

 of the diagonals of the cube.-^ There are also several 

 instances of plesiomorphism between the cubic and rhom- 

 bohedral systems. 



In organic classification, the discovery of intermediate 

 gi'oups is often of great importance for the purpose of 

 giving an insight into the true affinities of organisms and 

 the true homologies of their parts. It is the same in 

 crystalline classification. An important question, on 

 which authorities are divided, is, what are the true crystal- 

 lographic axes and the true fundamental form of the 

 rhombohedral system. Those whom I have followed 

 regard the fundamental form as the rhombohedron, and 

 the true crystallographic axes as those lines which connect 

 the centres of its opposite faces. Others call the system 

 hexagonal instead of rhombohedral : they regard the 

 hexagonal prism as the fundamental form, and the axis 

 of symmetry of that form as the vertical axis ; and they 

 draw three horizontal axes in the same plane, at right 

 angles to the vertical axis. The rhombohedron and the 

 hexagonal prism are forms that are both found in the 

 system ; both, indeed, are found in the one species of calc- 

 spar : and either may be derived from the othei', in strict 

 accordance with the geometrical laws of crystallography, 

 by supposing the angles of the primary form to be 

 truncated by secondary planes.^ 



* Pereira's Lecture on Polarised Light, p. 194. 



* Brooke and ^Miller adopt the rhombohedral theory ; Dana, the 

 hexagonal one. 



It may be said tliis is only a question of words, since either theory gives 

 true mathematical results. I believe, however, that an inaccurate classi- 

 fication always tends to obscure knowledge. 



In the text I have in some degree sacrificed accuracy to clearness and 

 intelligibility. There is not strictly any such thing as a fundamental 

 form ; the only constant crystallogi-aphic elements are the inclinations of 

 the axes, and the ratios of the parameters. In the cubic system, for in- 

 stance, the cube and the octohedron may with erpial accuracy be regarded 

 as fundamental ; and that system is called nrtobedral as often as cubic. 



