of the Trimetric System. 41 



3. General Habit of Crystals. — A resemblance in general habit 

 is often to be detected between species related in crystallization. 

 Thus Brookite, as figured in the American Journal of Science, 

 vol. xvii., p. 86, resembles Columbite in the general arrangement 

 of its planes ; and we cannot mistake, in comparing them, as to 

 the homologous prisms of the two. Again, it requires but a 

 glance at the forms of Feldspar and Pyroxene to see that the 

 habit here is wholly opposed to any homceomorphism between 

 the species, while the family resemblance among the feldspars 

 themselves is very striking. 



4. Frequency of Occurrence of Planes, or Zones of Planes. — 

 This criterion is sometimes of importance, and still it is very 

 likely to lead astray. It is the common principle on which 

 crystals are mathematically described, for that is usually assum- 

 ed as the fundamental form which will give the simplest mathe- 

 matical view of the crystallization. But it is well known that 

 in many species secondary forms are most common. In Quartz, 

 the fundamental form is rarely seen ; in Calcite, the rhombohe- 

 dron — -|R and scalenohedron E, 3 , are of far more frequent occur- 

 rence than R; in Fluor, cubes are more common than octahe- 

 drons, the cleavage form ; and octahedrons, when they occur, 

 often have their surfaces made up of the angles of minute cubes ; 

 and the same is true of many species. It is consequent!}' no 

 certain evidence, when a prism terminates in a pyramidal sum- 

 mit (as in Mesotype), that it is the unit pyramid, or even that 

 the occurring prism in a species is one of the three unit prisms. 

 It is natural to assume that an occurring zone of planes is one 

 having the simplest ratios, and that among them exists one 

 having the axial ratio of unity, Id : lb : 1c. But this may be 

 far otherwise. Anhydrite is a familiar example. The occur- 

 ring prisms, according to the view of the author,* are §7 (fP 56 ) 

 and f I (f P oo ), which bring out well the homoeomorphism of 



* Araer. Jour. Science (2), xvii. 



