TKIMETRIC, OK OKTHOEHOMBIC SYSTEM. 39 



for the three are written c : b : a ; b being the Longer lateral and a the 

 shorter lateral, in place of the square prism of the dimetric system. 

 i-i, there are the c^miprisms i-l and i-z, or the macropinacoid and brachy- 

 pinacoid, having the expressions ic : ib : Id and ic : lb : id. The form ./ 

 is the rhombic prism, having the expression ic : \0 : M, corresponding 

 to the square prism / in the dimetric system. The planes i-n or i-h 

 are other rhombic vertical prisms, the former corresponding to 

 ic : nb : Id, the other to ic : 1£ : nd. If » = 2, the plane_ is lettered 

 either i-2 or i-2. The plane ±*-3 has the expression lc : lb : 3 J. wa-w 

 and m-n comprise all possible rhombic prisms and octahedrons, and 

 correspond to the expressions mc : nb : la and mc : ib : na. When m — 

 infinity they become i-n and i-h, or expressions for vertical rhombic 

 prisms ; when n = infinity they become m-i and 7?i-i, or expressions f oi 

 macrodomes and bracbydomes. 



The question which of the three axes should be taken as the vertical 

 axis is often decided by reference simply to mathematical convenience. 

 Sometimes the crystals are prominently prismatic only in one direction, 

 as in topaz, and then the axis in tfiis direction is made the vertical. In 

 many cases a cleavage rhombic prism, when there is one, is made the 

 vertical, but exceptions to this are numerous. There is also no general 

 rule for deciding which octahedron should be taken for the unit octahe- 

 dron. But however decided, the axial relations for the planes will re- 

 /nain essentially the same. In fig. 10, had the plane lettered £ been 

 made the plane 1, then the series, instead of being as if is in the figure, 

 1« £> &> oi would have been 2, 1, £ , f , in which the mutual axial rela- 

 tions are the same. 



The relative values of the axes in the trimetric system may be calcu- 

 lated in the same way as that of the vertical axis in the dimetric sys- 

 tem, explained on page 34. The law of the tangents, as stated on page 

 35, holds for this system. 



3. Hemihedral Forms. — Heinihedral forms are not common 

 in this system. Some of those so considered have been proved 

 to owe their apparent hemihedrism to their being of the mono- 

 clinic system, as in the case of datolite and two species of the 

 chondrodite group. In a few kinds, as, for example, calamine, 

 one extremity of a crystal differs in its planes from the other. 

 Such forms are termed hemimorphic, from the Greek for half 

 and form. They become polar electric when heated, th-at is, 

 are py isoelectric, showing that this hefnimorphism is connected 

 wir.h polarity in the crystal. 



4. Cleavage. — Cleavage may take place in the direction i>f 

 either of the diametral plaues (that is, either face of the rectan- 

 gular prism) ; but it will be different in facility and in the sur- 

 face afforded for each. In anhydrite, however, the difference is 

 very small. Cleavage may also occur in the direction of the 

 planes of a rhombic prism, either alone or in connection with 

 cleavage in other directions. It also sometimes occurs, as in 

 Bulphur, parallel to the faces of a rhombic octahedron. 



