TRIMETRIC, OR ORTHORHOMBIC SYSTEM. 59 
v 
for the three are written¢: 6: da; 6 being the longer lateral and d@ the 
shorter lateral. in place of the square prism of the dimetric system, 
#-7, there are the .<miprisms 2-2 and 7-7, or the macropinacoid and brachy- 
pinacoid, having the expressions t¢ : 76: 1d and t¢ : 16: id. The form I 
is the rhombic prism, having the expression i¢ : 10: 1d, corresponding 
to the square prism / in the dimetric system. ‘The planes 72-7 or 7-” 
are other rhombic vertical prisms, the former corresponding to 
ic: nb:1d, the other to ic: 16: nd. If m= 2, tbe plane is lettered 
either 7-2 or 7-2. The plane 3 has the expression Jeo:16:384 m-n 
and m-7 comprise all possible rhombic prisms and octahedrons, and 
correspond to the expressions mc: nb: 1dé and me: 1b: nd. When m= 
infinity they become 7-71 and 7-7, or expressions for joided! rhoinbic 
prisms; when n = infinity they become m-7 and m-7, or expressions for 
macrodomes and brachydomes. 
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 tilis 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 
ruie for deciding which octahedron should be taken for the unit octahe- 
dron. But however decided, the axial relations for the planes will re- 
rain essentially the same. In fig. 10, had the plane lettered 4 been 
made the plane 1, then the series, instead of being as it is in the figure, 
1, 4, 4, 4, would have been 2, 1, 3, $, 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 
30, holds for this system. 
3. Hemihedral Forms.—Hemihedral 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 yorm. They become polar electric when heated, that is, 
are pyroelectric, showing that this hemimorphism is connected 
with polarity in the crystal. 
4, Cleavage.—Cleavage may take place in the direction of 
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 conrection with 
cleavage in other directions. It also sometimes occurs, as in 
sulphur, parallel to the faces of a rhombic octaliedron. 
