38 J. D. Dana on the Homaomorphism 
cannot mistake, in comparing them, as to the homologous prisms 
o 
the two. Again, it requires but a glance at the forms of 
feldspar and pyroxene to see that the habit here is wholly op-: 
posed 
to any homeomorphism 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 crys- 
tals are mathematically described, for that is usually assumed as 
the fundamental form which will give the simplest mathematical 
view of the crystallization. But it is well known that in many 
species secondary forms are most common. In Quartz, the fun- 
damental form is rarely seen; in Calcite, the rhombohedron —$R 
and scalenohedron R°, are of far more frequent occurrence than 
R; in fluor, cubes are more common than octahedrons, the cleav- 
age 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 consequently no certain evidence, 
when a prism terminates in a pyramidal summit (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, 
la:16: 1c. But this may be far otherwise. Anhydrite is 4 
familiar example. The occurring prisms, according to the vieW 
of the author,* are 27(2P@) and 2%(2P&), which bring out 
well the homeomorphism of the species: with the other allied 
sulphates; but the three octahedral planes are then 3%, $754 
and ¢%,"; and in any other view that recognizes the hom@0- 
morphism, the expressions for the planes are scarcely less complex 
We cannot be too guarded, therefore, when deducing the form 
for comparison with another species, in relying on the prevalence 
of certain planes. Valuable hints are often thus given, but they 
may lead to error. ; 
‘The lustre or smoothness of planes is a better guide, though 
far from certain. ‘The fundamental vertical prism in Barytes 18 
generally less highly polished than many other faces; and as We 
ve above remarked, the octahedrons of fluor have often rough 
surfaces. r 
The prevailing direction of the more extended zones of planes, 
especially the octahedral, often suggests rightly which is properly 
the terminal plane of the prism, these zones rising towards that 
plane; and they thereby afford a hint as to which is the vertica 
axis. In dimetric and hexagonal species, this criterion is a sure 
CPS iy) Set Aa Tomr, Bel, (2].27,/ 08. * ae 
- 

