Crystals requiring neither Measurement nor Calcidailon. 2S7 
Then, obviously, 
The second modification will be the result of a decrement by 
two rows in height on the edges h of the bases. 
The third is then the base of the prism. 
The fourth, from a decrement by one row on the lateral 
edges. 
The fifth can only be determined by the incidence of one of 
its planes on 1 . The angle given by Mr Phillips makes it the 
result of a decrement by three rows on the lateral edges. 
From the two parallelisms mentioned before, relative to the 
seventh modification, and by the use of the second formula, it 
will be found, that this modification is the result of a decrement 
by five rows in breadth on the angles of the lateral faces of the 
prism. 
The sixth modification, from the parallelisms before ascer- 
tained, will, in an analogous way, be found to result from a de- 
crement by five rows along the lateral edges. 
The faces of the ninth modification are at once parallel to an 
edge of the base of the primitive and to the interseetion of two 
planes of the seventh modification, (see Plate 21.) They are 
therefore produced by a decrement by five rows in height on the 
edges of the base. 
Lastly, the eleventh modification is produced on the same 
edges, by a deci^ement by one row being parallel to the line of 
intersection of two adjacent faces, Plate 23. There would be 
no difficulty now to find the indices of these modifications rela- 
tive to the octohedron, and to calculate the hicidences of any 
two planes having once measured 2 on 1, 
The conclusions to be drawn from the preceding observations 
are, that the parallelisms which frequently exist between the 
edges of a crystal, are of great importance ; they are a proof of 
the simplicity of the structure. They enable us, without mea- 
surement, to determine a secondary face, when they are observed 
to exist between two sides of that face and two known edges of 
the crystal. The measurements in that case have no other use 
than to try the accuracy of the goniometer, and the perfection 
of the crystal. When a crystal is described, these parallelisms 
should be carefully mentioned : in the rough drawings, they 
should be preserved as nearly as possible. In exact drawings, 
the orthographic projection should always be used. 
