ME. H. J. BEOOKE ON THE GEOMETEICAL ISOMOEPHISM OF CEYSTALS. 
3!) 
A guide to this selection presents itself in the crystals of Apophyllite, the angles of 
which scarcely differ from those of a cube, and therefore admit an elementary angle of 
exactly 45°, which angle has been assumed as a variable type of the elementary angles 
throughout the system. 
'WTiether this angle of 45° is accidental, or is the effect of any at present unknown 
relation between the cube and the square prism, the Avriter is not aware. But it is a 
rather curious fact that there should also be in the rhomb ohedral system a series of 
elementary angles of about 55°, not differing much from angles between two correspond- 
ing faces of a cube. 
On referriug to Table P 1 (Plate II.), it will be seen that the crystals of Somervillite, 
Faujasite and Eomeine are represented by single faces only, to each of which the symbol 
I 0 I has been hitherto applied. But as the occuiTence of only those particular faces on 
the three cr^’^stals must be regarded as piu'ely accidental, there is no reason for applying 
that particidar symbol to either of them. And as the symbols of faces are not in any 
manner indicated by the faces themselves, we are at liberty to assign to those or to any 
other faces any symbols which are consistent with the geometrical relations of the faces 
in question. And hence have arisen some of the differences of symbols shown in the 
Tables P I and P 2 (Plates II. and III.). 
The elementary angle of the crystals of Towanite being 44° 35', and as those crystals 
present as great a number of observed faces as those of any other mineral in this group, 
and as the position of the primary form may be assumed to be that of the prism «, the 
symbols and angles of this mineral have been used as standards for comparing and regu- 
lating the symbols of the remainder of the group, as shown in Table P 2 (Plate III.). 
The method of reducing the series of minerals in each of the pyramidal and rhombo- 
hedral systems to single groups, has been to form in the fii’st instance in each case small 
groups, and then to associate these into larger ones. 
Thus in Table P I (Plate II.), there appears in 
Towanite . an angle of 1 9° 1 3', corresponding to the symbol 1 1 4 
Anatase . . an angle of 19 34, corresponding to the symbol 1 1 7 
Apophyllite an angle of 19 30, corresponding to the symbol 115, 
forming a small geometrical group, to each member of which in Table P 2 the symbol 
1 1 4 of Towanite has been assigned as a common and connecting symbol of the group. 
Again, in Table P 1 (Plate II.), in 
Towanite . an angle of 33° 18' has the symbol 2 0 3 
Entile . . an angle of 32 47 has the symbol 101 
Ox. Tin . an angle of 33 55 has the symbol 101 
Zircon . . an angle of 32 38 has the symbol 101 
Someiwillite, an angle of 32 51 has the symbol 101, 
producing another analogous group under the connecting symbol 2 0 3 of Towanite, and 
thus directly associating four other minerals with Towanite. 
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