'38 ME. H. J. BEOOKE ON THE GEO^VIETEICAE ISOMOEPHISM OE CETSTAXS. 
case of each mineral two possible prisms, a and 5, of equal dimensions, but related to each 
other in position in the manner shown in the annexed sketch, fig. 7, 
which is a projection of the two intersecting prisms on a plane 
parallel to their common terminal face 0 01. When these prisms 
occui’ together in natural crystals, they present the outline sho'v\Ti 
in fig. 8. From which it is evident, that if the prism a be taken 
as the primary prism, the faces of h will appear to truncate the 
lateral edges of a ; and conversely, if h is taken as the primary. 
It is also clear that any face which truncates a terminal edge of 
a would be a truncation of a solid angle of J, and conversely. 
It does not appear that natural crystals afibrd any indication 
to govern our choice of one or the other of these prisms as the 
primary form of any mineral ; and as relates to the crystals of 
any single mineral, it is indifiereirt which prism we select. But 
it is not so with respect to the crystals of any group of two or 
more different minerals which have afterwards to be compared 
with each other. 
In these cases the same prism, a or should be assumed as 
the primary prism throughout the group. And as the position of a is that in which 
pyramidal crystals are usually dravm, the faces of all the crystals exhibited in the Tables 
P I and P 2, are referred to elementary prisms assumed to be in the position of a. 
It has hence been necessary where h has been given in previous works, and in Table 
P I (Plate II.), as the elementary prism of some of the minerals, to substitute a for Jin 
Table P 2 (Plate III.), and to make the rrecessary changes in the sjunbols of the other 
faces consequent upon the change of the elementary prism. 
It appears in Table P I (Plate II.), that the faces of differerrt minerals making equal 
or nearly equal angles with the face 0 01 have been referred by different observer's to 
a prism in the position of a in some cases, and to a prism h in others. 
Thus a face which in Towanite makes an angle of 54° 20' with the face 0 01, has for 
its symbol III, denotirrg a face replacing a solid angle ; while in Brarrnite, a face making 
the same angle with 0 01, has for its symbol Oil, denoting a face on an edge, arrd show- 
ing that if the prism a has been used for the primary of Towanite, the prism h has been 
used for that of Braunite. 
Again, it ulll be seen in Table P I (Plate ll.), that two of the faces of Scheehte make 
angles of 36° 34' and 46° 22' respectively with the face 0 01, arrd that two faces making 
the same angles with 0 01 occur in Wulferrite. Yet, instead of regardirrg these as angles 
between corresponding faces in the two minerals, they are referred in Scheehte to the 
prism a, and to J in Wulfenite. And as if further to complicate arrd corrceal the identity 
of these crystalline forms, the symbols assigned to their correspondiirg faces also disagree. 
Having reduced the elementary prisms throughout the systerrr to con-espondirrg 
positions, the rrext point for consideration has been the arrgle which might be selected 
as a proximate elementary angle of the group. 
Fig. 7. 
b 
Fig. 8. 
cc 
