254 A new system of Crystallographic Symbols. 
are the more common planes on the lateral angles,) it will be named 
according to the above law, that is, there will be no mark below, as 
none is used in marking the primitive planes. But if the comple- 
ment to the dominant is cut off, the inverted curve must be used be- 
low. Thus if the rhombohedron is obtuse, and a plane cuts off the 
acute plane angles, (complement to the dominant) from the lateral 
solid angle, the symbol for the planes will be a. In the right rhom- 
bic and right rhomboidal prisms, the superior and inferior basal edges 
are similar. ‘The latter must therefore receive the symbol of the 
former. The italic e is still retained for the side lateral or acute 
edge. It is however unnecessary in the right rectangular and nght 
square prisms, the lateral edges bemg similar. Hence they are gen- 
erally designated by e, and for the same reason all the angles are 
named a. 
We have now arrived at the cube, a solid with equal solid angles, 
equal plane angles and planes, and similar edges. ‘The planes are 
therefore lettered P, the angles a, the edges e. There is no necessi- 
ty of distinguishing them from one another. Planes on one edge or 
angle (with few exceptions to be noticed soon,) are attended with 
the same number similarly situated on the others. Hence to say, 
when a solid angle of a cube is replaced by six planes, that it is re- 
placed by one of these six, is saying: that every solid angle in the 
cube is replaced by six planes ; and generally with all the primitive 
forms, similar parts are similarly modified. ‘The exceptions to this 
law of nature are few; and when they do occur, still a symmetry 
of parts is always retained. Thus in Boracite four of the solid an- 
gles are similarly replaced, while the remaining four are left untouch- 
ed. It will be observed that these four angles are not all of them 
on one side of the crystal, but so disposed relatively to one another, 
that the figure is still symmetrical. ‘This is universally the case. 
To express the fact that but half of the angles or edges are similarly 
replaced, we have therefore but to add the fraction $. Thus ($a)? 
signifies that half the solid angles are replaced by the planes a?. 
More frequently it happens that all the angles or edges are similarly 
modified, but by half the usual number of planes. Thus it is in the 
cube, when it gives rise to the pentagonal dodecahedron. The fol- 
lowing form may then be given to the symbol, taking this dodecahe- 
9 
dron as an example, 9 sjonifying not as in the first case, that only 
half the edges are replaced, but on the contrary, that all are replaced, 
