300 F. Rutley — On Crystallographic Formulae. 



and convey as much information as the more lengthy ones which 

 are now in use. I would, however, wish those better qualified than 

 myself to form their judgment upon these points, and merely submit 

 this system to them in the hope that its simplicity may commend it, 

 and that, by trial, they may remedy any defects by devising some 

 more simple and better method. 



In writing the formula for any face of a crystal, I propose first to 

 draw a horizontal line or bar, which may be termed the common or 

 Jiolohedral bar, thus — ; while to indicate hemihedral forms one 

 end of the bar may be curved, thus C__. Any axis cut at a normal 

 distance may be represented by a short vertical line joined beneath to 

 the common bar, thus f- . For example, in the regular octahedron all 

 three axes are cut at normal distances, and the symbol would conse- 

 quently be TO* . In this case the old symbol is more simple, but the 

 advantages of this system will become more apparent as we proceed. 



The next innovation which I propose is to use a dot in place of 

 the old symbol for infinity. The formula for the cube would there- 

 fore be -^ instead of the old symbol oo co used by Naumann, and 

 the Ehombic Dodecahedron would in like manner be represented by 

 iir . It will now be seen that by this method the beginner has 

 the advantage of noting at a glance the number of cut and uncut 

 axes. The conventional distances m and n are represented by a 

 prolonged vertical cross line for the former "^, and by a curved line 

 for the latter, thus -€. So that the Hexakis Octahedron toOm of 

 Naumann would be represented by -W. If it be necessary to express 

 the linear values of m and n, then the formula may be written ■g-yf , 

 which would represent a Hexakis Octahedron, any face of which 

 intersects one parameter of normal length, and would, if produced, 

 cut a second of triple that length, and a third of one and a half 

 times the length of the normal parameter. In open forms the basal 

 plane may be conveniently represented by ♦ , which should be placed 

 over the mark which represents the axis cut by that plane : thus the 

 Tetragonal Prism would be ^ , and the Eight Ehombic Prism would 

 also be represented by the same symbol. The Hexagonal prism 

 would differ in having an additional infinity-dot affixed, thus Tm> to 

 show that there is a fourth axis which, is unavailable for the in- 

 dividual face formularized. The Ehombohedron would be repre- 

 sented by Vrr.j because each face concerns four parameters ; while the 

 Scalenohedron would be Sirf,' 



In the Ehombic system Macropinakoids would be •sir instead 



of CO P 00, and Brachypinakoids -r^ instead of oo P oo of Naumann 

 and the " i "s employed by Dana.^ 



In the Monoclinic system a slanting line indicates the clino- 

 diagonal, and the oblique rhombic pyramid and prism would there- 

 fore be TI7 and qy; while the oblique rectangular pyramid would 

 T7T and IT/, the disconnected slanting dash being used instead of a 

 dot to show that the clino-pyramidal faces do not cut the clino- 

 diagonal. The oblique Eectangular prism will be ^jr and rir, the 



^ The ordinary S3rmbol in Naumann's notation, P, does not show the relation of 

 each face of the hexagonal pyramid to the 3rd lateral axis. 



