322 Mr. E. J. Chapman on the Notation of Crystals. 



common symbol. In the Monometric or regular system, for 

 instance, the sign a^ expresses both the planes of the octahe- 

 dron and the cube; and the " primary form," often an arbi- 

 trary one, must be stated before we can determine to \ihich 

 solid the symbol is intended to apply. The sign i^, again, in 

 the same system, may denote either the planes of the rhombic 

 dodecahedron, or those of a particular leucitoid, or even of 

 the cube. The only method of avoiding this imperfection is 

 by the arbitrary assumption of one primary form for the entire 

 group ; but this, which is literally done by the German school, 

 is so manifest a contortion of nature to convenience, that the 

 French mineralogists have wisely rejected its employment. 

 Another disadvantage in the system of Levy and Dufrenoy, is 

 the non-recognition of the important bearings which the dif- 

 ferent crystallographic axes have on the study of the science ; 

 at least, these axes play no part in their notation. 



In this particular the German systems possess an undoubted 

 superiority ; but the employment of arbitrary and often hypo- 

 thetical primary or fundamental forms renders them objection- 

 able. Their practical application, moreover, is by no means 

 free from diflticulty and inconvenience; for even the abbre- 

 viated system of Naumann is not sufficiently brief to allow of 

 the symbols being placed upon the ordinary figures of cry- 

 stals; neither can it be communicated verbally with any ease. 

 That it possesses great uniformity no one can deny; but 

 it may be questioned whether this very uniformity do not 

 occasion an unnecessary effort to the memory, in the recogni- 

 tion of the designated planes. Dana, who adopts Naumann's 

 system, has been forced, in the lettering of his crystals, to 

 ntake use of another method ; but this, although ingenious, is 

 not exact enough for the purposes of notation — Tor which, 

 indeed, it was never intended by its author, — nor can it be 

 verbally employed. I need not extend these observations by 

 referring to the works, however meritorious, of Professor 

 Miller, Mr. Griffin, and various other authors; because in 

 no one case are the three essential points, indicated above, 

 fulfilled ; owing either to the length, or to the peculiar con- 

 struction of the notations*. For these reasons I have at- 

 tempted to frame a system which shall serve both for the let- 



* These remarks will, I am sure, be received in the spirit in which they 

 are made ; for, in the words of one to whose researches crystallography 

 first owed its rank as a science, " la critique, iorsqu'eile est juste et mo- 

 deree,loin d'alterer I'estiniequesedoivent reciproqueraent ceuxqui courent 

 la uieme carriere, ne fait que les exciter a de nouveaux efforts. Une telle 

 critique ne dephiit jamais qu'a des esprits superficiels, ou gates par les 

 6Joges outrt's de leurs contemporains.'' — Royn^ de I'Isle, Cristallographie, 

 <5"c., vol. i. p. xxiii (second edition), 1783. 



