CRYSTALLOGRAPHY MINERALOGY. 305 



systematic use of the contact-goniometer, constructed for him by 

 Carangeot ; the instrument that, in the hands of his great rival 

 and successor, Haiiy, enormously multiplied the data on which 

 was to be built up a science of Crystallography. 



That name, indeed, had been adopted by Rome de Lisle 

 (probably from an earlier work by Capeller), as the title of his 

 treatise Essai de Cristallographie, which first appeared a hundred 

 and four years ago; a work which, in a subsequent edition in 

 1783, assumed the form of a really scientific treatise, and was 

 enriched with the numerous- measurements, and the deductions 

 from them, whereby Rome de Lisle established the invariability of 

 the angles of certain simple forms of crystals. 



It was Haiiy who first sought to establish a general connection 

 between the simplest and other more complex groups of faces 

 shown by crystals. And he reduced their relations to a geo- 

 metrical shape, referring them to groups, while he recognised the 

 importance of cleavage and of certain physical properties, and 

 left Crystallography a science, while at the same time by its aid 

 he gave a new form to Mineralogy. (Traite de Min'eralogie, 1801.) 

 His pupil Weiss, shaking off the molecular hypothesis with 

 which Haiiy had trammelled his treatment of the geometry of 

 a crystal, gave to crystallography the power of dealing with its 

 problems from a more abstract point of view. As the originator 

 of the idea, though incomplete, of symmetry in respect to axes as 

 the ruling feature in a crystal, Weiss gave a new standing-point to 

 the science : he designated the crystallographic systems upon this 

 principle, and instituted a mode of crystallographic notation simpler 

 and more easily intelligible than that of Haiiy. 



In this notation we first (1816) have the faces of a crystal 

 referred, not to its external edges for geometrical comparison, but 

 to axes (parallel to certain of these edges) internal to the crystal ; 

 while parametral ratios, as we now term them, were recognised in 

 the relative distances along these axes at which some chosen face 

 would intersect them. Simple coefficients of these axial lengths, or 



x 



