Application of Elementary Geometry to Crystallography, 345 



Allophane from Charlton dried at 100° C. 



I. II. III. 



Alumina . . 46-34 49-53 50-82 



Silica . . . 30-31 26-00 22-11 



Water. . . 23-35 24-47 27-07 



100-00 100-00 10000 



It is scarcely conceivable that this very great loss of water 

 should be peculiar to the Charlton allophane ; but it yet seems 

 singular that no chemist but Guillemin should have made the 

 observation that such a loss occurred, and that in his case it 

 should have been comparatively so small : obviously in these 

 specimens, at least, the vpater in the native mineral exists in 

 two very different states of combination; whether the entire 

 amount is necessary or superfluous to its constitution as allo- 

 phane has yet to be shown. My present object is to draw atten- 

 tion to the fact, that, regarding the water expelled at 100° C, as 

 uncombined, or simply adherent, formulae may be assigned to 

 the mineral which do not militate against the generally received 

 views of the constitution of saline compounds. This, however, 

 cannot be urged in defence of such formulae as have hitherto been 

 given, — those of Dana for instance, 



3A12 03, 2SiO3 + 20HO 

 and 



3AP03, 2Si03 + 15H0; 



or of Gmelin, 



Al^O^, Si03 + 7HO 

 and 



AFO-, SiO^ + SHO, the dried specimen of Kersten, 



are scarcely in accordance with existing ideas, and certainly do 

 not tend to elucidate the confessedly obscure question of the 

 constitution of the silicates. 



XLVIII. On the Application of Elementary Geometry to Cry- 

 stallography. By W. H. Miller, M.A., F.R.S., Professor of 

 Mineralogy in the University of Cambridge"^. 



1. npHE instruments of analysis hitherto employed in investi- 

 M. gating the general geometrical properties of crystals, have 

 usually been either analytical geometry of three dimensions, or 

 spherical trigonometry. Lately, however, Professor Sella of 

 Turin has deduced the symbol of a zone containing two known 

 faces, the symbol of a face common to two known zones, and 



* Communicated by the Author. 



