Geology and Mineralogy. 351 



potash- and ammonia-alum. Brilliant and apparently perfect 

 octahedra of these salts show large variations in the octahedron 

 angle; other crystals show low vicinal planes in place of the octa- 

 hedron faces. It it be true, as is supposed, that the octahedron angle 

 varies in different crystals, it would be interesting to ascertain 

 whether progressive variations can be traced during the growth 

 of a single crystal, and whether some or all of the octahedron 

 faces change their direction in space if the crystal is held fixed 

 during growth. 



In order to solve this problem a new goniometer has been con- 

 structed, in which the crystal is fixed at the lower end of a 

 vertical axis, so that it can be immersed in a liquid during 

 measurement. This device is in reality an inversion of the 

 ordinary goniometer with horizontal disc; the liquid is contained 

 in a rectangular glass trough with parallel-plate sides ; one side 

 is placed rigidly perpendicular to the fixed collimator, and the 

 other is perpendicular to the telescope, which is set at 90° to the 

 collimator. The trough is supported on a table which can be 

 raised and lowered, so that the crystal can be placed at any 

 required depth in the liquid. If the liquid used be its own con- 

 centrated solution the crystal can be measured during growth, 

 and the changes of angle, if any, can be observed at different 

 stages. In order that it may be held rigidly, the crystal is 

 mounted, when small, in a platinum clip, which it envelops as it 

 grows larger. 



The results derived from the measurement of a large number 

 of alum crystals are as follows : — 



(1) The faces of the regular octahedron are never developed 

 upon alum growing from aqueous solution. 



(2) The reflecting planes (which are often very perfect) are 

 those of a very flat triangular pyramid (triakis octahedron) which 

 overlies each octahedron face. 



(3) The three faces of this triangular pyramid may be very 

 unequal in size. 



(4) The triakis octahedron which replaces one octahedron may 

 be different from that which replaces another octahedron face 

 upon the same crystal. 



(5) During the growth of the crystal the reflecting planes 

 change their mutual inclinations ; the triakis octahedron becomes 

 in general more acute, i. e. deviates further from the octahedron 

 which it replaces, as the crystal grows. 



(6) This change takes place not continuously, but per salturn, 

 each reflecting plane becoming replaced by another which is 

 inclined at a small angle (generally about three minutes) to it. 



(7) During growth the faces are always those of triakis octa- 

 hedra; if, owing to rise of temperature, re-solution begins to 

 take place, faces of icositetrahedra are developed. 



These observations prove that the growth of an alum crystal 

 expresses an ever-changing condition of equilibrium between the 

 crystal and the mother liquor. It does not take place by the 



