Mr. W. Barlow on Crystal Symmetry. 



3 



symmetry solely to the face-directions, that groupings of dis- 

 tinct crystals exist in which a mere consideration of the faces 

 does not reveal the composite structure*; but, apart from this, 

 a case is conceivable in which the effect of the employment 

 of Gadolin's definition is to place an individual crystal in as 

 class of a symmetry higher than can be attributed to the actual 

 internal structure. The case referred to is the one mentioned 

 by Gadolin in which what,, according to his definition of like 

 directions, is a trigonal axis, is not a crystal axisj : it may be 

 described as follows : — 



Suppose that three axes, to which Haiiy's law of rational 

 indices can be applied, are so situated in a certain crystal as 

 to form the edges of a regular right triangular pyramid, 

 while the minimum intercepts on the three axes respectively 



A, OB, C (fig. 1), measured from the vertex of the 

 pyramid for the purposes of the law, are a ; Vn . a; VrP . a, 



3 3 



n being an integer, but Vn and Vn 2 irrational. It can then 

 be easily proved that, judged solely by the directions of its 



* For example : — a group of crystal individuals of boracite in the 

 doubly-refracting' state. 



f Gadolin : Memoire &c. pp. 49 & 50. The assumption made by this 

 writer in his introduction, that two directions which are similarly related 

 to the external form of a crystal display identical physical relations, is 

 not universally true ; the case described by Gadolin himself, which 

 is referred to in the text, furnishes an exception to it. 



B 2 



