Mr. W. Barlow on Crystal Symmetry. 5 



Gadolin's method, because ifc dispenses with hypothesis, 

 has commended itself to all students of crystals alike — both to 

 those who adopt some hypothetical basis for the theory of 

 these bodies, and also to those who prefer to exclude all 

 hypothetical considerations whatever. The question is : Can 

 the weak point in the basis of his argument be obviated by 

 laying down a more precise definition of like directions in a 

 crystal, without employing some merely hypothetical concept? 



The answer is that if it be admitted that the state of 

 scientific research allows us to regard the existence of mole- 

 cular structure of some kind or other as proved*, a definition 

 of the requisite accuracy is attainable ; indeed, that such a 

 definition was, in substance, suggested by Camille Jordan 

 more than thirty years agof. 



For if molecules are present, an ultimate discontinuity of 

 matter exists, and the following quite general definition of 

 homogeneity of a rigid molecular aggregate can be given : — 



Fundamental Definition. — Homogeneity of structure con- 

 sists in a likeness of the ultimate parts or molecules of a body, 

 both as to their nature and their relative arrangement, of tlie 

 following kind: — Corresponding to every mathematical point 

 in the mass are found evenly distributed at finite intervals a 

 number of points whose relation to the ultimate structure, 

 regarded as of unlimited extent, is the same as that of the point 

 selected; so that the aspect of this structure viewed suc- 

 cessively from all such corresponding points is identically 

 ■ the same, although the actual orientations of the similar 

 aspects may be different J. 



Now when in such a homogeneous mass two or more directions 

 are found alike, their likeness may be defined by saying that 

 they are similarly disposed with respect to the molecular struc- 

 ture, or, more precisely, that they are the directions of right 

 lines not parallel to one another, which cut this structure 

 similarly. 



* Most persons will regard the law of rational indices as evidence of 

 the existence of some kind of molecular structure, and it is scarcely- 

 conceivable that Hauy's discovery of this law would have been made 

 without the aid of some such conception of crystal structure as the une 

 suggested by him. 



t See below, p. 9. 



X An example of different orientations of the same aspect observable 

 from different points of view is presented by a partitioning of space into 

 identical regular triangular prisms ; the structure of the mass viewed 

 from the centre of any prism presents the same appearance, but from the 

 standpoints at the centres of prisms of the one orientation an opposite 

 orientation of the aspect is found to that presented from the centres of 

 those of the other orientation. 



