4 Mr. W. Barlow on Crystal Symmetry. 



faces, as in Gadolin's definition, such a crystal will possess 

 trigonal symmetry, every face having corresponding to it 

 two other possible faces similarly related, as to direction, to 

 the system of axes. Such a relation between the faces does 

 not, however, involve actual trigonal symmetry, and indeed, 

 if Hatiy's conception of the existence of parallelepipedal 

 ultimate units *, or any other conception of molecular struc- 

 ture, as a cause of the law of rational indices, be adopted, it 

 is easy to see that, with such relations between the intercepts 

 as have just been postulated, the dimensions of the ultimate 

 units of the mass cannot be the same in the three different, 

 directions of tbe three axesf . 



Consequently, what trigonal symmetry there is in such a 

 case must be expected to subsist only at a critical point of 

 temperature and other physical conditions, and when it is 

 present to reveal itself merely by equality of angles, not by 

 any of the properties which, by producing obvious similarity 

 of different directions, ordinarily indicate symmetry : viz., 

 such properties as crystal habit, directional effects on light 

 or temperature, or on chemical solvents. 



A case such as that just described suffices to show that 

 Gadolin's definition is too superficial ; that it does not go 

 deep enough to coincide in all cases with the actual phe- 

 nomena ; what is wanted is a definition of the symmetry of 

 crystals which will in all respects harmonize with the variation 

 of property with direction which characterizes these bodies J. 



* Haiiy was led to the discovery of the law of rational indices by 

 tlie hypothesis that crystals have an ultimate atomic structure of such a 

 nature that they are always geometrically divisible by three systems of 

 parallel planes into similarly orientated parallelepipedal ideal units of 

 identical shape and composition, and the further conception that crystal 

 faces always have the direction of planes so drawn as to pass through 

 the centres of neighbouring units and be very thickly set with these 

 centres. 



t For the purposes of Haiiy 's law a great latitude in the choice of 

 units of length for the different axes is admissible in any given case ; 

 indeed, any set of appropriate units having been selected, it is allowable 

 to substitute for any one of them a unit which is an integral part or an 

 integral multiple of it, without altering the others, and this may be done 

 more than once. A substituted unit will, however, it is evident, alio ays 

 be commensurable with the unit from which it was derived. 



% There are bodies which probably owe their existence to the mani- 

 festations of the same physical qualities and changes as those which 

 determine the formation of ordinary crystals, but whose forms indicate 

 that they are not strictly homogeneous ; e. g., microscopic crystals whose 

 surfaces are highly curved, and what have been called by Lehmann liquid 

 crystals. It is, perhaps, needless to remark that such bodies, which do 

 not obey Haiiy 's law, are outside the scope of this inquiry, which is 

 limited to homogeneous structure. 



