ARRANGEMENT OE ATOMS IN A CRYSTAL. 131 



Sohncke's systems of points ; we will call them the A 

 system. 



It might be supposed, at first sight, that there can be 

 nothing of a right- or left-handed character about the per- 

 fectly symmetrical cubic structure here described. But it 

 will be found, on consideration, that there are, further, three 

 other points near each corner of the original cube, from 

 each of which the aspect of the whole structure is exactly 

 what it was before, with the exception that everything is 

 inverted as though in a mirror ; right hand has become left 

 hand, and the observer is contemplating, as it were, the 

 reflection of what was seen from the first position. 



The system composed of all the latter points, twenty- 

 four in each cube throughout the whole structure, is a 

 second Sohncke system, B. 



Next, suppose each cubic room to be similarly furnished; 

 and let the articles of furniture be of such a shape and so 

 placed with regard to the walls, floor and ceiling that the 

 aspect of the room from each point of A is the same, while 

 the aspect of it from any point of B is not the inverted 

 image of the view from A. The whole set of rooms with 

 its furniture is now a homogeneous structure, and will be 

 found to have the symmetry of an asymmetric cubic crystal 

 such as sal-ammoniac. Such a structure is not identical 

 with its image. Again, let the articles be so placed and of 

 such a nature that the aspect from each point B is the 

 inverted image of the view from each point A ; the struc- 

 ture is still a homogeneous one, but has now the complete 

 symmetry of a cubic crystal such as fluor, and is identical 

 with its image. 



Barlow regards this property of identity with its own 

 image as the only property compatible with its homo- 

 geneity which can increase the symmetry of a homogeneous 

 structure. He takes therefore as the basis of all con- 

 ceivable homogeneous structures the sixty -five regular 

 systems of points established by Sohncke ; he inquires 

 which of the sixty-five types of structure can possess the 

 additional property of identity with their own images, and in 

 how many ways they may do so ; and he finally arrives at 



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