826 



Professor William J. Pope 



[April 15, 



arranged in space, that is to say, of points of a homogeneous point- 

 system. Under these conditions, the space occupied by a crystalHne 

 element, a homogeneous assemblage of identically similar atoms, 

 may be partitioned into identically similar cells in such a manner 

 that the boundaries of a single cell shall enclose the entire domain 

 throughout which a particular atom exercises predominant influence. 

 Since it is postulated that every point in the space is subject to the 

 dominating influence of some next neighbouring atomic centre, it 

 follows that the cells fit together so as to occupy the whole availalile 

 space without interstices. Nothing is here said about the shape of 



FiG.l. 



the cells ; but since, in the case of an elementary substance, the 

 atomic = centres are all alike, so too will be the cells.'] Before pro- 

 ceeding to discuss the actual shapes of the cells f referred to, it will 

 be convenient to illustrate more graphically the mode "of treating 

 the problem which is here introduced with the aid of a particular 

 point-system connected with the crystalline structure of elementary 

 substances. 



The point-system in question may be derived in the following 

 manner. Space is first partitioned into cubes by three sets of 

 parallel planes at right angles to one another (Fig. 1) ; a point is 

 then placed at each cube corner and at the centre of each cubf ace. 



