113 



From this it is clear that the proper character of the pattrm 



intimately connected with that of the net-plane PP'P"P'", 



)r QQ'Q"Q'" etc.), which is, in a sense, its very foundation. 



3. It is thus of high importance for the study of homogeneous 

 -tribution in general, to examine first the properties of such 

 >mogeneous and regular systems of mathematical points. If for 

 u moment we make abstraction from the particular case of the 

 stribution of points in a "plane" only, and if we extend our 

 5onings to tridimensional systems of points, asking what their 



Fig. 102 



rangement in space must be in order to fulfil the condition of 

 >mogeneity as defined above, the answer will evidently be, that 

 lese points must be situated at the corners of an infinite number 

 congruent and contiguous parallelepiped cells, in which space 

 in be divided without leaving any room between them. In this 

 way these points appear situated like the knots of a net-work in space, 

 the meshes of which are the congruent and contiguously arranged 

 parallelepiped cells just mentioned. 



A general type of such network which bears the name of a space- 

 lattice, is reproduced in fig. 102. Starting with a point O, we can 

 look for the point P l nearest to it at a distance d lt then for the 

 second nearest point P 2 at a distance rf 2 , and finally for the third 

 nearest P 8 at a distance d 3 from 0. The directions of OP lt OP t , and 



8 



