i 3 o SCIENCE PROGRESS. 



stated as relating to points or molecules, or anything in 

 particular, but as one dealing with the arrangement of the 

 similar parts in a homogeneous rigid structure of any sort. 

 The author defines a homogeneous rigid structure as an 

 arrangement of material of any quality, and of constant 

 form which is uniformly repeated over its whole extent. 



The definition is more fully expressed as follows : A 

 homogeneous structure is one in which, if it be regarded 

 as without boundary, to every point correspond other 

 exactly similar or homologous points which are uniformly 

 distributed in space ; it is therefore a property of the struc- 

 ture that each infinite system obtained by selecting all similar 

 points is a regular system as defined by Sohncke ; that is 

 to say, round every point of such a system the arrangement 

 of the remainder is the same as round every other. 



A pile of cannon balls is a homogeneous structure ; so 

 is a stack of cubes packed together closely in as regular a 

 manner as possible. We will take the latter as an example 

 of the manner in which Barlow's method may be applied. 



Consider in such a structure the corner of any one 

 cube ; it is a point in which eight cubes meet : now take a 

 point within the cube ; the point may be anywhere, but for 

 convenience we will suppose it near the corner. It will be 

 found that there are two other points, at an equal distance 

 from the same corner, from each of which the aspect of the 

 whole structure is absolutely the same, and identical with 

 the aspect from the first point chosen ; further there are 

 three more homologous points near each of the remaining 

 corners of the same cube, making twenty-four in all, from 

 each of which the aspect of the structure is still the same. 

 It is easy to convince oneself of this by regarding the cubes 

 as rooms with transparent walls, within one of which the 

 observer is placed, and contemplates from it the remaining 

 rooms, above, below and on all sides ; he must of course be 

 prepared to stand upon his head, or put himself into any 

 required position, and take no account of the difference 

 between upwards and downwards, north and south, etc. 



All these points then, twenty-four in each cube, taken 

 together throughout the whole structure, constitute one of 



