PROCEEDINGS 



OF 



THE ROYAL SOCIETY 



January 18, 1894. 



The LORD KELVIN, D.C.L., LL.D., President, followed by Sir 

 JOHN EVANS, K.C.B., D.C.L., LL.D., Vice-President and 

 Treasurer, in the Chair. 



The Right Hon. James Bryce was admitted into the Society. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The following Papers were read : 



I. " On Homogeneous Division of Space." By LORD KELVIN, 

 P.R.S. Received January 17, 1894. 



1. The homogeneous division of any volume of space means the 

 dividing of it into equal and similar parts, or cells, as I shall call them, 

 all sameways oriented. If we take any point in the interior of one cell 

 or on its boundary, and corresponding points of all the other cells, 

 these points form a homogeneous assemblage of single points, accord- 

 ing to Bravais' admirable and important definition.* The general 

 problem of the homogeneous partition of space may be stated thus : 

 Given a homogeneous assemblage of single points, it is required to 

 find every possible form of cell enclosing each of them subject to the 

 condition that it is of the same shape and sameways oriented for all. 

 An interesting application of this problem is to find for a crystal 

 (that is to say, a homogeneous assemblage of groups of chemical 

 atoms) a homogeneous arrangement of partitional interfaces such 

 that each cell contains all the atoms of one molecule. Unless we 



* ' Journal de 1'^cole Poly technique,' tome 19, cahier 33, pp. 1 128 (Paris, 

 1860), quoted and used in my ' Mathematical and Physical Papers,' vol. 3, art. 97, 

 p. 400. 



VOL. LV. B 



