2 Lord Kelvin. [Jan. 18, 



knew the exact geometrical configuration of the constituent parts of 

 the group of atoms in the crystal, or crystalline molecule as we shall 

 call it, we could not describe the partitional interfaces between out- 

 molecule and its neighbour. 



Knowing as we do know for many crystals the exact geometrical 

 character of the Bravais assemblage of corresponding points of its 

 molecules, we could not be sure that any solution of the partitional 

 problem we might choose to take would give a cell containing only 

 the constituent parts of one molecule. For instance, in the case of 

 quartz, of which the crystalline molecule is probably 3(SiOj), a 

 form of cell chosen at random might be such that it would enclose 

 the silicon of one molecule with only some part of the oxygen belong- 

 ing to it, and some of the oxygen belonging to a neighbouring 

 molecule, leaving out some of its own oxygen, which would be 

 enclosed in the cell of either that neighbour or of another neighbour 

 or other neighbours. 



2. This will be better understood if we consider another illustra- 

 tion a homogeneous assemblage of equal and similar trees planted 

 close together in any regular geometrical order on a plane field either 

 inclined or horizontal, so close together that roots of different trees 

 interpenetrate in the ground, and branches and leaves in the air. 

 To be perfectly homogeneous, every root, every twig, and every leaf 

 of any one tree must have equal and similar counterparts in every 

 other tree. So far everything is natural, except, of course, the abso- 

 lute homogeneousness that our problem assumes ; but now, to make 

 a homogeneous assemblage of molecules in space, we must suppose 

 plane above plane each homogeneously planted with trees at equal 

 successive intervals of height. The interval between two planes may 

 be so large as to allow a clear space above the highest plane of leaves 

 of one plantation and below the lowest plane of the ends of roots in 

 the plantation above. We shall not, however, limit ourselves to this 

 case, and we shall suppose generally that leaves of one plantation 

 intermingle with roots of the plantation above, always, however, sub- 

 ject to the condition of perfect homogeneousness. Here, then, we 

 have a truly wonderful problem of geometry to enclose ideally each 

 tree within a closed surface containing every twig, leaf, and rootlet 

 belonging to it, and nothing belonging to any other tree, and to 

 shape this surface so that it will coincide all round with portions of 

 similar surfaces around neighbouring trees. Wonderful as it is, this 

 is a perfectly easy problem if the trees are given, and if they fulfil 

 the condition of being perfectly homogeneous. 



In fact we may begin with the actual bounding surface of leaves, 

 bark, and roots of each tree. Wherever there is a contact, whether 

 with leaves, bark, or roots of neighbouring trees, the areas of contact 

 form part of the required cell-surface. To complete the cell-surface we 



