Lord Kelvin. 



[Jan. 18, 



hexagon and between hexagons and quadrilaterals, and then by draw- 

 ing parallel equal and similar counterparts to these surfaces in the 

 remaining four hexagonal and three quadrilateral spaces in the 

 manner more particularly explained in 6 below. It is clear, or at 

 all events I shall endeavour to make it clear by fuller explanations 

 and illustrations below, that the figure thus constituted fulfils our 

 definition (1) of the most general form of cell fitted to the particular 

 homogeneous assemblage of points corresponding to the parallele- 

 piped with which we have commenced. This will be more easily 

 understood in general, if we first consider the particular case of 

 parallelepipedal partitioning, and of the deviations which, without 

 altering its corners, we may arbitrarily make from a plane-faced 

 parallelepiped, or which we may be compelled by the particular 

 figure of the molecule to make. 



5. Consider, for example, one of the trees of 2, or if you please 

 a solid of less complex shape, which for brevity we shall call S, being 

 one of a homogeneous assemblage. Let P be a point in unoccupied 

 space (air, we shall call it for brevity), which, for simplicity we may 

 suppose to be somewhere in tbe immediate neighbourhood of S, 

 although it might really be anywhere far off among distant solids of 

 the assemblage. Let PA, PB, PC be lines parallel to any three 

 Bravais rows not in one plane, and let A, B, C be the nearest points 

 corresponding to P in these lines. Complete a parallelepiped on the 

 lines PA, PB, PC, and let QD, QE, QP be the edges parallel to them 



(Fio. 7, OF 9.) 

 B 



through the opposite corner Q. Because of the homogeneousness of 

 the assemblage, and because A, B, C, D, E, F, Q are points correspond- 

 ing to P, which is in air, each of those seven points is also in air. 

 Draw any line through air from P to A and draw the lines of corre- 

 sponding points from B to F, D to Q, and C to E. Do the same 

 relatively to PB, AF, EQ, CD ; and again the same relatively to 



