Lord Kelvin. [Jan. 18. 



I >ut with one pair of frontiers left as straight lines, and the two 

 other pairs drawn by aid of two paper templets. It would he easy, 

 but not worth the trouble, to cut out a large number of pieces of 

 brass of the shapes shown in these diagrams and to show them fitted 

 together like the pieces of a dissected map. Figs. 5 and 6 are druwn 

 on the same principle ; fig. 6 showing, on a reduced scale, the result of 

 putting pieces together precisely equal and similar to that shown in 



Fio. 6. 



fig. 5. In these diagrams, unlike the cases represented in figs. 3 and 4, 

 the primitive hexagon is, as shown clearly in fig. 5, divided into iso- 

 lated parts. But if we are dealing with homogeneous division of 

 solid space, the separating channels shown in fig. 5 might be sections, 

 by the plane of the drawing, of perforations through the matter of 

 one cell produced by the penetration of matter, rootlets for example, 

 from neighbouring cells. 



9. Corresponding to the three ways by which two triangles can 

 be put together to make a parallelogram, there are seven, and 

 only seven, ways in which the six tetrahedrons of 4 can be put 

 together to make a parallelepiped, in positions parallel to those 

 which they had in the original parallelepiped. To see this, remark 

 first that among the thirty-six edges of the six tetrahedrons seven 

 different lengths are found which are respectively equal to the three 

 lengths of edges (three quartets of equal parallels) ; the three 



