68 Lord Kelvin. On the [June 15, 



and our expression (22), for the elastic energy of the strained solid, 

 becomes 



2w= 



.... (25) 



20. Using in (24) the equality B = n shown in (23), we find 



(26). 



This remarkable relation between the two rigidities and the com- 

 pressibility of an equilateral homogeneous assemblage of Boscovich 

 atoms was announced without proof in 27 of my paper on the 

 " Molecular Constitution of Matter."* In it n denotes what I called 

 the facial rigidity, being rigidity relative to shearings parallel to the 

 faces of the principal cube :f and HI the diagonal rigidity, being 

 rigidity relative to shearings parallel to any of the six diagonal 

 planes through pairs of mutually remotest parallel edges of the same 

 cube. By (24) and (23) we see that if the law of force be such that 



(27), 



we have n = n it and the body constituted by the assemblage is wholly 

 isotropic in its elastic quality. In this case (26) becomes 3k = 5n, 

 as found by Navier and Poisson ; and thus we complete the demon- 

 stration of the statements of 5 above. 



21. A case which is not uninteresting in respect to Boscovichian 

 theory, and which is very interesting indeed in respect to mechanical 

 engineering (of which the relationship with Boscovich's theory has 

 been pointed out and beautifully illustrated by M. Brillouin)4 is the 

 case of an equilateral homogeneous assemblage with forces only 

 between each point and its twelve equidistant nearest neighbours. 

 The annexed diagram (fig. 2) represents the point and three of its 

 twelve nearest neighbours (their distances X), being in the middles 

 of the near faces of the principal cube shown in the diagram ; and 

 ihree of its six next-nearest neighbours (their distances Xv/2), being 

 .at X, Y, Z, the corners of the cube nearest to it; and, at other 

 corners of the cube, three other neighbours K, L, M, which are next- 

 next-next-nearest (their distances 2\). The points in the middles of 

 the three remote sides of the cube, not seen in the diagram, are next- 

 next-nearest neighbours of O (their distances Xv/3). 



* 'R. S. E. Proc.,' July, 1889; Art. XCVII of my 'Math, and Phys. Papers,' 

 vol. iii. 



t That is to say, a cube whose edges are parallel to the three pairs of opposite 

 edges of a tetrahedron of four nearest neighbours. 



J. ' Conferences Scientifiques et Allocutions ' (Lord Kelvin), traduites et annotSes ; 

 P. Lugol et M. Brillouin : Paris, 1893, pp. 320325. 



