of a Crystal according to Boscovich, 



423 



compressibility 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 rela- 

 tive to shearings parallel to the faces of the principal cube f : 

 and n x the diagonal rigidity, being rigidity relative to shear- 

 ings 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 



= 3Si 



y* 2 



(27) : 



we have w=-n x , 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 demonstration of the statements of § 5 above. 

 § 21. A case which is not uninteresting in respect to Bos- 

 covichian 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. BrillouinJ), 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 



Fig. 2. 



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



* K. S. E. Proc. July 1889 ; Art. xcvu. of my < Math, and Phys. 

 Papers/ vol. iii. 



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

 opposite edges of a tetrahedron of four nearest neighbours. 



% Conferences Scientifiques et Allocutions (Lord Kelvin), traduites et 

 annotees, P. Lugol et M. Brillouin : Paris, 1893, pp. 320-325. 



