of a Crystal according to Boscovich, 425 



§ 24. Suppose now the points in the middles of the faces of 

 the cubes which in the equilateral assemblage are O's twelve 

 equidistant nearest neighbours to be removed, and the assem- 

 blage to consist of points in simplest cubic order ; that is to 

 say, of Boscovichian points at the points of intersection of 

 three sets of equidistant parallel planes dividing space into 

 cubes. Fig. 2 shows ; and at X, Y, Z, three of the six equi- 

 distant nearest neighbours which it has in the simple cubic 

 arrangement. Keeping \ with the same signification in 

 respect to fig. 2 as before, we have now for the coordinates of 

 O's six nearest neighbours : — 



(W2,0,0),(0,\V%0), (0,0, W2), 

 (-\v/2, 0, 0), (0, -\V% 0), (0, 0, -A ^2). 



Hence, and denoting by isr-, the value of vr for this case, we 

 find, by § 18 (23), 



A = N^ and B = n=0 (31) 



The explanation of n = (facial rigidity zero) is obvious when 

 we consider that a cube having for its edges twelve equal 

 straight bars, with their ends jointed by threes at the eight 

 corners, affords no resistance to change of the right angles of 

 its faces to acute and obtuse angles. 



§ 25. Replacing now the Boscovich points in the middles of 

 the faces of the cubes, from which we supposed them tempo- 

 rarily annulled in § 24, and putting the results of § 23 and 

 § 24 together, we find for our equilateral homogeneous assem- 

 blage its elasticity moduluses as follows :— 



} (32) 



A = N(^ + OTl ), 



B = ft=4N*sr , 



where, as we see by § 16 (20) above, 



^ =XF(A)-\ 2 FV \ m , 



^■ 1 =\^/2F(X v /2)-2X 2 F(X v /2), J ' ' ^ h 



F(r) being now taken to denote repulsion between any two 

 of the points at any distance r, which, with <f>(r) defined as in 

 § 10, is the meaning of — <£'(/'). To render the solid, con- 

 stituted of our homogeneous assemblage, elastically isotropic, 

 we must, by § 19 (24), have A — B = 2n, and therefore, by 



^0 = 2^ . (34) 



§ 26. The last three of the six equilibrium equations § 16 



