426 Lord Kelvin on the Elasticity 



(18) are fulfilled in virtue of symmetry in the case of an 

 equilateral assemblage of single points whatever be the law 

 of force between them, and whatever be the distance between 

 any point and its nearest neighbours. The first three of them 

 require in the case of § 23 that F (X) = ; and in the case of 

 (24) that F(A, N /2)=0, results of which the interpretation is 

 obvious and important. 



§ 27. The first three of the six equilibrium equations, 

 § 16 (18), applied to the case of § 25, yield the following- 

 equation : 



ViF(W2)=-F(X) (35); 



that is to say, if there is repulsion or attraction between each 

 point and its twelve nearest neighbours, there is attraction or 

 repulsion of */2 of its amount between each point and its six 

 next-nearest neighbours, unless there are also forces between 

 more distant points. This result is easily verified by simple 

 synthetical and geometrical considerations of the equilibrium 

 between a point and its twelve nearest and six next-nearest 

 neighbours in an equilateral homogeneous assemblage. The 

 consideration of it is exceedingly interesting and important 

 in respect to, and in illustration of, the engineering of jointed 

 structures with redundant links or tie-struts. 



§ 28. Leaving, now, the case of an equilateral homoge- 

 neous assemblage, let us consider what we may call a scalene 

 assemblage ; that is to say, an assemblage in which there are 

 three sets of parallel rows of points, determinately fixed as 

 follows, according to the system first taught by Bravais * : — ■ 



I. Just one set of rows of points at consecutively shortest 

 distances X x . 

 II. Just one set of rows of points at consecutively next- 

 shortest distances X 2 . 

 III. Just one set of rows of points at consecutive distances 

 shorter than those of all other rows not in the plane 

 of I. and II. 



To the condition X 3 > X 2 > X x we may add the condition that 

 none of the angles between the three sets of. rows is a right 

 angle, in order that our assemblage may be what we may call 

 wholly scalene. 



§ 29. Let A'OA, B'OB, C'OC be the primary rows thus 

 determinately found having any chosen point, 0, in common ; 

 we have 



* Journal de VEcole Polytechnique, tome xix. caliier xxxiii. pp. 1-128 : 





