144 



Lord Kelvin 



on 



(')■ 



§ 12. Using now §§ 9, 11 in (3) of § 4 we find, — 

 for assemblage I., 



^ = 12^(\)+6^(l-414\)+18^)(l-732X)+6(/)(2\) + . 

 for assemblage II. 



^=4^(-G13X) + 12^)(X) + 120(l-173X)+ .... 



These formulas prepare us for working out in detail the 

 practical dynamics of each assemblage, guided by the following 

 statements taken from §§ 18, 16 of M.'C. M. 



§ 13. Every infinite homogeneous assemblage of Boscovich 

 atoms is in equilibrium. So, therefore, is every finite homo- 

 geneous assemblage, provided that extraneous forces be 

 applied to all within influential distance of the frontier, equal 

 to the forces which a homogeneous continuation of the 

 assemblage through influential distance beyond the frontier 

 would exert on thorn. The investigation of these extraneous 

 forces for any given homogeneous assemblage of single atoms — 

 or groups of atoms as explained above (§ 1) — constitutes the 

 Boscovich equilibrium-theory of elastic solids. 



Fin-. :3. 



It is wonderful how much towards explaining the crystallo- 

 graphy and elasticity of solids, and the thermo-elastic 

 properties of solids, liquids, and gases, we find; without 

 assuming, in the Boscovichian law of force, more than one 

 transition from attraction to repulsion. Suppose, for instance, 

 that the mutual force between two atoms is zero for all 

 distances exceeding a certain distance I, which we shall call 

 the diameter of the sphere of influence ; is repulsive when 

 the distance between them is < J ; zero when the distance is 

 = J ; and attractive when the distance is >£ and <I. 



§ 14. Two different examples are represented on the two 

 curves of fig. 3, drawn arbitrarily to obtain markedly diverse 

 conditions of equilibrium for the monatomic equilateral 



