The London, Edinburgh and Dublin philosophical magazine and journal of science . useful, to work outfor D4, D5, D6, etc. 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 thepractical dynamics of each assemblage, guided by the followingstatements taken from §§ 18, 16 of M. § 13. Every infinite homogeneous assemblage of Boscovichatoms is in equilibrium. So, therefore, is every finite homo-gene
The London, Edinburgh and Dublin philosophical magazine and journal of science . useful, to work outfor D4, D5, D6, etc. 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 thepractical dynamics of each assemblage, guided by the followingstatements taken from §§ 18, 16 of M. § 13. Every infinite homogeneous assemblage of Boscovichatoms is in equilibrium. So, therefore, is every finite homo-geneous assemblage, provided that extraneous forces beapplied to all within influential distance of the frontier, equalto the forces which a homogeneous continuation of theassemblage through influential distance beyond the frontierwould exert on thorn. The investigation of these extraneousforces for any given homogeneous assemblage of single atoms—or groups of atoms as explained above (§ 1) — constitutes theBoscovich equilibrium-theory of elastic solids. Fin-. It is wonderful how much towards explaining the crystallo-graphy and elasticity of solids, and the thermo-elasticproperties of solids, liquids, and gases, we find; withoutassuming, in the Boscovichian law of force, more than onetransition from attraction to repulsion. Suppose, for instance,that the mutual force between two atoms is zero for alldistances exceeding a certain distance I, which we shall callthe diameter of the sphere of influence ; is repulsive whenthe distance between them is £ and <I. § 14. Two different examples are represented on the twocurves of fig. 3, drawn arbitrarily to obtain markedly diverseconditions of equilibrium for the monatomic equilateral Molecular Dynamics of a Crystal. 145 assemblage (I.), and also for the diatomic- assemblage (II.).The abscissa (a?) of each diagram, reckoned from a zero out-side the diagram on the left, represents the distance betweencentres of two ato
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