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LXXXII. On the Kinetic Theory of Solids (Metals) and the 

 Partition of Thermal Energy.— -Part II. By B. M. Sen, 

 Dacca College, Dacca, Bengal *. 



Preface. 



IX my previous paper on the " Kinetic Theory of Solids 

 (Metals)/' Part I.f, I investigated the theory of the solid 

 state with a rough working model of fourteen molecules placed 

 on a sphere about each individual molecule at the centre. 

 The idea was to make the distance between any two adjacent 

 molecules equal to the radius o£ the sphere (the body being 

 isotropic) so that the spherical distance between them is 60°. 

 This is geometrically impossible, but the model satisfies this 

 condition approximately together with the condition of 

 symmetry. 



In the present paper, I have restated the theory for the 

 cubic and face-centred cubic crystals. These are the two 

 arrangements which are common for the solid state. The 

 arguments have been put briefly. For a more detailed state- 

 ment the reader is referred to the previous paper. 



1. Potential energy of displacement. 



Let us suppose that six molecules are placed at a distance 

 I from the central molecule, two on each axis. Let the 

 components of the displacement of the central molecule be 

 x, y, z, the others being fixed in their mean positions. Then 

 the potential energy for the displacement x 



(1) due to the molecules on the ^-axis 



=/(J + x) + f(l- ,v) = 2 f(l) + a? f{l), 



(2) due to the pair of molecules on the v-axis 



2 /0+!r)= 2 /« + !/"«' 



(3) due to the pair of molecules on the ^r-axis 



2f(l)+°jf"(l). 



The combined effect of these six molecules for the general 

 displacement 



= 6/(1) + a 2 { 2 /' (0 +/".(0 } ^ where a?=x*+f 



* Communicated by the Author. 

 t Suvra, p. 672. 



r z + 2r* 



