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

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

 Dacca College, Dacca, Bengal*. 



Preface. 



TI1HE Kinetic Theory ©f Gases has been developed in 

 A great detail, but hardly any progress has been made 

 with that of the solids. In the absence o£ any such well- 

 developed theory, attempts are sometimes made to apply the 

 results of the Kinetic Theory of Gases to the case of solids, 

 as, for example, in the theory of electric conduction. The 

 results can hardly be regarded as satisfactory. One funda- 

 mental assumption of the Gas-theory is that the volume of 

 the molecules is negligible in comparison with that of the 

 gas itself. Clearly, this does not hold good even approxi- 

 mately for solids. Lately Nernst and others have approached 

 the subject from the standpoint of Planck's Quantum 

 Theory. In the present paper an attempt has been made to 

 develop the theory for metals on the basis of classical 

 mechanics. 



It is known that for 1° rise of temperature, every atom of 

 any metal absorbs 4x 10~ 16 erg in round numbers. On the 

 principle of equi-partition of energy, every atom having 

 three degrees of freedom of translation, this is explained by 

 the supposition that the translational motion absorbs one-half 

 of this quantity of energy 



[±mv 2 =u0, where a = 2'02 x 10" 16 ], 



and the other half is absorbed by the increase of potential 

 energy of vibration, whose mean value is the same as that 

 of the kinetic energy. But there are difficulties in the way, 

 as the specific heat increases gradually, whereas the degrees 

 of freedom can increase only by leaps f. It may be pointed 

 out that Born J and others have developed the theory of 

 crystal lattices, which gives the twenty-one constants required 

 by the mathematical theory of elasticity. Between two 

 neighbouring molecules there must be a force of attraction 

 and another of repulsion which keep the molecules at their 

 proper distance. Born assumed the form a\r + b\r n for the 

 mutual potential energy, the first term representing the 

 force of attraction and the second repulsion. But this does 



* Communicated by the Author, 

 t MacLewis, ' Physical Cherristry/ vol. ii. p. 29. 



t Born, Dynamik der Kristalgitter, Axifbau der Materie, where full 

 references are given. 



