684 Prof. B. M. Sen on the Kinetic Theory of Solids 

 The equation o£ energy is, therefore, 



|MV 2 + a 2 { 2 T fQ) +f" (0 } = const. 



If the molecule were at liberty to swing to its natural 

 amplitude, the mean kinetic energy would be equal to its 

 mean potential energy. We make the assumption that this 

 is not the case, the vibrating molecule coming into collision 

 with the adjacent one before reaching the extreme position 

 of the natural vibration *, 



2. Amplitude of molecular vibration. 



At each collision the forward motion is reversed, so that 

 there is a change of momentum at the point = 2MY/\/i\ at 



MV 



each collision, or —-^— per sec, where t 1 is the time from one 



extreme position to the other, and a the maximum displace- 

 ment. Putting £ 1 = 2 x /3a/V, the change of momentum per 

 _ MV 2 _ *d 

 6a 3a' 

 As there are N molecules per sq. cm., the pressure within the 



mass is found to be N 2/3 „- per sq. cm. 

 da 



To calculate the pressure at the surface, we suppose that 



the molecule on the positive side of the yz plane is missing. 



The potential energy for a displacement x along the #-axis 



= 4/ + -2T) +/( ^ 



The first term is a constant. The second gives a constant 

 force F =/'(/) in the direction of the inward normal. The 

 third term gives a force of restitution proportional to the 

 displacement and changing sign with it. Its mean value 

 is zero. 



The permanent force, therefore, is F along the inward 

 normal, where F is the attraction between two molecules. 

 The pressure at the surface is FN 2/3 . 



•• 37<= F or a= 3F- 



This is the equation which is to replace equation (2) in the 

 former paper. 



* A comparison of the relative magnitude of the kinetic and the 

 potential energy terms lias been given in the previous paper. 



