Law of Molecular Force. 177 



due to the same expansion is 1 1 j. But, apart from 



molecular theory entirely, we have Thomson's thermodynamic 

 equation for the cooling-effect 8 which a gas experiences 

 in expanding through a porous plug from volume i\ to 

 volume v 2 , — 



K p 8 = I ' \0J^—p\ dv +j> a v i —p l v 1 ; 



where it is to be noted that 6 means temperature taken as the 

 reciprocal of Carnot's function and measured on Thomson's 

 absolute thermodynamic scale, K p is the mean specific heat of 

 the gas in dynamic units between its temperatures on the high- 

 and low-pressure sides of the plug, p 2 an d p\ are the values of 

 the pressure on the low- and high-pressure sides respectively, 

 and v 2 and v x are the volumes occupied by a kilogramme of 

 the gas at the pressures p 2 and p 1 and at the temperature which 

 prevails on the high-pressure side of the plug. 

 From the characteristic equation we have 



OP „»"3f/i i h \ , e 



dT (, a vy/TJ + v 



Within the experimental range of temperature we may 

 consider ,. _ 



OP __ OP 



and within the range of volumes we can replace e°^ T by 

 b 



v VT 1 



1 ■] -= ; whence 



also 



OP , i ao , c • 4. 1 



v ?\0~ a * — 7¥ approximately; 



tT -I ^ -\ approximately; 



where, as before, A = — T. 



Now, in the formation of the original equation for 8 it is 

 supposed that heat is imparted to the gas on the low-pressure 

 side of the plug, until at the constant pressure p 2 prevailing 



Phil. Mag. S. 5. Vol 24. No. 147. August 1887. N 



