298 Prof. J. J. Thomson. Some Applications of [Apr. 21, 



paper. After this it is shown that for a collection of molecules in a 

 steady state, the equation (which for ordinary dynamical systems is 

 identical with the well-known Hamiltonian principle) 



«(T-V) = 



is satisfied, where T and V are respecfcively the mean values of the 

 kinetic and potential energies taken over unit time, and where the 

 variation denoted by 8 is of the following kind. 



The coordinates fixing the configuration of any physical system, 

 consisting according to the molecular theory of the constitution of 

 bodies of an immense number of molecules, may be divided into two 

 classes : — 



(a.) Coordinates, which we may call molar, which fix the con- 

 figuration of the system as a whole ; and 



(b.) Molecular coordinates which fix the configuration of individual 

 molecules. 



We have the power of changing the molar coordinates at our 

 pleasure, but we have no control over the molecular coordinates. 

 In the equation — 



a(T-V) = o 



only the molar coordinates are supposed to vary, all velocities remain- 

 ing unchanged. Hence in applying this equation we need only 

 consider those terms in T and V which involve the molar coordinates, 

 and expressions for these terms for gases, liquids, and solids are given 

 in the paper ; the rest of the paper after these have been obtained 

 consists of applications of the above equation. 



The density of a vapour in equilibrium with its own liquid is 

 obtained as a function of the temperature, and the effect upon the 

 density of such things as the curvature or electrification of the surface 

 of the liquid is determined. 



The phenomenon of dissociation is next investigated, and an 

 expression for the density of a dissociated gas obtained which agrees 

 substantially in form with that given by Professor Willard Gribbs in 

 his well-known paper on the "Equilibrium of Heterogeneous Sub- 

 stances." 



The effect of pressure upon the melting point of solids and 

 the phenomena of liquefaction are then investigated, and the results 

 obtained for the effect of pressure upon the solubility of salts are 

 shown to agree with the results of Sorby's experiments on this 

 subject. The effect of capillarity upon solubility is investigated, and 

 it is shown that if the surface-tension increases as the salt dissolves 

 then capillarity tends to diminish the solubility, and vice versa. 



The question of chemical combination is then considered, par- 



