496 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
The methods of calculating the potential energy due to strain, &c., are, of course, 
well known. The corresponding terms in the kinetic energy can be calculated in the 
following way. 
We saw, on p. 480, that if y is a coordinate of any type, and P a quantity such 
that, when y is increased by By, the energy in the system is increased by P3y, then 
dT _ _ - dP 
dy dd 
P may be regarded as a force of the type y, so that, if this force depends upon the 
temperature, there will be a term in the mean kinetic energy equal to 
so that the expression for the positional part of the kinetic energy equals 
e \te dv ~ et \ f^ ; 
the summation being extended over all the types of coordinates. The term in the 
potential energy corresponding to the coordinate of type y will be 
J P 0 dl J> 
where P 0 is the part of P which is independent of the temperature. 
By the above equations we can calculate the term in the expressions for both the 
kinetic and potential energies involving the coordinates of any type. If, however, 
we only require to calculate the value of L, a much simpler process is applicable. 
For when the system is in a steady state 
so that we have 
L = JPA/ .(38) 
Let us now apply these equations to calculate the effect which any change in the 
external circumstances has upon the solubility of a salt. Let us, for example, consider 
the effect of capillarity. Then, if the process of solution alters the volume of the 
mixture of salt and water, it will in general alter the surface, and so alter the energy 
due to the surface-tension. If it increases the energy, the surface-tension will tend to 
stop the solution ; if it diminishes the energy, the surface-tension will facilitate the 
solution. The energy due to the surface-tension will change even though the volume 
remains unaltered, if the surface-tension depends upon the quantity of salt dissolved 
in the liquid ; if the surface-tension diminishes as the salt dissolves, then the surface- 
tension will facilitate the solution; if it increases, it will tend to prevent the salt 
dissolving. This result, as well as the preceding, follows from equation (37). We 
see, by that equation, that anything which makes cl (g'Vo) /dq increase will increase 
