DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
511 
Putting, as before, 
py 
= <u, 
we see that 8<y, the change in oj due to a change 8 w in the value of the potential 
energy, is given by the equation 
1 + 
Boo 
0) 
cl. Sw 1 
^ t if K Q • 
(63) 
so that, if d . 8 w/dg is positive, 8w is positive, that is, in the state of equilibrium. 
£ and Tj are smaller than they would have been if Sw; had been zero; so that, if an 
increase in £ increases the additional potential energy, the value of £ in the state of 
equilibrium will be diminished. If, on the other hand, the additional potential energy 
diminishes as £ increases, the value of £ in the state of equilibrium will be increased. 
Effect of Capillarity. 
§ 16. Let us first consider the case when the additional potential energy is due to 
capillarity; then 
Siv = TS, 
where S is the area of the surface, and T the surface-tension. 
Hence we have, from Equation (63), 
1 
+ 
8co 
- - £ d£ kQ' 
Od 
(64) 
Thus, if either the surface-tension or the area of the surface alters as chemical 
combination proceeds, the final state of equilibrium will depend upon the extent 
of surface. The state of equilibrium will be different when the solution is spread 
out over a large surface from that which exists when the solution exposes only 
a small free surface. Considerations of this kind would explain the experiments of 
Professor Liebreich on the precipitation of chloroform by the mixture of hydrate of 
chloral and an alkaline solution. (‘Nature,’ vol. 35, p. 264.) In these experiments it 
was observed that when the solutions were mixed in a test-tube the top layer remained 
clear, no precipitation taking place inside it, and the same phenomenon occurred in the 
capillary space between two plates ; in short capillary tubes the reaction failed altogether. 
The equations obtained above apply to this case. Since the surface-tension of pure 
water is altered by the addition of other substances, the surface-tension of the mixture 
of chloral and alkaline solution will be altered by the withdrawal from the solution of 
chloral and alkali; let us suppose that it is increased; then the precipitation of the 
chloroform will increase the surface-tension, and therefore the potential energy due to it. 
Thus, if £ in this case is the number of equivalents of chloroform, d . S w/dfis positive, and 
