124 Preston—On the Continuity of Isothermal Transformation, Sc. 
normal saturated vapour pressure, we have saturated vapour in contact with 
convex liquid surfaces, and therefore at a pressure a, greater than =. 
Hence, in this limit, we may take the pressure on the enclosing piston to be 
that of the saturated vapour, namely a, the mass will be subject to an external 
pressure greater than a, namely p = a, and this brings us into the region 
CN (fig. 2) of the isothermal which lies above the normal pressure line B D. 
In this it is assumed that the mass is largely in the condition of saturated 
vapour, and that the liquid exists as a system of equal spherical droplets, 
swimming in their own vapour. 
If the drops were of different radii, equilibrium would be impossible, as 
evaporation would take place at the surfaces of the smaller drops, and con- 
densation at the surfaces of the larger. This instability is made evident by 
the equation 
which shows how the vapour pressure increases as the radii of the liquid drops 
diminish, and when the drops are small, « may exceed a by a considerable 
quantity. 
There is a limit, however, beyond which, if the radii of the drops be 
diminished, the foregoing equation will cease to apply, and the pressure a, after 
reaching a maximum, will gradually diminish and finally recede to the value a, 
when the drops of liquid vanish. This is the process which takes place along the 
falling part N D (fig. 2) of the isothermal. Similarly, in the initial phases of the 
transformation here imagined, namely, when small bubbles are beginning to be 
formed within the mass, it is clear that equation (2) ceases to apply, when the 
bubbles are so small that they cease to possess the distinctive properties of 
vapour, and it consequently follows, that although = may be very much less 
than =, at some part of the branch BMC, yet a condition is attained with 
bubbles of a certain diameter, in which = is a minimum, and from which it 
increases in both directions, to the normal vapour pressure a. 
Thus, the part BM (fig. 2) of the isothermal is accounted for, and therefore 
the whole succession of conditions represented by an isothermal, such as that 
imagined by James Thomson, is rendered conceivable. Such a succession, of 
course, cannot be regarded as realisable, for although the condition represented 
by every point of the curve is shown to be possible, and one of equilibrium, 
when the bubbles (or drops) are all of the same size, yet the equilibrium is 
essentially unstable, for when there is any departure from uniformity, all 
differences tend to become exaggerated, and the mass may depart from the 
condition of equilibrium with explosive violence. 
