Preston—On the Continuity of Isothermal Transformation, §c. 121 
bubbles of vapour are formed in the interior of the liquid mass, and by reason 
of the action of gravity these rise vertically upwards, and the result is, that the 
mass becomes separated into two portions, the upper part of the containing vessel 
being filled with vapour, and the lower part by the remaining liquid. ‘The action 
of gravity is thus to separate the vapour bubbles from the liquid, and it is on 
this account, as we shall see, that the part BD of the isothermal is, in practice, 
a right line as shown in fig. 1. If, however, we imagine the action of gravity to 
be removed, then a bubble of vapour when formed would remain in situ, except 
in so far as it might drift with currents in the mass. The formation of bubbles, 
under these conditions, would cause the mass to swell into a spongy condition— 
a heterogeneous mixture of liquid and vapour,—in which, if the equilibrium 
could be maintained, the volume and pressure would vary according to laws 
very different from the simple law of constant pressure which governs the 
transformation of ordinary boiling, under the action of gravity (fig. 1). 
In order to determine, under these conditions, how the pressure varies with 
the volume, at constant temperature, let us consider the case of a mass of liquid 
in which a spherical bubble of the vapour of the 
liquid has been formed, as shown in fig. 3. For 
the sake of clearness, let the mass be enclosed in a 
cylinder by means of a piston, so that the volume 
and external pressure can be varied at pleasure, 
then, if p be the pressure, applied through the 
piston (which we may term the external pressure 
of the mass, in the ordinary sense), the pressure 
at any point in the interior of the liquid will be 
p +c, where ¢ is a quantity depending on the 
surface film, and, as it arises from the mutual 
attraction of molecules well within each others 
sphere of action, may be very large. But, if o be 
the vapour pressure within the bubble, the relation connecting p and a is 
Fie. 3. 
‘ 
a= p+ = (1) 
where 7 is the radius of the bubble, and 7 the surface tension of the surface 
film separating the liquid and vapour. It is clear, therefore, that if = remains 
sensibly constant, p must increase as 7 increases, or in other words, the external 
pressure and the volume must increase simultaneously, if equilibrium is to be 
maintained. 
The saturated vapour pressure a, however, is not quite constant, but varies 
at constant temperature with the curvature of the film with which it is in contact, 
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