236 Mr. T. Preston on the Continuity of Isothermal 

 consequently, equation (3) becomes 



v=~ TT P2 r* ( )+- • • • («*>) 



or, denoting the specific volumes of the liquid and vapour by 

 i'! and v 2 , we have, from equation (5), 



4 

 Now equation (2) gives 



v — Vi= -irr 

 6 



(*-£) • • (6 > 



, = _2^._J!^. ..... (7 ) 



Therefore (6) becomes 



( „-, l)K _ i ,)s = |;^(^-J . . ( 8) 



Consequently, since the right-hand member of this equation 

 remains constant, the equation of the isothermal curve assumes 

 the hyperbolic form 



(v — vi) (txq—pY = constant (9) 



This equation holds for a spherical bubble of vapour sur- 

 rounded by its own liquid, and in this case it is to be noted 

 that p must always be less than -or , or the external pressure 

 of the mass must be less than the normal saturated vapour- 

 pressure, and this is what is indicated by the portion MC of 

 the isothermal lying below the right line BD in fig. 2. 



So far we have considered the case of a single bubble, 

 surrounded by its own liquid, but the foregoing reasoning 

 will apply when a number of equal bubbles are formed. If 

 the bubbles are of different sizes, however, the capillary 

 pressures arising from the curvatures of their surface films 

 will be different, and equilibrium will be impossible — the 

 larger bubbles tending to expand, and the smaller to collapse. 



It would appear, therefore, that the mass might be gradually 

 transformed from the liquid to the gaseous condition, by 

 allowing a system of equal bubbles to gradually increase in 

 size while the volume increased to v 2 and the external pressure 

 to «r , and this value would be reached if the bubbles could 

 be supposed to increase gradually till the whole mass reached 

 the state of vapour. Long before this final condition could be 

 reached, however, the liquid portions of the mass, which 

 interlace the bubbles and fill the spaces between them, would 

 be drawn out into thin films, and the conditions would be such 

 that the foregoing reasoning could not be applied. The 

 action of the distended surface film, in fact, will be such as to 

 draw the liquid parts which fill the spaces between the bubbles 



