238 Mr. T. Preston on the Continuity of Isothermal 



the drops be diminished, the foregoing equation will cease to 

 apply, and the pressure -st, after reaching a maximum, will 

 gradually diminish, and finally recede to the value w , when 

 the drops of liquid vanish. This is the process which takes 

 place along the falling part ND (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 vr may be very much less than w , at 

 some part of the branch BMC, yet a condition is attained 

 with bubbles of a certain diameter in which ot is a minimum, 

 and from which it increases in both directions to the normal 

 vapour-pressure «r . 



Thus, the part BM (fig. 2) of the isothermal is accounted 

 for, and therefore the whole succession of conditions repre- 

 sented by an isothermal, such as that imagined by James 

 Thomson, is rendered conceivable. Such a succession, of 

 course, cannot be regarded as realizable, for although the con- 

 dition 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. 



It is interesting to note that the mass may be transformed 

 from the condition B to the condition D by two distinct 

 routes of transformation — one along the right line BD, in 

 which the condition is stable, and the other along the curved 

 path BMCND, in which the condition is unstable, — yet the 

 principle of conservation of energy forces us to conclude that 

 the work done against external pressure, while the mass 

 expands from B to D, must be the same in the two cases, and 

 for this reason it has been concluded that whatever the shape 

 of the curve AMND may be, the area of the loop BMC 

 must be equal to the area of the loop CND. At first sight 

 we might apply the same reasoning to the transformation 

 from B to C, or from D to C, and rush to the conclusion that 

 the area of each loop must be zero, or else that we are here 

 presented with a violation of the principle of conservation of 

 energy. 



But it must be remarked that although at the point C of 

 the diagram the mass, in both cases, has the same tempera- 

 ture, pressure, and volume, yet in one case all the vapour is 



