212 



Lord Kayleigh on the 



the parabola without losing its uniformity or becoming un- 

 stable. If, however, there be sufficient attraction between 

 the walls of the vessel and the fluid, instability leading to 

 total collapse will set in before the vertex is reached. 



It will be seen that condensation to a denser state is easily 

 explained, without any reference to molecules, as a direct 

 consequence of self-attraction in a medium otherwise obeying 

 Boyle's law. The objection that may be raised at this point 

 is rather that the explanation is too good, inasmuch as it 

 points to indefinite collapse, instead of to a high, but finite, 

 contraction in the condensed part. 



A simple and well-known modification provides an escape 



from a conclusion which follows inevitably from a rigorous 



application of Boyle's law. A provision is required to prevent 



extreme collapse, and this we may find in the assumption that 



a constant must be subtracted from the volume in order to 



obtain the quantity to which the pressure is proportional. 



In this case it is usual and convenient to express the relation 



by the volume v of the unit mass, rather than by the density. 



We have , 7N . . 



p(v — o) = constant, 



or 



(ot + K/v 2 ) (v—F) = constant, 



(8) 



Fig. 2. 



the well-known equation of Van der Waals. Here b is the 

 smallest volume to which the fluid can be compressed ; and 

 under this law the collapse of the fluid is arrested at a cer- 

 tain stage, equilibrium being attained when the values of -or are 

 again equal for the condensed and uncondensed parts of the fluid. 

 According to (8) , there are three values of v corresponding 

 to a given w. Below the critical temperature the three 

 values are real, and the isothermal curve assumes the form 

 ABCDEFGH (fig. 2) suggested by Prof. James Thomson. 

 The part D F is unrealizable for 

 a fluid in mass, being essen- 

 tially unstable : but the parts 

 AD, FH represent stable con- 

 ditions, so far as the interior 

 of the homogeneous fluid is 

 concerned. The line C Gr re- 

 presents the (external) pressure 

 at which the vapour can exist 

 in contact with the liquid in 

 mass, and the isothermal found 

 by experiment is usually said 

 to be H G E C B A. This state- 

 ment can hardly be defended. 

 If a vapour be compressed from H through Gr, it can only 



