BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 107 



the molecule, and the kinetic energy of agitation is so small that at 

 no time is the molecule out of contact with both walls simultaneously. 

 The detailed mathematical solution shows that under these condi- 

 tions the momentum effect has no influence whatever, and the pres- 

 sure is determined simply by the relative magnitude of the volume 

 and the unstressed diameter of the molecule. Under these conditions 

 we obtain as the characteristic equation 



P = I (M. 



It is remarkable that the temperature has disappeared from the 

 characteristic ec^uation, or, in other words, the thermal dilatation 

 is zero. The substance still remains compressible, however. Some- 

 thing like this was expected for the liquids of these experiments ; that 

 is, it was expected that the dilatation would tend to vanish more 

 rapidly then the compressibility. 



III. Case II passes into this case when the violence of the tem- 

 perature vibration becomes so great that during part of the vibration 

 the molecule is in contact with only one wall. The critical tempera- 

 ture at which this occurs is when T = ki -— j . The mathematical 



analysis is more complicated for this case, because the motion must be 

 split up into two stages, during which the restoring forces are different 

 functions of the displacement. But just as in Case II, the change of 

 momentum of the molecule in unit time does not give the mean pres- 

 sure exerted on the wall. The complete equation of state for Case 

 III is complicated, involving antisines, so that it is hardly worth 

 giving. It reduces to one or the other of the other two cases, how- 

 ever, under proper critical conditions. In this case, the pressure 

 computed by the change of momentum is too low, as we should expect 

 it would be, because we have neglected an elasticity term which 

 modifies conditions when the molecule is in contact with both walls. 

 The sequence of events when we compress a substance at a given 

 temperature from a large volume is first Case I, then Case III, when 

 V = b, and then Case II, when the volume has been still further re- 

 duced by an amount depending on the temperature. Case I passes 

 smoothly into Case III without discontinuity in either compressibility 

 or dilatation. The difference between Cases I and III is that a higher 

 pressure corresponds to a given volume in Case III than we should 

 expect from the formula of Case I. The pressure at a given volume 

 in Cases I and III depends on temperature, but in Case II, the rela- 



