BKIDGMAN. THERMODYNAMIC PROPERTIES OF LIQUIDS. 99 



SO that the total energy of strain would be expected to increase more 

 rapidly than the square of the change of volume, as we found it to. 

 But any more detailed speculation as to the precise way in which the 

 number of molecules taking part in the strain, and the way in which 

 the strain energy of the average molecule varies with the total pres- 

 sure, would probably be useless because the argument as to the 

 attractive forces breaks down at small volumes. It is probable that 

 the molecules are not really homogeneous spheres, but that there are 

 localities in which the attractive forces are more or less concentrated. 

 Therefore, although we may regard the attraction exerted by the 

 molecule as toward its center, and inversely as the fifth power of the 

 distance when the molecules are separated by wide intervals, we can- 

 not conceive of this law continuing to hold when the molecules are so 

 close as to be in contact. Under these circumstances the force may 

 increase more rapidly than as the inverse fifth power. What is 

 more, the potential energy of the attractive forces will not under 

 these circumstances be a function of the ^'olume only, that is of the 

 mean distance apart of the centers of the molecules, but will also 

 vary with the orientation. We saw that the average orderliness of 

 orientation may be expected to vary with temperature, being on the 

 whole more haphazard for equal volumes at the high temperatures. 

 Even with this picture of what is happening, it would be difficult to 

 say whether the potential energy of attraction should be expected to 

 be greater at the higher or lower temperature. We have seen that 

 the lower temperature usually means a greater space open for occu- 

 pation, but it may still be that because of the greater approach to 

 order at the low temperatures the localities of intense force are brought 

 closer together, so that the potential of the attractive forces may be 

 less. 



The main conclusion to be drawn from the fact that the strain energy 

 of the molecules varies as the cube of the change of volume is, there- 

 fore, that at low pressures the greater part of the change of volume is 

 due to the decrease in the distance apart of the molecules, but that 

 at high pressures an increasingly large part of the change of volume 

 is occasioned by the actual change of volume of the molecules them- 

 selves. 



It is interesting that the initial slopes of the ciu-ves of change of 

 energy against volume are very nearly the same for all twelve liquids. 

 This is a little unusual. Previously we have found the twelve liquids 

 to become similar at high pressure, but in respect to the change of 

 energy they appear to be more alike at low pressures. 



