SURFACES OF DISCONTINUITY 513 



may readily exist even in the ''unstressed" state, when Xx, Xy, 

 etc., vanish. Just as the stress-constituents in the case of a 

 strained soHd arise from change of molecular configuration, i.e., 

 strain, so the experimentally observable pressure p in a liquid 

 arises from change Ln molecular repulsions and attractions due 

 to the change in average molecular separation which we con- 

 ceive to accompany compression. 



4- Molecular Potential Energy in a Liquid 



Having disposed of these considerations concerning pressure, 

 which will be of service presently, we turn our attention to a 

 treatment of the energy of a liquid from the point of view of 

 molecular dynamics. We shall not, of course, go into the de- 

 tailed mathematical analysis (which can be found by the reader 

 in the works of Laplace or Gauss, or in accounts such as that 

 of Gyemant in Geiger and Scheel's Handhuch der Physik, Vol. 

 7, p. 345) but shall content ourselves with quoting certain impor- 

 tant results. If we assume that there is a law of force between 

 two molecules we can obtain in a familiar manner their mutual 

 potential energy which we will represent by ^(r), where r is their 

 distance apart. The magnitude of ^(r) increases as the mole- 

 cules separate until r reaches a value at which the attractive 

 force vanishes. For values of r greater than this the potential 

 energy of the two molecules remains constant. In all expres- 

 sions for potential energy there is an indefinite constant of 

 integration and for purposes of calculation it is necessary to 

 assign a definite value to this constant. In the present instance 

 it is most convenient to choose the value of the integration 

 constant in the function </>(r) to be such that the maximum 

 value attained by </)(r) for sufficiently large separation of the 

 molecules is zero. This makes the value of 0(r), for smaller 

 values of r, negative, at all events until the critical separation 

 is reached at which the attractive force is changed into a repul- 

 sion. There we have the minimum value of 0(r). (Of course, 

 the numerical value of </>(r) will be greatest at this distance.) 

 Anj'" further decrease in r will produce an increase in <j){r), which 

 will very quickly reach zero and even positive values owing to 

 the enormous resistance to compression exhibited by liquids. 



