268 
MR. J, LAR^rOR A DYNA^^IICAL THEORY OF 
so transmitted tlirongh the mercury into the companion manometer tube containing 
perfect gas that is measured aud is represented on his diagram of isothermal lines. 
The two terms of which it is the difference, namely the reaction of the interface 
against molecular impacts, and the molecular attraction across the interface, are 
separately represented in Van her Waals’ characteristic equation. When the 
^’irial equation of Clausius is applied to a mass of liquid with a free surface 
abutting on a gaseous atmosphere, there results the relation that the pressure of 
this atmosphere against an outer boundaiy, which is the same as the transmitted 
pressure in the liquid, is equal to two-thirds of the part of the mean density of 
kinetic energy in the liquid that is connected with encounters and mutual forces 
between the molecules, together wdth one-third of the mean virial per unit volume 
of these intermolecular forces, the latter part being negative and, if polar forces 
could he assumed absent, of Clausius’ form ; and this without reference to 
the character of the transition between liquid and gas at the free surface. When 
on the other hand the virial equation is applied to a mass in the homogeneous 
interior of the liquid, bounded by an infinitely thin interface, the virial of each 
molecule vanishes because the attractions acting on it compensate each other on 
the average, and the result is that the kinetic pressure exerted by the fluid on this 
interface is simply two-thirds of the mean density of kinetic energy of the bodily 
motions of the molecules, their internal constitutive energies being excluded.* It 
follows that the mutual molecular attraction across the interface produces a pressure 
on the interface from each side equal to the mean \drial per unit volume; as in fact 
would flow directly from the principle that two statically equivalent force-systems 
have the same virial. 
54. Let us construct as above an ideal rigid tube, with infinitely thin walls which 
exert constraint on the molecules but no attraction, having one of its open ends A in 
the liquid and the other B outside it; but let us now suppose that the diameter of 
the tube is small compared with the radius of sensible molecular action, winch implies 
that this radius extends over a considerable number of molecules. The molecular 
forces acting on each molecule in the tube, whether near the end of it or not, are now 
almost v/holly due to molecules outside it, and are on the average self-balancing, 
except in the case of molecules at the free surface which are subject to the whole 
inward molecular attraction of the liquid. The equilibrium of the contents of the 
tube, which are liquid in one end and gaseous in the other, therefore requires that the 
kinetic pressure on the molecules in the liquid end A exceeds that on those in the 
gaseous end B by a constant amount, namely the pressure due to the inward attrac- 
* Some consideration is required as to the omission of the virials of mutual forces acting inside the 
separate molecules: these must he taken as wholly compensated by kinetic energy of internal motions 
not thermal, which is legitimate in so far ns molecular encounters do not sensibly excite radiation but 
only slow free precessional motions, and so do not sensibly distuib the configuration of the internal 
dynamical system of the molecule. 
