186 
&' = (p,—p)v of pe =p; =p. 
Now we find: 
PiP, = — GF + fzo de" = og" — fre do. 
Therefore 
dp, = #'do — ode", 
for which we may always write: 
dp, = edo — ode. 
Still it may be remarked, that when the condition of the thermo- 
: Wu ance 
dynamic theory that f— — — dh shall be a minimum, is satisfied 
v 
(the integration has here to be extended over the whole depth of 
the passage layer), one element of this integral is just equal to 
Pers p = ob and ME 
Suppose, we had started from the definition of the molecular 
pressure in the direction of the bounding layer that it was equal 
to — ge (with omission of the constant). Then this would evidently 
have led us to a value of the surface tension in agreement with 
the thermodynamic theory, which is a proof of the validity of the 
definition. But then we can at once write down the differential 
equation for the surface tension. For from 
Pi =p, = MM SM; 
it follows directly that 
— dp, = — doe + 20de = — edo + ode. 
When a fluid is in contact with a solid wall, the molecular 
pressure and therefore also the external pressure in the perpendicular 
to the passage layer will generally be different from the pressure 
in the direction of this layer. The action of the solid wall on the 
fluid at the wall influences the molecular pressure of the fluid at 
the wall. External forces like gravity, a magnetic or electric force 
will directly influenee the external pressure. As also in this case 
the molecular pressure in the direction of the passage layer M,’ may 
be represented by — ge and as JM, = — 2ede, we have here likewise: 
d(p, — p,) = — dp, = — doe + 20de = ode — edo. 
The calculation of the value of the molecular pressure of the fluid 
at the wall presents great difficulties, because the calculation is 
based upon the continuous division of the matter. In the immediate 
neighbourhood of the wall e.g. the value of the molecular pressure 
in the direction of the wall will be caused by the attraction 
of the wall and of the fluid, but in the case of equal spheres of 
action the contribution of the two will be due to unequal volumes. The 
tt, oo le es Pee 
