Theory of Capillarity. 315 
In (10) the three radicals are supposed to be positive, and H 13 
is the greatest. 
If we suppose that the third fluid is air, and put p 3 =0, we 
have 
-/H u =^H l - > /H s , (11) 
in which Hi > H 2 . From (11) 
H 12 =H 1 — H 2 — 2 V /H 12 v/H 2 , 
so that 
H U <(H 1 -H S ) (12) 
The reason why the capillary force should disappear when 
the transition between two liquids is sufficiently gradual will 
now be evident. Suppose that the transition from to p is 
made in two equal steps, the thickness of the intermediate 
layer of density ^p being large compared to the range of the 
molecular forces, but small in comparison with the radius of 
curvature. At each step the difference of capillary pressure 
is only ^ of that due to the sudden transition from to p, 
and thus altogether half the effect is lost by the interposition 
of the layer. If there were three equal steps, the effect would 
be reduced to one third, and so on. When the number of 
steps is infinite, the capillary pressure disappears altogether. 
Although the relation (12) is given by Quincke* as the 
result of experiment, the numerical values found by him do 
not agree with (11). In most cases the tension at the common 
surface of two liquids exceeds that calculated from the sepa- 
rate tensions in contact with air. This result, which must be 
considered to disprove the applicability of our special hypo- 
theses, need not much surprise us. There was really no ground 
for the assumption that the law of force is always the same 
with the exception of a constant multiplier. The action of 
one fluid upon another might follow an altogether different 
law from its action upon itself. Besides this we are not en- 
titled to assume that a fluid retains its properties close to the 
surface of contact with another fluid. Even if the hypothesis, 
which would refer every thing to a difference of " densities," ' 
were correct, its application would be rendered uncertain by 
any modifications which the contiguous layers of different 
liquids might impose upon one another. As we have seen, if 
this modification were of the nature of making the transition 
less abrupt, the capillary forces would be thereby diminished. 
September 18. 
* Loc. (At. pp. 27, 87. 
