cessarily imaginary, that one of
three fluids will always spread upon the interface of the other two.

Another point of importance may be easily illustrated by this theory,
viz. the dependency of capillarity upon abruptness of transition. "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 0 to [sigma] is made in two equal steps, the
thickness of the intermediate layer of density 1/2[sigma] 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 one-quarter of that due to the sudden transition from 0
to [sigma], 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." ("Laplace's
Theory of Capillarity," Rayleigh, _Phil. Mag._, 1883, p. 315.)

According to Laplace's hypothesis the whole energy of any number of
contiguous strata of liquids is least when they are arranged in order of
density, so that this is the disposition favoured by the attractive
forces. The problem is to make the sum of the interfacial tensions a
minimum, each tension being proportional to the square of the difference
of densities of the two contiguous liquids in question. If the order of
stratification differ from that of densities, we can show that each step
of approximation to this order lowers the sum of tensions. To this end
consider the effect of the abolition of a stratum [sigma]_(n+1),
contiguous to [sigma]_n and [sigma]_(n+2). Before the change we have
([sigma]_n - [sigma](n+1))^2 + ([sigma]_(n+1) - [sigma]_(n+2))^2, and
afterwards ([sigma]_n - [sigma]_(n+2))^2. The second _minus_ the first,
or the increase in the sum of tensions, is thus

2([sigma]_n - [sigma]_(n+1))([sigma]_(n+1) - [sigma]_(n+2)).

Hence, if [sigma]_(n+1) be intermediate in magnitude between [sigma]_n
and [sigma]_(n+2), the sum of tensions is increased by the abolition of
the stratum; but, if [sigma]_(n+1) be not intermediate, the sum is
decreased. We see, then, that the removal of a stratum from between
neighbours where it is out of order and its introduction between
neighbours where it will be in order is doubly favourable to the
reduction of the s