(2) The three surfaces may be all alike: as when a soap-bubble floats
upon soapy water, or when two soap-bubbles are joined together, on
either side of a partition-film. In this case, the three tensions are
all equal, and therefore the three angles are all equal; that is to
say, when three similar liquid surfaces meet together, they always
do so at an angle of 120°. Whether our two conjoined soap-bubbles
be equal or unequal, this is still the invariable rule; because the
specific tension of a particular surface is unaffected by any changes
of magnitude or form.
(3) If two only of the surfaces be alike, then two of the angles will
be alike, and the other will be unlike; and this last will be the
difference between 360° and the sum of the other two. A particular case
is when a film is stretched between solid and parallel walls, like
a soap-film within a cylindrical tube. Here, so long as there is no
external pressure applied to either side, so long as both ends of the
tube are open or closed, the angles on either side of the film will be
equal, that is to say the film will set itself at right angles to the
sides.
Many years ago Sachs laid it down as a principle, which has become
celebrated in botany under the name of Sachs’s Rule, that one cell-wall
always tends to set itself at right angles to another cell-wall.
This rule applies to the case which we have just illustrated; and
such validity as the rule possesses is due to the fact that among
plant-tissues it very frequently happens that one cell-wall has become
solid and rigid before another and later partition-wall is developed in
connection with it.
(4) There is another important principle which arises not out of our
equations but out of the general considerations by which we were
led to them. We have seen that, at and near the point of contact
between our several surfaces, there is a continued balance of forces,
carried, so to speak, across the interval; in other words, there is
_physical continuity_ between one surface and another. It follows
necessarily from this that the surfaces merge one into another by a
continuous curve. Whatever be the form of our surfaces and whatever
the angle between them, this small intervening surface, approximately
spherical, is always there to bridge over the line of contact[342];
and this little fillet, or “bourrelet,” {298} as Plateau called
it, is large enough to be a common and conspicuous feature in the
microscopy of tissues (Fig. 102). For instance, the so-called
“splitting” of the cell-wall, which is conspicuous at the angles of the
large “parenchymatous” cells in the succulent tissues of all higher
plants (Fig. 103), is nothing more than a manifestation of Plateau’s
“bourrelet,” or surface of continuity[343].
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