in which 3.8 replaces the 2[pi] of the faulty theory alluded to earlier
(see Rayleigh, _Phil. Mag._, Oct. 1899).]
_Phenomena arising from the Variation of the Surface-tension._--Pure
water has a higher surface-tension than that of any other substance
liquid at ordinary temperatures except mercury. Hence any other liquid
if mixed with water diminishes its surface-tension. For example, if a
drop of alcohol be placed on the surface of water, the surface-tension
will be diminished from 80, the value for pure water, to 25, the value
for pure alcohol. The surface of the liquid will therefore no longer be
in equilibrium, and a current will be formed at and near the surface
from the alcohol to the surrounding water, and this current will go on
as long as there is more alcohol at one part of the surface than at
another. If the vessel is deep, these currents will be balanced by
counter currents below them, but if the depth of the water is only two
or three millimetres, the surface-current will sweep away the whole of
the water, leaving a dry spot where the alcohol was dropped in. This
phenomenon was first described and explained by James Thomson, who also
explained a phenomenon, the converse of this, called the "tears of
strong wine."
If a wine-glass be half-filled with port wine the liquid rises a little
up the side of the glass as other liquids do. The wine, however,
contains alcohol and water, both of which evaporate, but the alcohol
faster than the water, so that the superficial layer becomes more
watery. In the middle of the vessel the superficial layer recovers its
strength by diffusion from below, but the film adhering to the side of
the glass becomes more watery, and therefore has a higher
surface-tension than the surface of the stronger wine. It therefore
creeps up the side of the glass dragging the strong wine after it, and
this goes on till the quantity of fluid dragged up collects into a drop
and runs down the side of the glass.
The motion of small pieces of camphor floating on water arises from the
gradual solution of the camphor. If this takes place more rapidly on one
side of the piece of camphor than on the other side, the surface-tension
becomes weaker where there is most camphor in solution, and the lump,
being pulled unequally by the surface-tensions, moves off in the
direction of the strongest tension, namely, towards the side on which
least camphor is dissolved.
If a drop of ether is held near the surface of water the vapour of ether
condenses on the surface of the water, and surface-currents are formed
flowing in every direction away from under the drop of ether.
If we place a small floating body in a shallow vessel of water and wet
one side of it with alcohol or ether, it will move off with great
velocity and skim about on the surface of the water, the part wet with
alcohol being always the stern.
The surface-tension of mercury is greatly altered by slight changes in
the state of the surface. The surface-tension of pure mercury is so
great that it is very difficult to keep it clean, for every kind of oil
or grease spreads over it at once.
But the most remarkable effects of change of surface-tension are those
produced by what is called the electric polarization of the surface. The
tension of the surface of contact of mercury and dilute sulphuric acid
depends on the electromotive force acting between the mercury and the
acid. If the electromotive force is from the acid to the mercury the
surface-tension increases; if it is from the mercury to the acid, it
diminishes. Faraday observed that a large drop of mercury, resting on
the flat bottom of a vessel containing dilute acid, changes its form in
a remarkable way when connected with one of the electrodes of a battery,
the other electrode being placed in the acid. When the mercury is made
positive it becomes dull and spreads itself out; when it is made
negative it gathers itself together and becomes bright again. G.
Lippmann, who has made a careful investigation of the subject, finds
that exceedingly small variations of the electromotive force produce
sensible changes in the surface-tension. The effect of one of a
Daniell's cell is to increase the tension from 30.4 to 40.6. He has
constructed a capillary electrometer by which differences of electric
potential less than 0.01 of that of a Daniell's cell can be detected by
the difference of the pressure required to force the mercury to a given
point of a fine capillary tube. He has also constructed an apparatus in
which this variation in the surface-tension is made to do work and drive
a machine. He has also found that this action is reversible, for when
the area of the surface of contact of the acid and mercury is made to
increase, an electric current passes from the mercury to the acid, the
amount of electricity which passes while the surface increases by one
square centimetre being sufficient to decompose .000013 gramme of water.
[The movements of camphor scrapings referred to above afford a useful
test of the condition of a water surface. If the contamination exceed a
certain limit, the scrapings remain quite dead. In a striking form of
the experiment, the water is contained, to the depth of perhaps one
inch, in a large flat dish, and the operative part of the surface is
limited by a flexible hoop of thin sheet brass lying in the dish and
rising above the water-level. If the hoop enclose an area of (say)
one-third of the maximum, and if the water be clean, camphor fragments
floating on the interior enter with vigorous movements. A touch of the
finger will then often reduce them to quiet; but if the hoop be
expanded, the included grease is so far attenuated as to lose its
effect. Another method of removing grease is to immerse and remove
strips of paper by which the surface available for the contamination is
in effect increased.
The thickness of the film of oil adequate to check the camphor movements
can be determined with fair accuracy by depositing a weighed amount of
oil (such as .8 mg.) upon the surface of water in a large bath.
Calculated as if the density were the same as in a normal state, the
thickness of the film is found to be about two millionths of a
millimetre.
Small as is the above amount of oil, the camphor test is a comparatively
coarse one. Conditions of a contaminated surface may easily be
distinguished, upon all of which camphor fragments spin vigorously.
Thus, a shallow tin vessel, such as the lid of a biscuit box, may be
levelled and filled with tap-water through a rubber hose. Upon the
surface of the water a little sulphur is dusted. An application of the
finger for 20 or 30 seconds to the under surface of the vessel will then
generate enough heat to lower appreciably the surface-tension, as is
evidenced by the opening out of the dust and the formation of a bare
spot perhaps 1-1/2 in. in diameter. When, however, the surface is but
very slightly greased, a spot can no longer be cleared by the warmth of
the finger, or even of a spirit lamp, held underneath. And yet the
greasing may be so slight that camphor fragments move with apparently
unabated vigour.
The varying degrees of contamination to which a water surface is subject
are the cause of many curious phenomena. Among these is the _superficial
viscosity_ of Plateau. In his experiments a long compass needle is
mounted so as to swing in the surface of the liquid under investigation.
The cases of ordinary clean water and alcohol are strongly contrasted,
the motion of the needle upon the former being comparatively sluggish.
Moreover, a different behaviour is observed when the surfaces are
slightly dusted over. In the case of water the whole of the surface in
front of the needle moves with it, while on the other hand the dust
floating on alcohol is scarcely disturbed until the needle actually
strikes it. Plateau attributed these differences to a special quality of
the liquids, named by him "superficial viscosity." It has been proved,
however, that the question is one of contamination, and that a water
surface may be prepared so as to behave in the same manner as alcohol.
Another consequence of the tendency of a moderate contamination to
distribute itself uniformly is the calming effect of oil, investigated
by B. Franklin. On pure water the propagation of waves would be attended
by temporary extensions and contractions of the surface, but these, as
was shown by O. Reynolds, are resisted when the surface is contaminated.
Indeed the possibility of the continued existence of films, such as
constitute foam, depends upon the properties now under consideration.
If, as is sometimes stated, the tension of a vertical film were
absolutely the same throughout, the middle parts would of necessity fall
with the acceleration of gravity. In reality, the tension adjusts itself
automatically to the weight to be supported at the various levels.
Although throughout a certain range the surface-tension varies rapidly
with the degree of contamination, it is remarkable that, as was first
fully indicated by Miss Pockels, the earlier stages of contamination
have little or no effect upon surface-tension. Lord Rayleigh has shown
that the fall of surface-tension _begins_ when the quantity of oil is
about the half of that required to stop the camphor movements, and he
suggests that this stage may correspond with a complete coating of the
surface with a single layer of molecules.]
Spherical soap-bubble.
_On the Forms of Liquid Films which are Figures of Revolution._--A soap
bubble is simply a small quantity of soap-suds spread out so as to
expose a large surface to the air. The bubble, in fact, has two
surfaces, an outer and an inner surface, both exposed to air. It has,
therefore, a certain amount of surface-energy depending on the area of
these two surfaces. Since in the case of thin films the outer and inner
surfaces are approximately equal, we shall consider the area of the film
as representing either of them, and shall use the symbol T to denote the
energy of unit of area of the film, both surfaces being taken together.
If T' is the energy of a single surface of the liquid, T the energy of
the film is 2T'. When by means of a tube we blow air into the inside of
the bubble we increase its volume and therefore its surface, and at the
same time we do work in forcing air into it, and thus increase the
energy of the bubble.
That the bubble has energy may be shown by leaving the end of the tube
open. The bubble will contract, forcing the air out, and the current of
air blown through the tube may be made to deflect the flame of a candle.
If the bubble is in the form of a sphere of radius r this material
surface will have an area