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really close by. On one occasion, during the launch of the Great Eastern,
the fog was reported so dense that the workmen could neither see nor hear.

2. It has also been observed that mist in air or steam renders them
very dull as regards motion. This is observed particularly in the pipes and
passages in a steam-engine. Mr D. K. Clark found in his experiments
that it required from 3 to 5 times as much back pressure to expel misty
steam from a cylinder as when the steam was dry.

3. My object in this paper is to give, and to investigate, what appears to
me to be an explanation of these phenomena; from which it appears that
they are intimately connected, that, in fact, they are both due to the same
cause. This explanation will be the clearer for a few preliminary remarks.

4. The nature of a fog, and the manner in which the small spherical
drops are suspended against their weight, is well understood. So long as the
fog is at rest or moving uniformly, the drops being heavier than the air
tend to sink like a stone in water, and consequently they are not at rest
in the air, but are moving through it with greater or less velocities, according
as they are large like rain, or small like haze. This motion is caused entirely


by the difference in the specific gravity of the air and water ; if the drops
were merely little hard portions of air they would have no tendency to

In some fogs the drops are so fine that they appear to be absolutely
at rest, and will remain for a long time without any appreciable motion.
The force which retards the downward motion of the drops is the friction of
the air, and this is proportional to the surface of the drop, and the square of
the velocity*. As the drops get smaller their weight diminishes faster
than their surface, and consequently the friction will balance the weight
with a less velocity. The exact law is that the velocity caused by the weight
of a drop is proportional to the square root of its diameter.

This is the general explanation of what goes on under the action of
gravity when the fog is at rest or moving uniformly, and we may make use
of it to illustrate what goes on when the fog is subjected to accelerating
or retarding forces.

5. If we imagine a vessel, full of such a compound as the fog is made of,
to be set in motion or stopped, the accelerating or retarding force will have
to be transmitted from the sides of the vessel to the fluid within it by means
of pressure. These pressures will act equally throughout the fluid, and, if
the fluid were homogeneous, they would produce the same effect throughout
it, and it would all move together ; but the pressures will obviously produce
less effect on the drops of water, than they do on the corresponding volumes
of air, and the result will be that the drops of water will move with a
different velocity to the air that the drops of water will in fact move
through the air just as they do under the action of gravity. In fact, if
the air is subject to an acceleration of 32 feet per second, the effect on
the drops (their motion through the air) will be the same as that due
to their weight. It is easy to conceive the action between the air and
the drops of water. If a mass of air and water is retarded, it is obvious
that the water, by virtue of its greater density, will move on through
the air. This property has, in fact, been made use of to dry the steam
used in steam-engines. The steam is made to take a sharp turn, when
the water, moving straight on through it, is deposited on the side of the

6. Owing to this motion of the water through the air, it would clearly
take longer, with the same force, to impress the same momentum on foggy
air, than on the same when dry. This is obvious, for at the end of a certain
time the particles of water would not be moving as fast as the air, and

* [This is not the case. The resistance is as the velocity, as was pointed out by Trof. G. G.


consequently the air and water would have less momentum than the same
weight of dry air all moving together: that is to say, if we had two light
vessels containing the same weight of fluid, the one full of dry air and the
other full of fog, and both subjected to the same force for the same time,
at the end of this time, although they would have exactly the same motion,
their contents would not, for the drops of water in the fog would not be
moving so fast as the vessel. Now the energy expended on each of
these vessels would be the same, but, inasmuch as the effects are different,
the energy acquired by the foggy air would be less than that acquired by
the dry air, the difference having gone to move the water through the air :
that is to say, it would require a greater pressure to impress in the same
time the same velocity on foggy air, than on dry air of the same density.

7. This then fully explains the dulness with which foggy air acquires
motion. In the passages of a steam-engine the steam is subjected to
continual accelerations and retardations, each of which requires more force,
in the manner described, with misty than with dry steam, and at each of
which the particles of water moving through the steam destroy energy in
creating eddies.

8. Although not so obvious, the same is true in the case of sound. The
effect of waves of sound traversing a portion of air is, first to accelerate and
then to retard it. And if there are any drops of water in the air, these will
not take up the motion of the air so readily as the air itself. They will
allow the air to move backwards and forwards past them, and so cause
friction and diminish the effect of the wave as it proceeds, just as a loose
cargo will diminish the rolling of a ship.

9. It is important to notice that this action of the particles of water is
not analogous to their action in reflecting the waves of light.

It has been assumed, as an explanation of the action of fog on sound, that
the particles of water break up the wave of sound by small reflections, in the
same way as they scatter the waves of light. The analogy however is not
admissible; for in the case of light the wave length is shorter than the
thickness of the drops, and the surface of the drop acts in the same way as
if the drop were of large extent ; but in the case of sound the wave's length
may be thousands of times the thickness of the drop, and instead of the
whole wave being reflected, it will only be a very small portion of it. Even
this portion can hardly be called a reflection ; it is due to the motion of the
air past the drops, like the waves of sound caused by a bullet, or the waves
thrown off by the bow of a ship.

10. A certain portion of the resistance which the air offers to the
motion of the water through it is this what is called in naval science


wave resistance; but it can be shown that the proportion of this resistance, to
the resistance in causing eddies, diminishes with the velocity, and con-
sequently it can have very little to do with the effect of the drops of water
on the waves of sound, in which the velocity of the water through the air
must be very small*.

11. So far, then, I have shown the manner in which the fog diminishes
the sound ; it remains to consider the connection between the size of the
drops and their effects. I am not aware that any observations have been
made with respect to this. I do not know whether it has ever been noticed
whether a fine or a coarse mist produces the most effect on sound. It does
not appear, however, that rain produces the same effect as fog; and con-
sidering rain as a coarse fog, we must come to the conclusion that a certain
degree of fineness is necessary.

If we examine theoretically into the relation between the size of the
drops and the effect they produce, always assuming the same quantity of
water in the air, we find in the first place that if the air is subjected to
a uniform acceleration, which acts for a sufficient time for the drops to
acquire their maximum velocity through the air, the effect of the drops in a
given time that is to say, the energy dissipated in a given time is
proportional to the square root of the diameters of the drops. This appears
from the action of gravity. As previously stated, the maximum downward
motion of the drops, and hence the distance they will have fallen in a given
time, and the energy destroyed, is proportional to the square root of their
diameters. Hence where the acceleration acts continuously for some time,
as would be the case in a steam-pipe, the effect will increase with the size of
the drops.

This effect may be represented by a parabolic curve, in which distances
measured from the vertex along the axis represent the size of the drops, and
the corresponding ordinates represent their effect in destroying energy.

If on the other hand the acceleration alternates very rapidly, then there
will not be time for the drop to acquire its maximum velocity, and if the
time be very short the drop will practically stand still, in which case the
effect of the drops will be proportional to the aggregate surface which they
expose. And this will increase as the diameter diminishes, always supposing
the same quantity of water to be present.

This latter is somewhat the condition when a fog is traversed by waves
of sound, so long as the drops are above a certain size ; when, however, they
are very small, compared with the length of the waves, there will be time for

* This reflection has nothing to do with the reverberation from clouds which occurs in a
thunder-storm, which is probably due to the different density of the clouds, and takes place at
their surfaces.


them to acquire their maximum velocity. So that starting from drops the
size of rain, their effect will increase as their size diminishes, at first in the
direct proportion, then more and more slowly, until a certain minuteness
is reached, after which, as the drops become still smaller, their effect will
begin to diminish, at first slowly, but in an increasing ratio, tending towards
that of the square root of the diameter of the drops.

This effect may be represented by a curve which coincides with the
previously described parabola at the vertex, but which turns off towards the
axis, which it finally approaches as a straight line.

This completes the investigation, so far as I have been able to carry it.
The complete mathematical solution of the equations of motion does not
appear to be possible, as they are of a form that has not as yet been
integrated. However, so far it appears to me to afford a complete ex-
planation of the two phenomena, and further to show, a fact not hitherto
noticed, that for any note of waves of sound there is a certain size of drop
with which a fog will produce the greatest effect.



[From the Thirteenth Volume of the " Proceedings of the Literary and
Philosophical Society of Manchester." Session 1873-4.]

(Read February 24, 1874.)

IT will be remembered that at a previous meeting of this Society
M r W. H. Johnson exhibited some iron and steel wire, in which he had observed
some very singular effects produced by the action of sulphuric acid. In the
first place the nature of the wire was changed in a marked manner, for
although it was soft charcoal wire, it had become short and brittle ; the
weight of the wire was increased ; and what was the most remarkable
effect of all, was that when the wire was broken, and the face of the fracture
wetted with the mouth, it frothed up as if the water acted as a powerful
acid. These effects, however, all passed off if the wire were allowed to
remain exposed to the air for some days, and if it were warmed before
the fire they passed off in a few hours.

By Mr Johnson's permission I took possession of one of these pieces of
wire and subjected it to a farther examination, and from the result of that
examination I was led to what appears to me to be a complete explanation
of the phenomena.

I observed that when I broke a short piece from the end of the wire,
the two faces of the fracture behaved very differently that on the long
piece frothed when wetted, and continued to do so for some seconds, while
that on the short piece would hardly show any signs of froth at all. This
seemed to imply that the gas which caused the froth came from a consider-
able depth below the surface of the wire, and was not generated on the
freshly exposed face. This view was confirmed, when, on substituting oil
for water, I found the froth just the same.


These observations led me to conclude that the effect was due to
hydrogen, and not to acid, as Mr Johnson appeared to think, having entered
into combination with the iron during its immersion in the acid, which
hydrogen gradually passed off when the iron was exposed.

It was obvious however that this conclusion was capable of being further
tested. It was clearly possible to ascertain whether or not the gas was
hydrogen ; and whether hydrogen penetrated iron when under the action
of acid. With a view to do this I made the following experiments.

First, however, I would mention that after 24 hours I examined what
remained of the wire, when I found that all appearance of frothing had
vanished and the wire had recovered its ductility, so much so that it would
now bend backwards and forwards two or three times without breaking,
whereas on the previous evening a single bend had sufficed to break it.

I then obtained a piece of wrought iron gas-pipe 6 inches long and f inch
external diameter, and rather more than -^ of an inch thick; I had this
cleaned in a bath both inside and outside ; over one end I soldered a piece
of copper so as to stop it, and the other I connected with a piece of glass
tube by means of indiarubber tube. I then filled both the glass and iron
tubes with olive oil, and immersed the iron tube in diluted sulphuric acid
which had been mixed for some time and was cold. Under this arrangement
any hydrogen which came from the inside of the glass tube must have
passed through the iron.

After the iron had been in the acid about 5 minutes small bubbles
began to pass up the glass tube. These were caught at the top and were
subsequently burnt and proved to be hydrogen. At first, however, they
came off but very slowly, and it was several hours before I had collected
enough to burn. With a view to increase the speed I changed the acid
several times without much effect until I happened to use some acid which
had only just been diluted and was warm; then the gas came off twenty
or thirty times as fast as it previously had done. I then put a lamp
under the bath and measured the rate at which the gas came off, and I
found that when the acid was on the point of boiling, as much hydrogen
was given off in 5 seconds as had previously come off in 10 minutes, and
the rate was maintained in both cases for several hours.

After having been in acid for some time the tube was taken out, and well
washed with cold water and soap so as to remove all trace of the acid ; it
was then plunged into a bath of hot water, upon which gas came off so
rapidly from both the outside and inside of the tube as to give the
appearance of the action of strong acid. This action lasted for some time,
but gradually diminished. It could be stopped at any time by the sub-
stitution of cold water in place of the hot, and it was renewed again after
o. R. 4


several hours by again putting the tube in hot water. The volume of
hydrogen which was thus given off by the tube, after it had been taken out
of acid, was about equal to the volume of the iron.

At the time I made these experiments I was not aware that there had
been any previous experiments on the subject; but I subsequently found,
on referring to Watt's Dictionary of Chemistry, that Cailletet had in 1868
discovered that hydrogen would pass into an iron vessel immersed in
sulphuric acid. See Compt. rend. Ixvi, 847.

The facts thus established appear to afford a complete explanation of the
effects observed by Mr Johnson.

In the first place, with regard to the temporary character of the effect,
it appears that hydrogen leaves the iron slowly even at ordinary temperatures
so much so that after two or three days' exposure I found no hydrogen
given off when the tube was immersed in hot water. With regard to the
effect of warming the wire ; at the temperature of boiling, the hydrogen
passed off 120 times as fast as at the temperature of 60. Also when the
saturated iron was plunged into warm water the gas passed off as if the
iron had been plunged into strong acid ; so that we can easily understand
how the hydrogen would pass off from the wire quickly when warm, although
it would take long to do so at the ordinary temperatures. With regard
to the frothing of the wire when broken and wetted ; this was not due,
as at first sight it appeared to be, simply to the exposure of the interior
of the wire, but was due to warmth caused in the wire by the act of
breaking. This was proved by the fact that the froth appeared on the
sides of the wire in the immediate neighbourhood of the fracture, as well
as the end, when these were wetted; and by simply bending the wire it
could be made to froth at the point where it was bent.

As to the effect on the nature and strength of the iron I cannot add
anything to what Mr Johnson has already observed. The question, however,
appears to be one of very considerable importance, both philosophically
and in connection with the use of iron in the construction of ships and
boilers. If, as is probable, the saturation of iron with hydrogen takes
place whenever oxidation goes on in water, then the iron of boilers and
ships may at times be changed in character and rendered brittle in the
same manner as Mr Johnson's wire, and this, whether it can be prevented
or not, is at least an important point to know, and would repay a further
investigation of the subject.



[From the "Transactions of the Institution of Naval Architects," 1873.]

(Read April 3rd, 1873.)

THE tendency which the screws of steam ships have, under certain
circumstances, to lose their hold on the water, and consequently to let the
engines start off at a great speed a tendency which is one of the greatest
sources of difficulty and danger with which steam navigation is attended
appears as yet to have its cause enveloped in mystery, and to require
further explanation than has yet been given to it. For although the
circumstances under which this racing occurs are such as appear primd
facie to afford an explanation of it although we should naturally expect the
pitching and tossing of the vessel, and the exposure of the screw to affect
its speed yet, when we come to look closer, it appears that something more
than this is required. The partial exposure of the screw and the diminution
of its resistance accounts for some increase of speed ; and the backward and
forward motion of the water on the tops and in the hollows of the waves
also accounts for some, but neither of these is sufficient to account for
the way in which the screw loses its hold on the water. And besides, it is
not only in storms that racing occurs; whenever the vessel is moving slowly,
and the screw working against great resistance as, for instance, when
it is starting the vessel or towing another there is a liability for racing
to occur. In fact, this liability prevents the screw from being used for
tugs or boats which are required to stop and start frequently.

Whilst making some experiments on a screw model driven by a spring,
I noticed a phenomenon in connection with racing which seems to me to
throw new and important light on the subject. It probably would not have
attracted my attention had it 'not been for some remarks of Mr H. Brunei



(made last autumn) as to the insufficiency of the mere exposure of the
screw to account for the phenomena of racing, which remarks rendered me
alive to any other explanation that might present itself to my notice.

The phenomenon consisted in the connection between the racing of the
screw and the breaking of the surface of the water, and the consequent
admission of air to the blades of the screw. Whenever the screw raced, the
water in its wake was broken up and mixed with air ; and although at first
sight this seemed to be a very natural result of the increased speed of the
screw, yet, when I observed that these phenomena invariably happened in
conjunction, and that not only did the screw never race without getting air,
but that the admission of air was always followed by racing, then I came to
think that there was more in it, and that the air must be the cause, and not
merely the result of the racing.

With a view to ascertain if this was the case, I carried out the system of
experiments I am about to describe ; and these, again, led me to the
theoretical explanation set forth in the last part of the Paper.

Some of the experiments were made with the model which had first
called my attention to the subject. This model is 2 feet 6 inches in length,
and has a screw 2 inches in diameter, driven by a spring, the spring being
changeable, so that the boat will raise weights at a dead pull varying from
half-an-ounce to 4 ounces.

The results of these experiments were as follows :

1. When the boat was placed at one end of the trough, and allowed to
start and run to the other end the screw being so deeply immersed that it
did not froth either in starting or running (this with the strongest spring
required to be about half-an-inch under the surface) then the screw would
make just 180 revolutions, whatever might be the power of the spring.

2. If there were a few small waves on the trough, just sufficient to
expose the top of the screw, then at such times the screw would apparently
slip round without resistance, throwing up froth and water, and turning the
boat out of its course. The number of revolutions required to take the boat
the same distance as before was greatly increased, being between 250 and
300 ; and as the screw was not racing for the sixth of its time, during that
time it must have turned at many times its ordinary speed. When the screw
was not racing, the boat went very fairly straight forwards, but the moment
racing commenced it turned to one side.

3. When the boat was so loaded that the screw was but slightly
beneath the surface, then the screw raced until the boat got under way,
causing froth, and turning the boat to one side; afterwards the. racing ceased,
or only occurred at intervals, but whenever it did so it was attended with


froth and turning to one side. The number of revolutions was about 250
under these circumstances.

4. When the load was so placed that the screw was just at the surface,
then racing commenced, and continued until the spring was down, which
happened before the boat got to the end of its course, after having made
350 turns.

5. When the boat was held by a suspended weight, and the screw was
immersed deeply enough, it would raise a weight proportional to the strength
of the spring without any undue racing, turning steadily all the time ; but if,
while suspending such a weight, the load on the boat was shifted forwards,
the moment the surface was broken, away went the screw, the spring ran
down almost with a rush, the water flew out in a jet behind the boat,
and the boat was drawn backwards by the weight screwing over to one
side as before.

These experiments, conducted with the small spring model, show con-
clusively that racing is a reality, and that it does not require the exposure of
any part of the screw, but that it depends on the depth of the screw below
the surface. The results were substantially the same whether the strongest
or weakest spring was used, the only difference being, that the strong spring
required that the screw should be rather more deeply immersed, in order to
prevent racing at starting.

These experiments did not show whether the frothing was the result
or the cause of the racing.

6. With a view to do this, a boat was loaded so that it would start with-
out racing ; and then a larger screw was substituted for the previous one,

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