IT is now many years ago since, as a student, I was present at a
college lecture delivered by a certain learned professor on the
subject of friction. At this lecture a discussion arose out of a
question addressed to our teacher: "How is it we can skate on ice
and on no other substance?"
The answer came back without hesitation: "Because the ice is so
smooth."
It was at once objected: "But you can skate on ice which is not
smooth."
This put the professor in a difficulty. Obviously it is not on
account of the smoothness of the ice. A piece of polished plate
glass is far smoother than a surface of ice after the latter is
cut up by a day's skating. Nevertheless, on the scratched and
torn ice-surface skating is still quite possible; on the smooth
plate glass we know we could not skate.
Some little time after this discussion, the connection between
skating and a somewhat abstruse fact in physical science occurred
to me. As the fact itself is one which has played a part in the
geological history of the earth,
[1] A lecture delivered before the Royal Dublin Society in 1905.
260
and a part of no little importance, the subject of skating,
whereby it is perhaps best brought home to every one, is
deserving of our careful attention. Let not, then, the title of
this lecture mislead the reader as to the importance of its
subject matter.
Before going on to the explanation of the wonderful freedom of
the skater's movements, I wish to verify what I have inferred as
to the great difference in the slipperiness of glass and the
slipperiness of ice. Here is a slab of polished glass. I can
raise it to any angle I please so that at length this brass
weight of 250 grams just slips down when started with a slight
shove. The angle is, as you see, about 12½ degrees. I now
transfer the weight on to this large slab of ice which I first
rapidly dry with soft linen. Observe that the weight slips down
the surface of ice at a much lower angle. It is a very low angle
indeed: I read it as between 4 and 5 degrees. We see by this
experiment that there is a great difference between the
slipperiness of the two surfaces as measured by what is called
"the angle of friction." In this experiment, too, the glass
possesses by far the smoother surface although I have rubbed the
deeper rugosities out of the ice by smoothing it with a glass
surface. Notwithstanding this, its surface is spotted with small
cavities due to bubbles and imperfections. It is certain that if
the glass was equally rough, its angle of friction towards the
brass weight would be higher.
261
We have, however, another comparative experiment to carry out. I
made as you saw a determination of the angle at which this weight
of 250 grams just slipped on the ice. The lower surface of the
weight, the part which presses on the ice, consists of a light,
brass curtain ring. This can be detached. Its mass is only 6½
grams, the curtain ring being, in fact, hollow and made of very
thin metal. We have, therefore, in it a very small weight which
presents exactly the same surface beneath as did the weight of
250 grams. You see, now, that this light weight will not slip on
ice at 5 or 6 degrees of slope, but first does so at about io
degrees.
This is a very important experiment as regards our present
inquiry. Ice appears to possess more than one angle of friction
according as a heavy or a light weight is used to press upon it.
We will make the same experiment with the plate of glass. You see
that there is little or no difference in the angle of friction of
brass on glass when we press the surfaces together with a heavy
or with a light weight. The light weight requires the same slope
of 12½ degrees to make it slip.
This last result is in accordance with the laws of friction. We
say that when solid presses on solid, for each pair of substances
pressed together there is a constant ratio between the force
required to keep one in motion over the other, and the force
pressing the solids together. This ratio is called"the
coefficient of friction."The coefficient is, in fact, constant or
approximately
262
so. I can determine the coefficient of friction from the angle of
friction by taking the tangent of the angle. The tangent of the
angle of friction is the coefficient of friction. If, then, the
coefficient is constant, so, of course, must the angle of
friction be constant. We have seen that it is so in the case of
metal on glass, but not so in the case of metal on ice. This
curious result shows that there is something abnormal about the
slipperiness of ice.
The experiments we have hitherto made are open to the reproach
that the surface of the ice is probably damp owing to the warmth
of the air in contact with it. I have here a means of dealing
with a surface of cold, dry ice. This shallow copper tank about
18 inches (45 cms.) long, and 4 inches (10 cms.) wide, is filled
with a freezing 'mixture circulated through it from a larger
vessel containing ice melting in hydrochloric acid at a
temperature of about -18° C. This keeps the tank below the
melting point of ice. The upper surface of the tank is provided
with raised edges so that it can be flooded with water. The water
is now frozen and its temperature is below 0° C. It is about
10° C. I can place over the ice a roof-shaped cover made of two
inclined slabs of thick plate glass. This acts to keep out warm
air, and to do away with any possibility of the surface of the
ice being wet with water thawed from the ice. The whole tank
along with its roof of glass can be adjusted to any angle, and a,
scale at the
263
raised end of the tank gives the angle of slope in degrees. A
weight placed on the ice can be easily seen through the glass
cover.
The weight we shall use consists of a very light ring of
aluminium wire which is rendered plainly visible by a ping-pong
ball attached above it. The weight rests now on a copper plate
provided for the purpose at the upper end of the tank. The plate
being in direct contact beneath with the freezing mixture we are
sure that the aluminium ring is no hotter than the ice. A light
jerk suffices to shake the weight on to the surface of the ice.
We find that this ring loaded with only the ping-pong ball, and
weighing a total of 2.55 grams does not slip at the low angles. I
have the surface of the ice at an angle of rather over 13½, and
only by continuous tapping of the apparatus can it be induced to
slip down. This is a coefficient of 0.24, and compares with the
coefficient of hard and smooth solids on one another. I now
replace the empty ping-pong ball by a similar ball filled with
lead shot. The total weight is now 155 grams. You see the angle
of slipping has fallen to 7°.
Every one who has made friction experiments knows how
unsatisfactory and inconsistent they often are. We can only
discuss notable quantities and broad results, unless the most
conscientious care be taken to eliminate errors. The net result
here is that ice at about -10° C. when pressed on by a very light
weight possesses a
264
coefficient of friction comparable with the usual coefficients of
solids on solids, but when the pressure is increased, the
coefficient falls to about half this value.
The following table embodies some results obtained on the
friction of ice and glass, using the methods I have shown you. I
add some of the more carefully determined coefficients of other
observers.
Wt. in On Plate On Ice On Ice
Grams. Glass. at 0° C. at 10° C.
Angle. Coeff. Angle. Coeff. Angle. Coeff
Aluminium 2.55 12½° 0.22 12° 0.21 13½° 0.24
Same 155 12½° 0.22 6° 0.11 7° 0.12
Brass 6.5 12½° 0.22 10° 0.17 10½° 0.18
Same 107 12½° 0.22 5° 0.09 6° 0.10
Steel on steel (Morin) - - - - 0.14
Brass on cast iron (Morin) - - 0.19
Steel on cast iron (Morin) - - 0.20
Skate on ice (J. Müller) - - - 0.016--0.032
Best-greased surfaces (Perry) - 0.03--0.036
You perceive from the table that while the friction of brass or
aluminium on glass is quite independent of the weight used, that
of brass or aluminium on ice depends in some way upon the weight,
and falls in a very marked degree when the weight is heavy. Now,
I think that if we had been on the look out for any abnormality
in the friction of hard substances on ice, we would have rather
anticipated a variation in the
265
other direction. We would have, perhaps, expected that a heavy
weight would have given rise to the greater friction. I now turn
to the explanation of this extraordinary result.
You are aware that it requires an expenditure of heat merely to
convert ice to water, the water produced being at the temperature
of the ice, _i.e._ at 0° C., from which it is derived. The heat
required to change the ice from the solid to the liquid state is
the latent heat of water. We take the unit quantity of heat to be
that which is required to heat 1 kilogram of water 1° C. Then if
we melt 1 kilogram of ice, we must supply it with 80 such units
of heat. While melting is going on, there is no change of
temperature if the experiment is carefully conducted. The melting
ice and the water coming from it remain at 0° C. throughout the
operation, and neither the thermometer nor your own sensations
would tell you of the amount of heat which was flowing in. The
heat is latent or hidden in the liquid produced, and has gone to
do molecular work in the substance. Observe that if we supply
only 40 thermal units, we get only one-half the ice melted. If
only 10 units are supplied, then we get only one eighth of a
kilogram of water, and no more nor less.
I have ventured to recall to you these commonplaces of science
before considering a mode of melting ice which is less generally
known, and which involves no supply of heat on your part. This
method involves for its
266
understanding a careful consideration of the thermal properties
of water in the solid state.
It must have been observed a very long time ago that water
expands when it freezes. Otherwise ice would not float on water;
and, what is perhaps more important in your eyes, your water
pipes would not burst in winter when the water freezes therein.
But although the important fact of the expansion of water on
freezing was so long presented to the observation of mankind, it
was not till almost exactly the middle of the last century that
James Thomson, a gifted Irishman, predicted many important
consequences arising from the fact of the expansion of water on
becoming solid. The principles lie enunciated are perfectly
general, and apply in every case of change of volume attending
change of state. We are here only concerned with the case of
water and ice.
James Thomson, following a train of thought which we cannot here
pursue, predicted that owing to the fact of the expansion of
water on becoming solid, pressure will lower the melting point of
ice or the freezing point of water. Normally, as you are aware,
the temperature is 0° C. or 32° F. Thomson said that this would
be found to be the freezing point only at atmospheric pressure.
He calculated how much it would change with change of pressure.
He predicted that the freezing point would fall 0.0075 of a
degree Centigrade for each additional atmosphere of pressure
applied to the water. Suppose,
267
for instance, our earth possessed an atmosphere so heavy to as
exert a thousand times the pressure of the existing atmosphere,
then water would not freeze at 0° C., but at -7.5° C. or about
18° F. Again, in vacuo, that is when the pressure has been
reduced to the relatively small vapour pressure of the water, the
freezing point is above 0° C., _i.e._ at 0.0075° C. In parts of
the ocean depths the pressure is much over a thousand
atmospheres. Fresh water would remain liquid there at
temperatures much below 0° C.
It will be evident enough, even to those not possessed of the
scientific insight of James Thomson, that some such fact is to be
anticipated. It is, however, easy to be wise after the event. It
appeals to us in a general way that as water expands on freezing,
pressure will tend to resist the turning of it to ice. The water
will try to remain liquid in obedience to the pressure. It will,
therefore, require a lower temperature to induce it to become
ice.
James Thomson left his thesis as a prediction. But he predicted
exactly what his distinguished brother, Sir William Thomson--later
Lord Kelvin--found to happen when the matter was put to the test
of experiment. We must consider the experiment made by Lord
Kelvin.
According to Thomson's views, if a quantity of ice and water are
compressed, there must be _a fall of temperature_. The nature of
his argument is as follows:
268
Let the ice and water be exactly at 0° C. to start with. Then
suppose we apply, say, one thousand atmospheres pressure. The
melting point of the ice is lowered to -7.5° C. That is, it will
require a temperature so low as -7.5° C. to keep it solid. It
will therefore at once set about melting, for as we have seen,
its actual temperature is not -7.5° C., but a higher temperature,
_i.e._ 0° C. In other words, it is 7.5° above its melting point.
But as soon as it begins melting it also begins to absorb heat to
supply the 80 thermal units which, as we know, are required to
turn each kilogram of the ice to water. Where can it get this
heat? We assume that we give it none. It has only two sources,
the ice can take heat from itself, and it can take heat from the
water. It does both in this case, and both ice and water drop in
temperature. They fall in temperature till -7.5° is reached. Then
the ice has got to its melting point under the pressure of one
thousand atmospheres, or, as we may put it, the water has reached
its freezing point. There can be no more melting. The whole mass
is down to -7.5° C., and will stay there if we keep heat from
flowing either into or out of the vessel. There is now more water
and less ice in the vessel than when we started, and the
temperature has fallen to -7.5° C. The fall of temperature to the
amount predicted by the theory was verified by Lord Kelvin.
Suppose we now suddenly remove the pressure; what will happen? We
have water and ice at -7.5° C.
269
and at the normal pressure. Water at -7.5° and at the normal
pressure of course turns to ice. The water will, therefore,
instantly freeze in the vessel, and the whole process will be
reversed. In freezing, the water will give up its latent heat,
and this will warm up the whole mass till once again 0° C. is
attained. Then there will be no more freezing, for again the ice
is at its melting point. This is the remarkable series of events
which James Thomson predicted. And these are the events which
Lord Kelvin by a delicate series of experiments, verified in
every respect.
Suppose we had nothing but solid ice in the vessel at starting,
would the experiment result in the same way? Yes, it assuredly
would. The ice under the increased pressure would melt a little
everywhere throughout its mass, taking the requisite latent heat
from itself at the expense of its sensible heat, and the
temperature of the ice would fall to the new melting point.
Could we melt the whole of the ice in this manner? Again the
answer is "yes." But the pressure must be very great. If we
assume that all the heat is obtained at the expense of the
sensible heat of the ice, the cooling must be such as to supply
the latent heat of the whole mass of water produced. However, the
latent heat diminishes as the melting point is lowered, and at a
rate which would reduce it to nothing at about 18,000
atmospheres. Mousson, operating on ice enclosed in a conducting
cylinder and cooled to -18° at starting
270
appears to have obtained very complete liquefaction. Mousson must
have attained a pressure of at least an amount adequate to lower
the melting point below -18°. The degree of liquefaction actually
attained may have been due in part to the passage of heat through
the walls of the vessel. He proved the more or less complete
liquefaction of the ice within the vessel by the fall of a copper
index from the top to the bottom of the vessel while the pressure
was on.
I have here a simple way of demonstrating to you the fall of
temperature attending the compression of ice. In this mould,
which is strongly made of steel, lined with boxwood to diminish
the passage of conducted heat, is a quantity of ice which I
compress when I force in this plunger. In the ice is a
thermoelectric junction, the wires leading to which are in
communication with a reflecting galvanometer. The thermocouple is
of copper and nickel, and is of such sensitiveness as to show by
motion of the spot of light on the screen even a small fraction
of a degree. On applying the pressure, you see the spot of light
is displaced, and in such a direction as to indicate cooling. The
balancing thermocouple is all the time imbedded in a block of ice
so that its temperature remains unaltered. On taking off the
pressure, the spot of light returns to its first position. I can
move the spot of light backwards and forwards on the screen by
taking off and putting on the pressure. The effects are quite
instantaneous.
271
The fact last referred to is very important. The ice, in fact, is
as it were automatically turned to water. It is not a matter of
the conduction of heat from point to point in the ice. Its own
sensible heat is immediately absorbed throughout the mass. This
would be the theoretical result, but it is probable that owing to
imperfections throughout the ice and failure in uniformity in the
distribution of the stress, the melting would not take place
quite uniformly or homogeneously.
Before applying our new ideas to skating, I want you to notice a
fact which I have inferentially stated, but not specifically
mentioned. Pressure will only lead to the melting of ice if the
new melting point, _i.e._ that due to the pressure, is below the
prevailing temperature. Let us take figures. The ice to start
with is, say, at -3° C. Suppose we apply such a pressure to this
ice as will confer a melting point of -2° C. on it. Obviously,
there will be no melting. For why should ice which is at -3° C.
melt when its melting point is -2° C.? The ice is, in fact,
colder than its melting point. Hence, you note this fact: The
pressure must be sufficiently intense to bring the melting point
below the prevailing temperature, or there will be no melting;
and the further we reduce the melting point by pressure below the
prevailing temperature, the more ice will be melted.
We come at length to the object of our remarks I don't know who
invented skating or skates. It is said that in the thirteenth
century the inhabitants of
272
England used to amuse themselves by fastening the bones of an
animal beneath their feet, and pushing themselves about on the
ice by means of a stick pointed with iron. With such skates, any
performance either on inside or outside edge was impossible. We
are a conservative people. This exhilarating amusement appears to
have served the people of England for three centuries. Not till
1660 were wooden skates shod with iron introduced from the
Netherlands. It is certain that skating was a fashionable
amusement in Pepys' time. He writes in 1662 to the effect: "It
being a great frost, did see people sliding with their skates,
which is a very pretty art." It is remarkable that it was the
German poet Klopstock who made skating fashionable in Germany.
Until his time, the art was considered a pastime, only fit for
very young or silly people.
I wish now to dwell upon that beautiful contrivance the modern
skate. It is a remarkable example of how an appliance can develop
towards perfection in the absence of a really intelligent
understanding of the principles underlying its development. For
what are the principles underlying the proper construction of the
skate? After what I have said, I think you will readily
understand. The object is to produce such a pressure under the
blade that the ice will melt. We wish to establish such a
pressure under the skate that even on a day when the ice is below
zero, its melting
273
point is so reduced just under the edge of the skate that the ice
turns to water.
It is this melting of the ice under the skate which secures the
condition essential to skating. In the first place, the skate no
longer rests on a solid. It rests on a liquid. You are aware how
in cases where we want to reduce friction--say at the bearing of a
wheel or under a pivot--we introduce a liquid. Look at the
bearings of a steam engine. A continuous stream of oil is fed in
to interpose itself between the solid surfaces. I need not
illustrate so well-known a principle by experiment. Solid
friction disappears when the liquid intervenes. In its place we
substitute the lesser difficulty of shearing one layer of the
liquid over the other; and if we keep up the supply of oil the
work required to do this is not very different, no matter how
great we make the pressure upon the bearings. Compared with the
resistance of solid friction, the resistance of fluid friction is
trifling. Here under the skate the lubrication is perhaps the
most perfect which it is possible to conceive. J. Müller has
determined the coefficient by towing a skater holding on by a
spring balance. The coefficient is between 0.016 and 0.032. In
other words, the skater would run down an incline so little as 1
or 2 degrees; an inclination not perceivable by the eye. Now
observe that the larger of these coefficients is almost exactly
the same as that which Perry found in the case of well-greased
surfaces. But evidently no
274
artificial system of lubrication could hope to equal that which
exists between the skate and the ice. For the lubrication here
is, as it were, automatic. In the machine if the lubricant gets
squeezed out there instantly ensues solid friction. Under the
skate this cannot happen for the squeezing out of the lubricant
is instantly followed by the formation of another film of water.
The conditions of pressure which may lead to solid friction in
the machine here automatically call the lubricant into
existence.
Just under the edge of the skate the pressure is enormous.
Consider that the whole weight of the skater is born upon a mere
knife edge. The skater alternately throws his whole weight upon
the edge of each skate. But not only is the weight thus
concentrated upon one edge, further concentration is secured in
the best skates by making the skate hollow-ground, _i.e._
increasing the keenness of the edge by making it less than a
right angle. Still greater pressure is obtained by diminishing
the length of that part of the blade which is in contact with the
ice. This is done by putting curvature on the blade or making it
what is called "hog-backed." You see that everything is done to
diminish the area in contact with the ice, and thus to increase
the pressure. The result is a very great compression of the ice
beneath the edge of the skate. Even in the very coldest weather
melting must take place to some extent.
As we observed before, the melting is instantaneous,
275
Heat has not to travel from one point of the ice to another;
immediately the pressure comes on the ice it turns to water. It
takes the requisite heat from itself in order that the change of
state may be accomplished. So soon as the skate passes on, the
water resumes the solid state. It is probable that there is an
instantaneous escape, and re-freezing of some of the water from
beneath the skate, the skate instantly taking a fresh bearing and
melting more ice. The temperature of the water escaping from
beneath the skate, or left behind by it, immediately becomes what
it was before the skate pressed upon it.
Thus, a most wonderful and complex series of molecular events
takes place beneath the skate. Swift as it passes, the whole
sequence of events which James Thomson predicted has to take
place beneath the blade Compression; lowering of the melting
point below the temperature of the surrounding ice; melting;
absorption of heat; and cooling to the new melting point, _i.e._
to that proper to the pressure beneath the blade. The skate now
passes on. Then follow: Relief of pressure; re-solidification of
the water; restoration of the borrowed heat from the congealing
water and reversion of the ice to the original temperature.
If we reflect for a moment on all this, we see that we do not
skate on ice but on water. We could not skate on ice any more
than we could skate on glass. We saw that with light weights and
when the pressure
276
{Diagram}
Diagram showing successive states obtaining in ice, before,
during, and after the passage of the skate. The temperatures and
pressures selected for illustration are such as might occur under
ordinary conditions. The edge of the skate is shown in magnified
cross-section.
277
Was not sufficient to melt the ice, the friction was much the
same as that of metal on glass. Ice is not slippery. It is an
error to say that it is. The learned professor was very much
astray when he said that you could skate on ice because it is so
smooth. The smoothness of the ice has nothing to do with the
matter. In short, owing to the action of gravity upon your body,
you escape the normal resistance of solid on solid, and glide
about with feet winged like the messenger of the Gods; but on
water.
A second condition essential to the art of skating is also
involved in the melting of the ice. The sinking of the skate
gives the skater "bite." This it is which enables him to urge
himself forward. So long as skates consisted of the rounded bones
of animals, the skater had to use a pointed staff to propel
himself. In creating bite, the skater again unconsciously appeals
to the peculiar physical properties of ice. The pressure required
for the propulsion of the skater is spread all along the length
of the groove he has cut in the ice, and obliquely downwards. The
skate will not slip away laterally, for the horizontal component
of the pressure is not enough to melt the ice. He thus gets the
resistance he requires.
You see what a very perfect contrivance the skate is; and what a
similitude of intelligence there is in its evolution. Blind
intelligence, because it is certain the true physics of skating
was never held in view by
278
the makers of skates. The evolution of the skate has been truly
organic. The skater selected the fittest skate, and hence the fit
skate survived.
In a word, the possibility of skating depends on the dynamical
melting of ice under pressure. And observe the whole matter turns
upon the apparently unrelated fact that the freezing of water
results in a solid more bulky than the water which gives rise to
it. If ice was less bulky than the water from which it was
derived, pressure would not melt it; it would be all the more
solid for the pressure, as it were. The melting point would rise
instead of falling. Most substances behave in this manner, and
hence we cannot skate upon them. Only quite a few substances
expand on freezing, and it happens that their particular melting
temperatures or other properties render them unsuitable to
skating. The most abundant fluid substance on the earth, and the
most abundant substance of any one kind on its surface, thus
possesses the ideally correct and suitable properties for the art
of skating.
I have pointed out that the pressure must be such as to bring the
temperature of melting below that prevailing in the ice at the
time. We have seen also, that one atmosphere lowers the melting
point of ice by the 1/140 of a degree Centigrade; more exactly by
0.0075°. Let us now assume that the skate is so far sunken in the
ice as to bear for a length of two inches, and for a width of
one-hundredth of an inch. The skater weighs,
279
let us say--150 pounds. If this weight was borne on one square
inch, the pressure would be ten atmospheres. But the skater rests
his weight, in fact, upon an area of one-fiftieth of an inch. The
pressure is, therefore, fifty times as great. The ice is
subjected to a pressure of 500 atmospheres. This lowers the
melting point to -3.75° C. Hence, on a day when the ice is at
this temperature, the skate will sink in the ice till the weight
of the skater is concentrated as we have assumed. His skate can
sink no further, for any lesser concentration of the pressure
will not bring the melting point below the prevailing
temperature. We can calculate the theoretical bite for any state
of the ice. If the ice is colder the bite will not be so deep. If
the temperature was twice as far below zero, then the area over
which the skater's weight will be distributed, when the skate has
penetrated its maximum depth, will be only half the former area,
and the pressure will be one thousand atmospheres.
An important consideration arises from the fact that under the
very extreme edge of the skate the pressure is indefinitely
great. For this involves that there will always be some bite,
however cold the ice may be. That is, the narrow strip of ice
which first receives the skater's weight must partially liquefy
however cold the ice.
It must have happened to many here to be on ice which was too
cold to skate on with comfort. The
280
skater in this case speaks of the ice as too hard. In the
Engadine, the ice on the large lakes gets so cold that skaters
complain of this. On the rinks, which are chiefly used there, the
ice is frequently renewed by flooding with water at the close of
the day. It thus never gets so very cold as on the lakes. I have
been on ice in North France, which, in the early morning, was too
hard to afford sufficient bite for comfort. The cause of this is
easily understood from what we have been considering.
We may now return to the experimental results which we obtained
early in the lecture. The heavy weights slip off the ice at a low
angle because just at the points of contact with the ice the
latter melts, and they, in fact, slip not on ice but on water.
The light weights on cold, dry ice do not lower the melting point
below the temperature of the ice, _i.e._ below -10° C., and so
they slip on dry ice. They therefore give us the true coefficient
of friction of metal on ice.
This subject has, more recently been investigated by H. Morphy,
of Trinity College, Dublin. The refinement of a closed vessel at
uniform temperature, in which the ice is formed and the
experiment carried out, is introduced. Thermocouples give the
temperatures, not only of the ice but of the aluminium sleigh
which slips upon it under various loads. In this way we may be
certain that the metal runners are truly at the temperature of
the ice. I now quote from Morphy's paper
281
"The angle of friction was found to remain constant until a
certain stage of the loading, when it suddenly fell to about half
of its original value. It then remained constant for further
increases in the load.
"These results, which confirmed those obtained previously with
less satisfactory apparatus, are shown in the table below. In the
first column is shown the load, _i.e._ the weight of sleigh +
weight of shot added. In the second and third columns are shown,
respectively, the coefficient and angle of friction, whilst the
fourth gives the temperature of the ice as determined from the
galvanometer deflexions.
Load. Tan y. y. Temp.
5.68 grams. 0.36±.01 20°±30' -5.65° C.
10.39 -5.65°
11.96 -5.75°
12.74 -5.60°
13.53 -5.65°
14.31 -5.65°
15.10 grams. 0.17±.01 9°.30'±30' -5.60°
16.67 -5.55°
19.81 -5.60°
24.52 -5.60°
5.68 grams. 0.36±.01 20°±30' -5.60°
"These experiments were repeated on another occasion with the same
result and similar results had been obtained with different
apparatus.
"As a result of the investigation the following points are
clearly shown:--
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"(1) The coefficient of friction for ice at constant temperature
may have either of two constant values according to the pressure
per unit surface of contact.
"(2) For small pressures, and up to a certain well defined limit
of pressure, the coefficient is fairly large, having the value
0.36±.01 in the case investigated.
"(3) For pressures greater than the above limit the coefficient
is relatively small, having the value 0.17±.01 in the case
investigated."
It will be seen that Morphy's results are similar to those
arrived at in the first experimental consideration of our
subject; but from the manner in which the experiments have been
carried out, they are more accurate and reliable.
A great deal more might be said about skating, and the allied
sports of tobogganing, sleighing, curling, ice yachting, and
last, but by no means least, sliding--that unpretentious pastime
of the million. Happy the boy who has nails in his boots when
Jack-Frost appears in his white garment, and congeals the
neighbouring pond. But I must turn away at the threshold of the
humorous aspect of my subject (for the victim of the street
"slide" owes his injured dignity to the abstruse laws we have
been discussing) and pass to other and graver subjects intimately
connected with skating.
James Thomson pointed out that if we apply compressional stress
to an ice crystal contained in a vessel
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which also contains other ice crystals, and water at 0° C., then
the stressed crystal will melt and become water, but its
counterpart or equivalent quantity of ice will reappear elsewhere
in the vessel. This is, obviously, but a deduction from the
principles we have been examining. The phenomenon is commonly
called "regelation." I have already made the usual regelation
experiment before you when I compressed broken ice in this mould.
The result was a clear, hard and almost flawless lens of ice. Now
in this operation we must figure to ourselves the pieces of ice
when pressed against one another melting away where compressed,
and the water produced escaping into the spaces between the
fragments, and there solidifying in virtue of its temperature
being below the freezing point of unstressed water. The final
result is the uniform lens of ice. The same process goes on in a
less perfect manner when you make--or shall I better say--when you
made snowballs.
We now come to theories of glacier motion; of which there are
two. The one refers it mainly to regelation; the other to a real
viscosity of the ice.
The late J. C. M'Connel established the fact that ice possesses
viscosity; that is, it will slowly yield and change its shape
under long continued stresses. His observations, indeed, raise a
difficulty in applying this viscosity to explain glacier motion,
for he showed that an ice crystal is only viscous in a certain
structural
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direction. A complex mixture of crystals such, as we know glacier
ice to be, ought, we would imagine, to display a nett or
resultant rigidity. A mass of glacier ice when distorted by
application of a force must, however, undergo precisely the
transformations which took place in forming the lens from the
fragments of ice. In fact, regelation will confer upon it all the
appearance of viscosity.
Let us picture to ourselves a glacier pressing its enormous mass
down a Swiss valley. At any point suppose it to be hindered in
its downward path by a rocky obstacle. At that point the ice
turns to water just as it does beneath the skate. The cold water
escapes and solidifies elsewhere. But note this, only where there
is freedom from pressure. In escaping, it carries away its latent
heat of liquefaction, and this we must assume, is lost to the
region of ice lately under pressure. This region will, however,
again warm up by conduction of heat from the surrounding ice, or
by the circulation of water from the suxface. Meanwhile, the
pressure at that point has been relieved. The mechanical
resistance is transferred elsewhere. At this new point there is
again melting and relief of pressure. In this manner the glacier
may be supposed to move down. There is continual flux of
conducted heat and converted latent heat, hither and thither, to
and from the points of resistance. The final motion of the whole
mass is necessarily slow; a few feet in the day or, in winter,
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even only a few inches. And as we might expect, perfect silence
attends the downward slipping of the gigantic mass. The motion
is, I believe, sufficiently explained as a skating motion. The
skate is, however, fixed, the ice moves. The great Aletsch
Glacier collects its snows among the highest summits of the
Oberland. Thence, the consolidated ice makes its way into the
Rhone Valley, travelling a distance of some 20 miles. The ice now
melting into the youthful Rhone fell upon the Monch, the Jungfrau
or the Eiger in the days when Elizabeth ruled in England and
Shakespeare lived.
The ice-fall is a common sight on the glacier. In great lumps and
broken pinnacles it topples over some rocky obstacle and falls
shattered on to the glacier below. But a little further down the
wound is healed again, and regelation has restored the smooth
surface of the glacier. All such phenomena are explained on James
Thomson's exposition of the behaviour of a substance which
expands on passing from the liquid to the solid state.
We thus have arrived at very far-reaching considerations arising
out of skating and its science. The tendency for snow to
accumulate on the highest regions of the Earth depends on
principles which we cannot stop to consider. We know it collects
above a certain level even at the Equator. We may consider, then,
that but for the operation of the laws which James Thomson
brought to light, and which his illustrious brother,
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Lord Kelvin, made manifest, the uplands of the Earth could not
have freed themselves of the burthen of ice. The geological
history of the Earth must have been profoundly modified. The
higher levels must have been depressed; the general level of the
ocean relatively to the land thereby raised, and, it is even
possible, that such a mean level might have been attained as
would result in general submergence.
During the last great glacial period, we may say the fate of the
world hung on the operation of those laws which have concerned us
throughout this lecture. It is believed the ice was piled up to a
height of some 6,000 feet over the region of Scandinavia. Under
the influence of the pressure and fusion at points of resistance,
the accumulation was stayed, and it flowed southwards the
accumulation was stayed, and it flowed southwards over Northern
Europe. The Highlands of Scotland were covered with, perhaps,
three or four thousand feet of ice. Ireland was covered from
north to south, and mighty ice-bergs floated from our western and
southern shores.
The transported or erratic stones, often of great size, which are
found in many parts of Ireland, are records of these long past
events: events which happened before Man, as a rational being,
appeared upon the Earth.
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