Chapter 17

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

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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

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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

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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

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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

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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,

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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:

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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.

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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

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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.

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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

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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

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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

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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,

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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

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{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.

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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

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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.