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 gla.s.s, 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. Gla.s.s. at 0 C. at 10 C.

Angle. Coeff. Angle. Coeff. Angle. Coeff Aluminium 2.55 12 0.22 12 0.21 13 0.24 Same 155 12 0.22 6 0.11 7 0.12 Bra.s.s 6.5 12 0.22 10 0.17 10 0.18 Same 107 12 0.22 5 0.09 6 0.10

Steel on steel (Morin) - - - - 0.14 Bra.s.s on cast iron (Morin) - - 0.19 Steel on cast iron (Morin) - - 0.20 Skate on ice (J. Muller) - - - 0.016--0.032 Best-greased surfaces (Perry) - 0.03--0.036

You perceive from the table that while the friction of bra.s.s or aluminium on gla.s.s is quite independent of the weight used, that of bra.s.s 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 antic.i.p.ated 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 quant.i.ty 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 antic.i.p.ated. 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 quant.i.ty 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 a.s.sume 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 ma.s.s 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 ma.s.s 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 a.s.suredly would. The ice under the increased pressure would melt a little everywhere throughout its ma.s.s, 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 a.s.sume 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 ma.s.s 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 pa.s.sage 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 pa.s.sage of conducted heat, is a quant.i.ty 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 ma.s.s. 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 h.o.m.ogeneously.

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 amus.e.m.e.nt 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 amus.e.m.e.nt 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 ill.u.s.trate so well-known a principle by experiment. Solid friction disappears when the liquid intervenes. In its place we subst.i.tute 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. Muller 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 pa.s.ses 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 pa.s.ses, 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 pa.s.ses 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.