Part 43

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. Mueller 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.

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 deg.. 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,

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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 deg. 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

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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 deg. C., and so they slip on dry ice. They therefore give us the true coefficient of friction of metal on ice.