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 gla.s.s. We saw that with light weights and when the pressure

276

{Diagram}

Diagram showing successive states obtaining in ice, before, during, and after the pa.s.sage of the skate. The temperatures and pressures selected for ill.u.s.tration 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 gla.s.s. 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 G.o.ds; 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 a.s.sume 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 a.s.sumed. 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 2030' -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 2030' -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:--

282

"(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 pa.s.s 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

283

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 quant.i.ty 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 s.p.a.ces 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 s...o...b..a.l.l.s.

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

284

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 ma.s.s 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 ma.s.s 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 a.s.sume, 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 ma.s.s is necessarily slow; a few feet in the day or, in winter,

285

even only a few inches. And as we might expect, perfect silence attends the downward slipping of the gigantic ma.s.s. 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 pa.s.sing 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 acc.u.mulate 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 ill.u.s.trious brother,

286

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 acc.u.mulation was stayed, and it flowed southwards the acc.u.mulation 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 sh.o.r.es.