Chapter 18

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,

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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° 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° 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

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"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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A SPECULATION AS TO A PREMATERIAL UNIVERSE [1]

"And therefore...these things likewise had a birth; for things which are of mortal body could not for an infinite time back... have been able to set at naught the puissant strength of immeasurable age."--LUCRETIUS, _De Rerum Natura._

"O fearful meditation! Where, alack! Shall Time's best jewel from Time's chest lie hid?" --SHAKESPEARE.

IN the material universe we find presented to our senses a physical development continually progressing, extending to all, even the most minute, material configurations. Some fundamental distinctions existing between this development as apparent in the organic and the inorganic systems of the present day are referred to elsewhere in this volume.[2] In the present essay, these systems as having a common origin and common ending, are merged in the same consideration as to the nature of the origin of material systems in general. This present essay is occupied by the consideration of the necessity of limiting material interactions in past time. The speculation originated in the difficulties which present themselves when we ascribe to these interactions infinite duration in the past. These difficulties first claim our consideration.

[1] Proc. Royal Dublin Soc., vol. vii., Part V, 1892.

[2] _The Abundance of Life._

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Accepting the hypothesis of Kant and Laplace in its widest extension, we are referred to a primitive condition of wide material diffusion, and necessarily too of material instability. The hypothesis is, in fact, based upon this material instability. We may pursue the sequence of events assumed in this hypothesis into the future, and into the past.

In the future we find finality to progress clearly indicated. The hypothesis points to a time when there will be no more progressive change but a mere sequence of unfruitful events, such as the eternal uniform motion of a mass of matter no longer gaining or losing heat in an ether possessed of a uniform distribution of energy in all its parts. Or, again, if the ether absorb the energy of material motion, this vast and dark aggregation eternally poised and at rest within it. The action is transferred to the subtle parts of the ether which suffer none of the energy to degrade. This is, physically, a thinkable future. Our minds suggest no change, and demand none. More than this, change is unthinkable according to our present ideas of energy. Of progress there is an end.

This finality _â parte post_ is instructive. Abstract considerations, based on geometrical or analytical illustrations, question the finiteness of some physical developments. Thus our sun may require eternal time to attain the temperature of the ether around it, the approach to this condition being assumed to be asymptotic in

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character. But consider the legitimate _reductio ad absurdum_ of an ember raked from a fire 1000 years ago. Is it not yet cooled down to the constant temperature of its surroundings? And we may evidently increase the time a million-fold if we please. It appears as if we must regard eternity as outliving every progressive change, For there is no convergence or enfeeblement of time. The ever-flowing present moves no differently for the occurrence of the mightiest or the most insignificant events. And even if we say that time is only the attendant upon events, yet this attendant waits patiently for the end, however long deferred.

Does the essentially material hypothesis of Kant and Laplace account for an infinite past as thinkably as it accounts for the infinite future? As this hypothesis is based upon material instability the question resolves itself into this:-- Is the assumption of an infinitely prolonged past instability a probable or possible account of the past? There are, it appears to me, great difficulties involved in accepting the hypothesis of infinitely prolonged material instability. I will refer here to three principal objections. The first may be called a metaphysical objection; the second is partly metaphysical and partly physical, the third may be considered a physical objection, as it is involved directly in the phenomena presented by our universe.

The metaphysical objection must have presented itself to every one who has considered the question. It may

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be put thus:--If present events are merely one stage in an infinite progress, why is not the present stage long ago passed over? We are evidently at liberty to push back any stage of progress to as remote a period as we like by putting back first the one before this and next the stage preceding this, and so on, for, by hypothesis, there is no beginning to the progress.

Thus, the sum of passing events constituting the present universe should long ago have been accomplished and passed away. If we consider alternative hypotheses not involving this difficulty, we are at once struck by the fact that the future of material development is free of the objection. For the eternity of unprogressive events involved in the future on Kant's hypothesis, is not only thinkable, but any change is, as observed, irreconcilable with our ideas of energy. As in the future so in the past we look to a cessation to progress. But as we believe the activity of the present universe must in some form have existed all along, the only refuge in the past is to imagine an active but unprogressive eternity, the unprogressive activity at some period becoming a progressive activity--that progressive activity of which we are spectators. To the unprogressive activity there was no beginning; in fact, beginning is as unthinkable and uncalled for to the unprogressive activity of the past as ending is to the unprogressive activity of the future, when all developmental actions shall have ceased. There is no beginning or ending to the activity of the universe.

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There is beginning and ending to present progressive activity. Looking through the realm of nature we seek beginning and ending, but "passing through nature to eternity" we find neither. Both are justified; the questioning of the ancient poet regarding the past, and of the modern regarding the future, quoted at the head of this essay.

The next objection, which is in part metaphysical, is founded on the difficulty of ascribing any ultimate reality or potency to forces diminishing through eternal time. Thus, against the assumption that our universe is the result of material aggregation progressing over eternal time, which involves the primitive infinite separation of the particles, we may ask, what force can have acted between particles sundered by infinite distance? The gravitational force falling off as the square of the distance, must vanish at infinity if we mean what we say when we ascribe infinite separation to them. Their condition is then one of neutral stability, a finite movement of the particles neither increasing nor diminishing interaction. They had then remained eternally in their separated condition, there being no cause to render such condition finite. The difficulty involved here appears to me of the same nature as the difficulty of ascribing any residual heat to the sun after eternal time has elapsed. In both cases we are bound to prolong the time, from our very idea of time, till progress is no more, when in the one case we can imagine no mutual approximation of the

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particles, in the other no further cooling of the body. However, I will riot dwell further upon this objection, as it does not, I believe, present itself with equal force to every mind. A reason less open to dispute, as being less subjective, against the aggregation of infinitely remote particles as the origin of our universe, is contained in the physical objection.

In this objection we consider that the appearance presented by our universe negatives the hypothesis of infinitely prolonged aggregation. We base this negation upon the appearance of simultaneity ~ presented by the heavens, contending that this simultaneity is contrary to what we would expect to find in the case of particles gathered from infinitely remote distances. Whether these particles were endowed with relative motions or not is unimportant to the consideration. In what respects do the phenomena of our universe present the appearance of simultaneous phenomena? We must remember that the suns in space are as fires which brighten only for a moment and are then extinguished. It is in this sense we must regard the longest burning of the stars. Whether just lit or just expiring counts little in eternity. The light and heat of the star is being absorbed by the ether of space as effectually and rapidly as the ocean swallows the ripple from the wings of an expiring insect. Sir William Herschel says of the galaxy of the milky way:-- "We do not know the rate of progress of this mysterious chronometer, but it is nevertheless certain that it cannot

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last for ever, and its past duration cannot be infinite." We do not know, indeed, the rate of progress of the chronometer, but if the dial be one divided into eternal durations the consummation of any finite physical change represents such a movement of the hand as is accomplished in a single vibration of the balance wheel.

Hence we must regard the hosts of glittering stars as a conflagration that has been simultaneously lighted up in the heavens. The enormous (to our ideas) thermal energy of the stars resembles the scintillation of iron dust in a jar of oxygen when a pinch of the dust is thrown in. Although some particles be burnt up before others become alight, and some linger yet a little longer than the others, in our day's work the scintillation of the iron dust is the work of a single instant, and so in the long night of eternity the scintillation of the mightiest suns of space is over in a moment. A little longer, indeed, in duration than the life which stirs a moment in response to the diffusion of the energy, but only very little. So must an Eternal Being regard the scintillation of the stars and the periodic vibration of life in our geological time and the most enduring efforts of thought. The latter indeed are no more lasting than

"... the labour of ants In the light of a million million of suns."

But the myriad suns themselves, with their generations, are the momentary gleam of lights for ever after extinguished.

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Again, science suggests that the present process of material aggregation is not finished, and possibly will only be when it prevails universally. Hence the very distribution of the stars, as we observe them, as isolated aggregations, indicates a development which in the infinite duration must be regarded as equally advanced in all parts of stellar space and essentially a simultaneous phenomenon. For were we spectators of a system in which any very great difference of age prevailed, this very great difference would be attended by some such appearance as the following:--

The aupearance of but one star, other generations being long extinct or no others yet come into being; or, perhaps, a faint nebulous wreath of aggregating matter somewhere solitary in the heavens; or no sign of matter beyond our system, either because ungathered or long passed away into darkness.[1]