Chapter VIII: Part 8

Let us see how many millicuries we will in future be able to turn out in the week in our new Dublin Radium Institute.[1] We shall have about 130 milligrammes of radium. In 3.8 days we get 65 millicuries from this--_i.e._ half the equilibrium amount of 130 millicuries. Hence in the week, we shall have about 130 millicuries.

This is not much. Many experts consider this little enough for one tube. But here in Dublin we have been using the emanation in a more economical and effective manner than is the usage elsewhere; according to a method which has been worked out and developed in our own Radium Institute. The economy is obtained by the very simple expedient of minutely subdividing the' dose. The system in vogue, generally, is to treat the tumour by inserting into it one or two very active

[1] Then recently established by the Royal Dublin Society.

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tubes, containing, perhaps, up to 200 millicuries, or even more, per tube. Now these very heavily charged tubes give a radiation so intense at points close to the tube, due to the greater density of the rays near the tube, and, also, to the action of the softer and more easily absorbable rays, that it has been found necessary to stop these softer rays--both the y and ß--by wrapping lead or platinum round the tube. In this lead or platinum some thirty per cent. or more of the rays is absorbed and, of course, wasted. But in the absence of the screen there is extensive necrosis of the tissues near the tubes.

If, however, in place of one or two such tubes we use ten or twenty, each containing one-tenth or one-twentieth of the dose, we can avail ourselves of the softer rays around each tube with benefit. Thus a wasteful loss is avoided. Moreover a more uniform "illumination" of the tissues results, just as we can illuminate a hall more uniformly by the use of many lesser centres of light than by the use of one intense centre of radiation. Also we get what is called "cross-radiation,"which is found to be beneficial. The surgeon knows far better what he is doing by this method. Thus it may be arranged for the effects to go on with approximate uniformity throughout the tumour instead of varying rapidly around a central point or--and this may be very important-- the effects may be readily concentrated locally.

Finally, not the least of the benefit arises in the easy technique of this new method. The quantities of

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emanation employed can fit in the finest capillary glass tubing and the hairlike tubes can in turn be placed in fine exploring needles. There is comparatively little inconvenience to the patient in inserting these needles, and there is the most perfect control of the dosage in the number and strength of these tubes and the duration of exposure.[1]

The first Radium Institute in Ireland has already done good work for the relief of human suffering. It will have, I hope, a great future before it, for I venture, with diffidence, to hold the opinion, that with increased study the applications and claims of radioactive treatment will increase.

[1] For particulars of the new technique and of some of the work already accomplished, see papers, by Dr. Walter C. Stevenson, _British Medical Journal_, July 4th, 1914, and March 20th, 1915.

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SKATING [1]

IT is now many years ago since, as a student, I was present at a college lecture delivered by a certain learned professor on the subject of friction. At this lecture a discussion arose out of a question addressed to our teacher: "How is it we can skate on ice and on no other substance?"

The answer came back without hesitation: "Because the ice is so smooth."

It was at once objected: "But you can skate on ice which is not smooth."

This put the professor in a difficulty. Obviously it is not on account of the smoothness of the ice. A piece of polished plate glass is far smoother than a surface of ice after the latter is cut up by a day's skating. Nevertheless, on the scratched and torn ice-surface skating is still quite possible; on the smooth plate glass we know we could not skate.

Some little time after this discussion, the connection between skating and a somewhat abstruse fact in physical science occurred to me. As the fact itself is one which has played a part in the geological history of the earth,

[1] A lecture delivered before the Royal Dublin Society in 1905.

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and a part of no little importance, the subject of skating, whereby it is perhaps best brought home to every one, is deserving of our careful attention. Let not, then, the title of this lecture mislead the reader as to the importance of its subject matter.

Before going on to the explanation of the wonderful freedom of the skater's movements, I wish to verify what I have inferred as to the great difference in the slipperiness of glass and the slipperiness of ice. Here is a slab of polished glass. I can raise it to any angle I please so that at length this brass weight of 250 grams just slips down when started with a slight shove. The angle is, as you see, about 12½ degrees. I now transfer the weight on to this large slab of ice which I first rapidly dry with soft linen. Observe that the weight slips down the surface of ice at a much lower angle. It is a very low angle indeed: I read it as between 4 and 5 degrees. We see by this experiment that there is a great difference between the slipperiness of the two surfaces as measured by what is called "the angle of friction." In this experiment, too, the glass possesses by far the smoother surface although I have rubbed the deeper rugosities out of the ice by smoothing it with a glass surface. Notwithstanding this, its surface is spotted with small cavities due to bubbles and imperfections. It is certain that if the glass was equally rough, its angle of friction towards the brass weight would be higher.

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We have, however, another comparative experiment to carry out. I made as you saw a determination of the angle at which this weight of 250 grams just slipped on the ice. The lower surface of the weight, the part which presses on the ice, consists of a light, brass curtain ring. This can be detached. Its mass is only 6½ grams, the curtain ring being, in fact, hollow and made of very thin metal. We have, therefore, in it a very small weight which presents exactly the same surface beneath as did the weight of 250 grams. You see, now, that this light weight will not slip on ice at 5 or 6 degrees of slope, but first does so at about io degrees.

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.

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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