Part 41

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,

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 121/2 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 61/2 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 121/2 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 deg. 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 deg. C. It is about 10 deg. 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 131/2, 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 deg..

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 deg. 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 deg. C. at 10 deg. C.

Angle. Coeff. Angle. Coeff. Angle. Coeff Aluminium 2.55 121/2 deg. 0.22 12 deg. 0.21 131/2 deg. 0.24 Same 155 121/2 deg. 0.22 6 deg. 0.11 7 deg. 0.12 Brass 6.5 121/2 deg. 0.22 10 deg. 0.17 101/2 deg. 0.18 Same 107 121/2 deg. 0.22 5 deg. 0.09 6 deg. 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. Mueller) - - - 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 deg. 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 deg. 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 deg. 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.