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let us say—­150 pounds.  If this weight was borne on one square inch, the pressure would be ten atmospheres.  But the skater rests his weight, in fact, upon an area of one-fiftieth of an inch.  The pressure is, therefore, fifty times as great.  The ice is subjected to a pressure of 500 atmospheres.  This lowers the melting point to -3.75 deg.  C. Hence, on a day when the ice is at this temperature, the skate will sink in the ice till the weight of the skater is concentrated as we have assumed.  His skate can sink no further, for any lesser concentration of the pressure will not bring the melting point below the prevailing temperature.  We can calculate the theoretical bite for any state of the ice.  If the ice is colder the bite will not be so deep.  If the temperature was twice as far below zero, then the area over which the skater’s weight will be distributed, when the skate has penetrated its maximum depth, will be only half the former area, and the pressure will be one thousand atmospheres.

An important consideration arises from the fact that under the very extreme edge of the skate the pressure is indefinitely great.  For this involves that there will always be some bite, however cold the ice may be.  That is, the narrow strip of ice which first receives the skater’s weight must partially liquefy however cold the ice.

It must have happened to many here to be on ice which was too cold to skate on with comfort.  The

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skater in this case speaks of the ice as too hard.  In the Engadine, the ice on the large lakes gets so cold that skaters complain of this.  On the rinks, which are chiefly used there, the ice is frequently renewed by flooding with water at the close of the day.  It thus never gets so very cold as on the lakes.  I have been on ice in North France, which, in the early morning, was too hard to afford sufficient bite for comfort.  The cause of this is easily understood from what we have been considering.

We may now return to the experimental results which we obtained early in the lecture.  The heavy weights slip off the ice at a low angle because just at the points of contact with the ice the latter melts, and they, in fact, slip not on ice but on water.  The light weights on cold, dry ice do not lower the melting point below the temperature of the ice, i.e. below -10 deg.  C., and so they slip on dry ice.  They therefore give us the true coefficient of friction of metal on ice.

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