( 654 ) 



of ice by a force perpendicular to its axis. The [)henomenon is 

 the same in each normal section. I suppose round the wire a 

 layer of water whose thickness is small in comparison with the 

 diameter of the wire. At the bounding surface of water and ice 

 there is a pressure, which decreases from the lower to the upper 

 side of the boundary. This pi-essure depends on the force by which 

 the wire is acted on pro unit of length. As the motion is very 

 slow the temperature in each point may be supposed to be the 

 meltingpoint corresponding to the pressure existing in the point. 

 The flow of heat, determined by the distribution of temperature 

 is the same as if the wire were at rest. At the upperside of the 

 bounding surface of ice and water heat flows away and water is 

 frozen, at the lo\ver side the ice is melted by the heat that is carried 

 towards the surface. If we can determine the quantity that is melted 

 we shall be able to determine the velocity acquired by the wire. 

 Let M be tlie centre of the circular section of the wire and R 

 the radius, the boundary between ice and water being a circle of 

 radius R -\- d. 



The pressure at the 

 circle A B' C' in any point 

 E' may be represented by 

 the formula 



P — P„ + ^ cos y) , 

 <p being the angle between 

 the radius ME' and the line 

 MA which has been taken 

 for axis of ordinates. The 

 corresponding temperatui-e 

 is 



cos if) 



— I being the change of 



the meltingpoint per unit increase of pressure near 0° C. 



Let ^1, be the coefficient of conductivity within the circle ABC, 

 h^ that of the layer of water, and ^, that of the ice without ABC. 



The differential equation for the temperature is in every one of 

 these fields 



¥x 

 The conditions at the limits of the fields are: 



bH 



+ ¥• = ' 



