412 



H. M. Deeley — Viscous Flow of Glacier- Ice. 



a constant for each particular liquid. It is denoted by ;«,, and 

 is called the coefficient of viscosity. We may consequently make 



F = 



and 



:= F 



V, 



' (4) 



(5) 



It will be seen that as long as F^ and r^ retain the same relative 

 proportions, i.e. as long as the rate of distortion is unaltered, 

 the shearing stress F has the same value at all planes parallel to 

 XX and Y Y. 



In these illustrations no slip at the boundaries has been regarded 

 as taking place. ^ In the case of such fluids as have had their 

 viscosities determined by their rate of flow through capillary tubes, 

 slipping at the boundaries, if it took place at all, must have been 

 less than a thousandth of the mean flow, although the tangential 

 force at the boundary was as much as 6 lbs. per square foot at a 

 speed of ] -23 feet per second. Considering that the skin-resistance 

 of a steamer going at 25 knots is not 6 lbs. per square foot, it is 

 clear that slipping at the boundaries does not take place in practice, 

 unless in very exceptional cases. The resistance to slipping at the 



Fig. 2. 



boundaries is in most cases probably greater than is the resistance 

 to local shear of the liquid itself. In the case of ice the conditions 

 are usually very different. Below the freezing point the ice may 

 adhere to the boinidarj' walls, and under such circumstances there is 

 no slipping. But above the freezing point ice is always separated 

 from other substances by a film of water, and as the viscosity of 

 water is very much less than that of ice, slipping at the boundary 

 readily takes place. Two surfaces of ice under the same conditions 

 cohere strongly. This makes it impossible under such conditions 

 for one portion of ice to flow over another portion resting in a 

 hollow without imparting motion to it, for regelation takes place 

 and the stresses are transmitted by the viscous resistance. It is 



1 "Dynamical Theory of Incompressible Fluids," by Osborne Reynolds, Phil. 

 Trans. 1895, p. 123. 



