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



413 



quite possible that the coefficient of viscosity ^i is not a constant for 

 glacier-ice, as such ice varies much in structure at different points, 

 and its viscosity appears to be rather a molar than a molecular 

 phenomenon. At present we do not appear to have any complete 

 theory of viscosity ; consequently it would be premature to declare 

 that glacier-ice is not truly viscous. Before we can safely go so far 

 we must be able to show that the same theory will not apply, for 

 example, to both ice and water. 



In Fig. 1 we have regarded the flow as resulting from the action 

 of a stress applied at a plane surface parallel to the direction of 

 flow, the viscosity of the fluid setting in motion the whole mass in 

 such a way that the rate of distortion is everj' where the same. 



In Fig. 2 the viscous liquid is supposed to be flowing over 

 a plane surface under the action of a uniform pressure acting upon 

 a surface at right angles to the direction of flow. Here in place 

 of a force F acting on unit area of F F parallel to the direction of 

 motion, we have a pressure F, acting on unit ai'ea of the surface 

 h r^ normal to the direction of flow. This may be due either to 

 the pressure of a liquid column, or it may be regarded as the effect 

 of gravity acting with an equal force on each particle of the liquid, 

 the lower plane being inclined so as to give uniform conditions of 

 flow between the parallel planes XX and Y Y. In either case the 

 nature of the flow is the same. 



At the bounding plane X X the whole pressure on b r^ is acting 

 to distort the liquid, and the rate of distortion 



V^ 



r 



' o 



is the same as before for the same total force acting on the liquid. 

 However, at any given distance r from the surface YY the 

 shearing stress is obviously proportional to the area acted on by 

 the pressure, divided by the length of the line over which the 



1 . , h r 



shearing stress acts, i.e. to -^ or simply to r. 



A B 

 In Fig. 3, B G—r, and -g-^ = rate of distortion at the point C; 



^Tp is, therefore, proportional to B C. 



