R. 31. Deeley — Viscous Flow of Glacier-Ice. 411 



upper one of whicti is moving at a uniform speed in the direction 

 of the arrow. Observation shows that in such a case, owing to the 

 resistance offered by the liquid to shear, the stress is transmitted 

 from layer to layer of the liquid, and each portion of the fluid 

 moves at a velocity which increases uniformly as we recede from 

 X X and approach Y Y. Of course the motion of the fluid is 

 regarded as having, reached a steady state ; inertia-effects con- 

 sequently do not show themselves. Hence the particles originally 

 forming the lines Bi Ci in the figure after a certain interval of time 

 have positions on the lines Ai C^. As these lines are on the same 

 base and between the same parallels, the inclosed space retains its 

 original area. Distortion only has been jDroduced, each horizontal 

 layer having moved over the one below it. It must be clearly 

 understood that to produce these conditions of motion the stress 

 must not act with equal force on each particle of the fluid, but 

 solely along the plane YY, and be transmitted from particle to 

 particle owing to the viscosity of the fluid. 



With a solid between the surfaces, if the planes be relatively 

 fixed whilst the material is under stress, the stress persists. On the 

 other hand, in the case of a liquid the stresses very soon die away. 

 The time required for this to take place, Maxwell called the "time 

 of relaxation." For highly viscous liquids it may be measured by 

 hours, or even days; for ordinary liquids a fraction of a second 

 suffices ; whilst for a gas such as air. Maxwell estimated the stress 

 as lasting about the fifty-thousand millionth of a second. 



The force R required to produce such continuous relative motion 

 is a shearing stress, and it is measured by the stress per unit area 

 of either of the planes, in which a is the length and b is the 

 breadth of the area over which the force acts ; and we may write 



R = Fab . . . (1) 



In Fig. 1 we have a mass of liquid Bi C^, Bi C-^ for our purpose 

 being regarded as free from the action of gravity, occupying the 

 space between two horizontal parallel planes, X X and Y Y. The 

 plane YY is, moving under the action of a force, R. Let the 

 distance between the planes be denoted by Vq and the speed at 

 which the plane YY is moving by V^. Then the rate of distortion 

 may be written — 



h .... (2) 



Making s the velocity of any plane, at the distance r from Y Y 

 we have 



-^ -^ . . (3) 



which expresses the fact that the rate of distortion is uniform across 

 the section. 



To maintain this rate of distortion a shearing stress F, acting 

 parallel with the planes, is required. The ratio of this force to the 

 rate of distortion, the temperature and pressure being unaltered, is 



