﻿1004 Research Staff of the G. E. C, London, on 



outer surface of C, this tension will produce an increase of 

 pressure in C which will not be balanced by any corre- 

 sponding pressure over the ends of the layer. Accordingly, 

 the liquid in the layer will be squeezed out of it at the lower 

 end, and, possibly, at the upper. 



The balance of these forces must be such that the outer 

 layer of is at rest relatively to the liquid B in order that 

 the continuity of the liquid surface may be preserved. 



This last condition may appear puzzling; for if the solid 

 is continually moving upwards carrying the liquid C with it, 

 it would seem that the outer layer of this liquid must be 

 moving upwards. What really happens is that the inner 

 layer, next to the solid, moves upward with the velocity of the 

 solid ; the other layers move upwards with a velocity con- 

 tinually decreasing outwards, the difference between the 

 velocities of different layers providing viscous forces neces- 

 sary to counteract gravity or surface tension. If the layer 

 at distance,. x from the solid moves upward with velocity v> 

 it will require a time l/v after the drawing starts before a 

 layer of thickness x is found at a height / above the liquid* 

 Strictly speaking, it will require an infinite time before the 

 layer of full thickness, corresponding to v = 0, appears at a 

 finite height above the surface. 'But a consideration of the 

 numerical values in the equation about to be deduced will 

 show that the time required for a layer of thickness differing 

 inappreciably from x to form at a distance of several centi- 

 metres above the surface amounts only to a few seconds. 

 Accordingly, if we wait a few seconds between starting the 

 drawing and taking observations the thickness of the liquid 

 on the surface will be practically equal to that corresponding 

 to v = 0. 



With these considerations in mind the complete solution 

 of the case of the infinite slab is easy. 



If x be taken horizontal and z vertical, with the origin on 

 the surface of the slab ; and if p is the density, y the viscosity 

 of the liquid, v its velocity relative to B, we have 



i(''S =w ' ■ (1) 



dv 

 with the boundary condition that at x — t, — = 0. 



ax 



Hence ^ = ~(|~^)+V; (?) 



at x = if there is no slip v = v , the velocity with which the- 



