﻿A Problem in Viscosity. 1003 



I. Theory. 



The factors which must be effective appear at once from 

 fig. 1, which shows a longitudinal section of the solid A 

 drawn vertically with velocity r out of the liquid B. 

 Observation shows at once that at least in some circum- 

 stances, the thickness of the liquid layer C is constant for a 

 distance above B very much greater than t. 



Consequently it is reasonable to assume that in C the 

 stream lines are vertical ; and if they are vertical, continuity 

 requires that the velocity v along any one stream line is 

 constant. This constant velocity must represent a balance 



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between the forces acting on any element of the layer, and 

 of these forces one must be that due to viscosity of the 

 liquid and another that due to gravity. If the solid is a 

 plain slab of infinite breadth perpendicular to the diagram. 

 it is difficult to see what other force can act; it is possible 

 that, if it is sufficiently small, some special force of cohesion 

 between liquid and solid is effective, but we shall' see that 

 the facts can be explained adequately without introducing 

 such a force. If, on the other hand, A is a cylinder, surface 

 tension may be effective ; for, owing to the curvature of the 



3 T 2 



