﻿1006 Research Staff o£ the Gr. E. C, London, on 



If both gravitational and surface tension forces are appre- 

 ciable, we must have 



Ai, x ^ ^ = o, . . . . (8) 



where r s are lengths and a no-dimensional magnitude 

 characteristic of the system. We shall see later that con- 

 ditions can be found in which the gravitational forces are 

 inappreciable compared with those due to surface tension. 

 If we assume that this condition is fulfilled and assume 

 further that there is only one independent length r s , viz. r Q , 

 then (8) reduces to 



s-/(?) < s > 



It should be pointed out, however, that the last assumption 

 is precarious. For when surface tension is effective, z the 

 height of the meniscus over which the pressure due to 

 surface tension varies from y(r ~\-t) to zero is likely to be as 

 important as r . (8) can be valid over the whole range only 

 if z is proportional to r . But iF it is true, we should 

 expect the importance of the surface tension relative to the 



gravitational terms to be measured bv — —„ so that the 



. * P9 r *\ 



gravitational terms may be neglected when this expression 



is large. 



The dimensional argument cannot, of course, prove that 

 the distribution of the liquid as an even layer is stable. 

 The analogy of a water jet strongly suggests that it will 'not 

 be stable. If it is not stable, the conditions may be entirely 

 altered hy freezing the layer as soon as it is formed. This 

 possibility will be considered later ; but if they are not 

 greatly altered, the effect of freezing will merely be, as 

 before, to introduce a constant factor. The form of (9) will 

 not be changed. 



Another case of some interest may be mentioned briefly, 

 although we have not investigated it experimentally. If a 

 cylindrical tube is drawn out of the liquid, the gravitational 

 and surface tension forces will act in the same direction in 

 the layer on the outside o£ the tube and will act in opposite 

 directions in the layer on the inside. If the dimensions of 

 the tube are such that the two sets of forces are comparable, 

 the layer will therefore be thicker on the inside. It is 

 interesting to speculate what will happen inside the tube 

 when the surface tension forces are great compared with the 

 gravitational. It is easy to see that in such conditions the 



