Theory of Surface Forces. 469 



solid. If <7 2 were zero, the deficiency would be 2<r 1 2 T . If 

 o- 2 were equal to cr^ there would be no deficiency. Under the 

 actual circumstances the deficiency is accordingly 



2o- 1 ((7 1 — (j 2 )T ; 



so that the expression for the total pressure operative across 

 M N is 



<Ti{M N . o-iKo-20-Jo sec 0-2(oi-<r 8 )T o }. 



If we now equate the expressions for the pressure and the 

 resolved attraction, we find as before 



<r x (1 — cos 6) = 2 (o - ! — cr 2 ). 



In connexion with edge-angles it may be well here to refer 

 to a problem, which has been the occasion of much difference 

 of opinion — that- of the superposition of several liquids in 

 a capillary tube. Laplace's investigation led him to the con- 

 clusion that the whole weight of liquid raised depends only 

 upon the properties of the lowest liquid. Thereupon Young* 

 remarks : — " This effect may be experimentally illustrated by 

 introducing a minute quantity of oil on the surface of the 

 water contained in a capillary tube, the joint elevation, 

 instead of being increased as it ought to be according to Mr. 

 Laplace, is very conspicuously diminished ; and it is obvious 

 that since the capillary powers are represented by the squares 

 of the density of oil and of its difference from that of water, 

 their sum must be less than the capillary power of water, 

 which is proportional to the square of the sum of the separate 

 quantities.'" 



But the question is not to be dismissed so summarily. 

 That Laplace's conclusion is sound, upon the supposition that 

 none of the liquids wets the walls of the tube, may be shown 

 without difficulty by the method of energy. In a hypothetical 

 displacement the work done against gravity will balance the 

 work of the capillary forces. Now it is evident that the 

 liquids, other than the lowest, contribute nothing to the latter, 

 since the relation of each liquid to its neighbours and to the 

 walls of the tube is unaltered by the displacement. The only 

 effect of the rise is that a length of the tube before in contact 

 with air is replaced by an equal length in contact with the 

 lowest liquid. The work of the capillary forces is the same 

 as if the upper liquids did not exist, and therefore the total 

 weight of the column supported is independent of these 

 liquids. 



* Works, vol. i. p. 46-3. 



