442 SURFACE WAVES. [CHAP. IX 



Capillarity. 



244. The part played by Cohesion in certain cases of fluid 

 motion has long been recognized in a general way, but it is only 

 within recent years that the question has been subjected to exact 

 mathematical treatment. We proceed to give some account of 

 the remarkable investigations of Lord Kelvin and Lord Rayleigh 

 in this field. 



It is, of course, beyond our province to discuss the physical 

 theory of the matter*. It is sufficient, for our purpose, to know 

 that the free surface of a liquid, or, more generally, the common 

 surface of two fluids which do not mix, behaves as if it were in a 

 state of uniform tension, the stress between two adjacent portions 

 of the surface, estimated at per unit length of the common 

 boundary-line, depending only on the nature of the two fluids 

 and on the temperature. We shall denote this surface-tension/ 

 as it is called, by the symbol T 1 . Its value in c.G.s. units (dynes 

 per linear centimetre) appears to be about 74 for a water-air 

 surface at 20C.f ; it diminishes somewhat with rise of temperature. 

 The corresponding value for a mercury-air surface is about 540. 



An equivalent statement is that the potential energy of any 

 system, of which the surface in question forms part, contains a 

 term proportional to the area of the surface, the amount of this 

 superficial energy per unit area being equal to T^. Since the 

 condition of stable equilibrium is that the energy should be a 

 minimum, the surface tends to contract as much as is consistent 

 with the other conditions of the problem. 



The chief modification which the consideration of surface- 

 tension will introduce into our previous methods is contained in 

 the theorem that the fluid pressure is now discontinuous at a 

 surface of separation, viz. we have 



* For this, see Maxwell, Encyc. Britann., Art. &quot;Capillary Action&quot;; Scientific 

 Papers, Cambridge, 1890, t. ii., p. 541, where references to the older writers are 

 given. Also, Lord Kayleigh, &quot;On the Theory of Surface Forces,&quot; Phil. Mag., 

 Oct. and Dec., 1890, and Feb. and May, 1892. 



f Lord Kayleigh &quot; On the Tension of Water-Surfaces, Clean and Contaminated, 

 investigated by the method of Hippies,&quot; Phil. Mag. Nov. 1890. 



See Maxwell, Theory of Heat, London, 1871, c. xx. 



