CAPILLARY ACTION. 



M onlj when the point /' b within the distance c of the surface of the liquid 

 thk COMOO to be possible. 

 If we now substitute. for x te value from equation (4), we obtain 



2Ap 2B = 2A'/o + 2L-r? + 2 J/ T~ + Ac., 

 linear differential equation in p, the solution of which is 



p - jj- 

 where n,, ,, 4 are the roots of the equation 



The coefficient J/ is less than JL, where is the range of the attractive 

 force. Hence we may consider M very small compared with L. If we neglect 

 .!/ altogether, 



n,= - 



If we assume a quantity a such that a'K=2L, we may call a the cur/"</< 

 range of the molecular forces. If we also take b, so that 6n=l, we may call 

 b the modulus of the variation of the density near the surface. 



Our calculation hitherto has been made on the hypothesis that a is small 

 when compared with b, and in that case we have found that a' : 6' :: A K : K. 



But it appears from experiments on liquids that A K is in general large 

 when compared with AT, and sometimes very large. Hence we conclude, first, 

 that the hypothesis of our calculation is incorrect, and, secondly, that the 

 phenomena of capillary action do not in any very great degree depend on the 

 variation of density near the surface, but that the principal part of the force 

 depends on the finite range of the molecular action. . 



In the following table, Ap is half the cubical elasticity of the liquid, and 

 Kp the molecular pressure, both expressed in atmospheres (the absolute value 

 of an atmosphere being one million in centimetre-gramme-second measure, see 

 below, p. 589). p is the density, T the surface-tension, and a the average range 

 of the molecular action, as calculated by Van der Waals from the values of 

 T and K. 



