Law of Molecular Force. 



309 



the 



meniscus 



developed in Laplace^s theory, seeing that there are assump- 

 tions involved in them which are not required or permissible 

 with the law of the inverse fourth power. 



For the purposes of this paper it will suffice to consider 

 the surface-tension in a meniscus in a circular tube of so small 

 diameter that its surface may be regarded as portion of a 

 sphere, not necessarily a hemisphere, as we must provide for 

 the case where the contact-angle is not zero. 



We desire to find the force exerted by 

 A P B C P D (fig. 1) on a column 

 of water, P Q, of small section 

 lying along the axis of the tube. 

 The meniscus consists of two 

 parts : one, the surface layer, of 

 variable density, which is en- 

 closed between the two surfaces 

 APB and A^FB'; let the 

 mean density in this layer be p, 

 while p is the density in the body 

 of the fluid. The other part of 

 the meniscus A' E D, B' F C is 

 therefore of density p ; but we 



may regard the whole meniscus as of density p, seeing that 

 the parts A' E D and B' F C will contribute a small part of the 

 whole force. In the same way we can regard the column P Q 

 as throughout of density p, seeing that the force exerted 

 on P^ Q is a small part of the whole. Now, for purposes of 

 integration, we wish to replace the discontinuous distribution 

 of molecules in the meniscus and column by an equivalent 

 uniform distribution of matter. Accordingly, as I pointed 

 out in a previous paper, we must be careful to provide a cer- 

 tain distance between our continuous meniscus and the base 

 of the continuous column. This distance is not necessarily 

 the same as the mean diameter of the molecular domain, but 

 is a quantity of the same order of 

 magnitude. The problem then 

 reduces itself to the determina- 

 tion of the resultant attraction of 

 a meniscus A P B C P D (fig. 2), 

 the centre of whose surface is at 

 0, on a column Q T, of sectional 

 area a, and with its base at Q 

 at a distance h from P. If 

 the molecular force between 

 two molecules of the Hquid is 

 ^Am^/r^, then, expressing the 



