Theory of Surface Forces, 289 



extraordinarily well with modern numbers. I propose to 

 return to this estimate, and to the remarkable argument which 

 Young founded upon it. 



The first great advance upon the theory of Young and 

 Laplace was the establishment by Gauss of the principle of 

 surface-energy. He observed that the existence of attractive 

 forces of the kind supposed by his predecessors leads of neces- 

 sity to a term in the expression of the potential energy pro- 

 portional to the surface of the liquid, so that a liquid surface 

 tends always to contract, or, what means precisely the same 

 thing, exercises a tension. The argument has been put into 

 a more general form by Boltzmann*. It is clear that all 

 molecules in the interior of the liquid are in the same con- 

 dition. Within the superficial layer, considered to be of finite 

 but very small thickness, the condition of all molecules is the 

 same which lie at the same very small distance from the surface. 

 If the liquid be deformed without change in the total area of 

 the surface, the potential energy necessarily remains unaltered ; 

 but if there be a change of area the variation of potential 

 energy must be proportional to such change. 



A mass of liquid, left to the sole action of cohesive forces, 

 assumes a spherical figure. We may usefully interpret this 

 as a tendency of the surface to contract ; but it is important 

 not to lose sight of the idea that the spherical form is the 

 result of the endeavour of the parts to get as near to one 

 another as is possible! . A drop is spherical under capillary 

 forces for the same reason that a large gravitating mass of 

 (non-rotating) liquid is spherical. 



In the following sketch of Laplace's theory we will com- 

 mence in the manner adopted by Maxwell J. If / be the 

 distance between two particles m, m', the cohesive attraction 

 between them is denoted in Laplace's notation by m w! </>(/)> 

 where </>(/) * s a function of / which is insensible for all 

 sensible values of /, but which becomes sensible and even 

 enormously great, when /is exceedingly small. 



" If w r e next introduce a new function of/ and write 



1 



*(/)#= n(/), (i) 



then mm'TL(f) will represent (1) the work done by the 



* Fogg. Ann. cxli. p. 582 (1870). See also Maxwell's 'Theory of 

 Heat/ 1870; and article " Capillarity," Enc. Brit. 



t See Sir W. Thomson's lecture on Capillary Attraction (Proc. Eoy 

 Inst. 1886), reprinted in ' Popular Lectures and Addresses.' 



\ Enc. Brit, " Capillarity?' 



