1884] 



On the Surface Forces in Fluids. 



351 



II. " On the Surface Forces in Fluids." By A. M. WORTHING- 

 TON. Communicated by Professor B. Stewart, F.R.S. 

 Received February 22, 1884. 



(Abstract.) 



The object of the paper is to deduce from consideration of the 

 known thermal and elastic properties of fluids, the fact that at their 

 bounding surface there is a rapid variation of density, on account of 

 which the surface layers exert either a tension or a pressure on any 

 material wall which cuts them transversely, from which action the 

 phenomena of capillarity are easily deduced; and to exhibit clearly 

 the manner in which the intrinsic energy per unit of volume of the 

 surface layers exceeds or falls short of that in the interior of the 

 fluid, and also to point out a certain important change which it is 

 necessary to introduce into the commonly accepted explanation of the 

 equilibrium of a fluid in contact with a solid ; and, finally, to show why 

 the erroneous assumption of a constant density near the surface, made 

 by Laplace, did not prevent his obtaining the true equation to the 

 liquid surface, while it did prevent him from perceiving the reality of 

 the surface-tension. 



The first step is to examine the significance of statical theories of 

 molecular equilibrium, and to show that a statical theory, if framed in 

 accordance with the observed phenomena of expansion of the substance 

 with heat, and of its elastic resistance to compression or extension, is 

 really equivalent to a statistical description of any internal dynamical 

 phenomena that are taking place. The value of Poisson's "repulsive 

 force of heat " as a statical representation of the rate of transfer of 

 molecular momentum, or of the internal pressure within the substance, 

 is pointed out, and the nature of the equilibrium between this force 

 and the force of molecular attraction is examined. 



The relation of the two forces may be advantageously exhibited by 

 means of a diagram of two curves drawn to rectangular co-ordinates, 

 whose horizontal abscissa? represent the intra-molecular distance, and 

 whose vertical ordinates represent, in each case the corresponding 

 value of the force. It is shown that the equilibrium of the substance 

 is stable only when the tangent to the curve of repulsion slopes more 

 steeply than the tangent to the corresponding point of the attraction 

 curve, and the difference between the ordinates to the two curves 

 corresponds to the ordinate of an isothermal curve for the same 

 substance as usually drawn. 



The equilibrium of a non-volatile liquid, whose plane surface is 

 exposed to a vacuum, is then studied in the following manner : — 



The molecules are supposed at first to be distributed at the equal 



vol. xxxvi. 2 B 



