334 Mr. A. M. Worthington on the 



to employ KirchhofF 3 s equation in place of HelmhohVs ; but 

 in abler hands than mine, the experimental results may per- 

 haps be of some assistance in determining one or more of the 

 points involved in these formulae. 



XXXVII. On the Surface Forces in Fluids. 

 By A. M. Worthington, M.A., Clifton College, Bristol*. 



[Plate VIII.] 



1. rTIHE object of the following paper is to deduce from 

 J- consideration of the internal equilibrium of fluids 

 the fact that at their bounding-surface there is a rapid varia- 

 tion 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 all the known 

 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 the 

 intrinsic energy of the unit of volume in the interior of the 

 liquid; 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 

 by Laplace of a constant density near the surface did not 

 prevent him from obtaining the correct equation to the liquid 

 surface. 



That a variation of density will usually take place at the 

 surface of a liquid was indeed admitted by Laplace f; but the 

 variation was not taken into consideration in his theory, nor 

 was its significance perceived by him, but seems first to have 

 been pointed out by PoissonJ, in whose investigation all 

 necessary considerations are taken into account. But the 

 methods of Poisson leave much to be desired in point of sim- 

 plicity and directness ; aud to many readers the issue must 

 appear unnecessarily obscured by mathematical difficulties. 

 Moreover, he did not realize — perhaps it was impossible before 

 the researches of Quincke that any one should realize — 

 that the one quantity which alone we can measure experimen- 

 tally is a surface-tension; and consequently he did not aim at 

 proving the reality of its existence. Yet the argument which 

 I shall make use of follows so naturally from the considera- 

 tions adduced in his chapter " Sur la Constitution intime des 



* Communicated by the Author. 



f Mecanique Celeste, Supplement au livre x. p. 494 (Paris 1880). 



\ Nouvelle Theorie de V Action capillaire (Paris 1831). 



