Surface Forces in Fluids. 363 



terms each of which pairs is proportional to the quantity 



( "R ~^~w)> * s ^ se ^ proportional to this quantity; and this 



integral action is what is called the normal pressure or tension 

 at the point 0, due to the curvature of the surface ; and by 

 equating the expression thus obtained to the hydrostatic 

 pressure or tension at the same point expressed as a function 

 of the distance of the point from the level of the free hori- 

 zontal surface, we obtain the well-known equation to the 

 liquid surface. 



It is to be observed that that part of our own investiga- 

 tion in which we showed that the effect of the curvature on 

 the surface-tension was insensible, is equivalent to proving 

 that the action of the differential matter of the present instance 

 parallel to the surface is insensible in comparison with the 

 total tangential action. The existence of the effect normal to 

 the surface is, in our own investigation, a consequence of the 

 inclination between consecutive elements of the surface. 



To ignore, as Laplace does, the variation of density near 

 the surface is equivalent, as we can now see, to supposing 

 the liquid to be inextensible and incompressible, or rather to 

 supposing that the extension or compression near the surface, 

 which we have found to be a necessity of the molecular equi- 

 librium, is insensibly small. 



Now, in our own investigation, it has not been necessary 

 to inquire into the absolute value of the compression or 

 extension at any point; such value must depend upon the co- 

 efficients of compressibility and of expansion with heat, and 

 will be small when these are small ; and we may imagine our 

 investigation to be made in precisely the same manner with a 

 liquid for which both of these coefficients are insensibly small 

 in all experiments. For such a liquid the uniform distribution 

 of molecules, with which it was our method to start, must be 

 only insensibly altered, but must still be altered near the 

 surface to secure equilibrium, and a state of tension or of 

 pressure will still be produced ; and we may still regard the 

 free surface of such a liquid as a portion in which heat-energy 

 has been spent in doing work against molecular attractions, 

 though, since one factor of the work (viz. the increase of 

 molecular distance) has now become an exceedingly small 

 quantity, the other factor (viz. the molecular attraction) must 

 now be correspondingly large if the surface-energy is to 

 remain a quantity of the same order as before. 



But if all liquids were like this which we are imagining, we 

 should not have been able to make the experimental observa- 

 tions on expansion with heat and on compressibility necessary 



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