APPENDIX F. 



THE MOLECULAR PRESSURE IN A LIQUID. 



Laplace's result, so far as concerns the question raised in the text, may be stated 

 thus. If MM'<f>(r) be the molecular force between masses M, M' of the liquid, 

 at distance r, the whole attraction on unit mass, at a distance x within the 

 surface, is 



,,00 /.00 



X = 2ir P f rdr/ 4>(r)</r, 



where p is the density of the liquid. The density is supposed constant, even in the 

 surface-skin. As we are not concerned with what are commonly called capillary forces, 

 the surface is supposed to be plane. 



The pressure, p, is found from the ordinary hydrostatic equation 



£-* 



Hence the pressure in the interior of the liquid is 



~K — pl Hdx, 

 J o 



where a is the limit at which the molecular force ceases to be sensible. 



But the expression for K is numerically the work required to carry unit volume 



of the liquid from the interior, through the skin, to the surface. It is easy to see that 



the further work, required to carry it wholly out of the range of the molecular forces, 



has precisely the same value. Thus the whole work required to carry, particle by 



particle, a cubic inch of the liquid from the interior to a finite distance from its 



surface is 



2K x 1 cub. in. 



This investigation assumes p to be constant throughout the liquid, and thus 

 ignores the (almost certain) changes of density in the various layers of the surface- 

 skin ; so that its conclusions, even when the question is regarded as a purely statical 

 one, are necessarily subject to serious modification. With our present knowledge of the 

 nature of heat, we cannot regard this mode of treatment as in any sense satisfactory. 



