56 PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 



we should know the law of variation of density at the surface. For 

 the sake of obtaining the former, let the density be supposed uniform, 



Le~ a€ 

 then instead of -5-7= ^ the term will become 



e l (1 - e~ ae ) 



T /»-"« 7? T 



e 2 (l-<r") e 2 ^^ «*(l,-*-«« ) {l re h 



the particle being distant by pe from the surface: 



by substituting this expression, the force of attraction becomes 



„ 4>vAMPe- aa (l + aa) ri „ T l—re—'*),, i-n-PP . 

 lS = - ~^r ~l\ K - L eHl - e -n) ( ~3W q) 



~T~ J " 



This is a very simple expression for the mutual action of two 

 particles of matter. As e diminishes, the attractive part of the force 

 diminishes, so that there is a resistance to the approach of the particles 

 toAvards each other. 



Suppose a particle situated at or near the confines of the medium 

 to be in equilibrium : then the sum of all expressions similar to the 

 above, taken throughout the medium must equal zero. 



35. I shall only very approximately find the action on a particle 

 bounding a medium : for it is obvious that in general the force on 

 it from the surrounding caloric will differ widely from the force on 

 a particle in the interior of the medium ; the former depending only 

 on the particles on one side of that in question, the latter depending 

 on two sets of particles acting in opposite directions, and tending to 

 counteract each other's efforts. On this account there will in general 

 be a rapid diminution of density towards the surface of the medium. 

 The law of this diminution I have attempted to investigate, but from 

 the circumstance that the resulting equations involve the mixed dif- 

 ferences of discontinuous functions, I have not hitherto arrived at any 

 satisfactory conclusion. I shall therefore satisfy myself with finding the 

 force on a particle bounding a medium, on the supposition that the 

 medium is homogeneous. 



