Kinetic Theory of Gases. 793 



Since <£(r)=— II'(V), it can be integrated in finite terms, 

 giving 



JF=^^(e 2jU{z) -l), (z>a) . . . (8) 



Whan z< cr the conditions change, for now the body ol 

 the selected molecule prevents any attracting molecule from 

 being present in the slab for values of r less than a. The 

 total attraction of the slab is therefore obtained by replacing £, 

 the lower limit of integration, by a, and we have 



^F^^l^'^nw-l), (*<»).. . . (9) 



Formulae (8) and (9) can be combined into the single 

 formula 



dFs= 2W# (/ ,-n W _ 1); , , , . (10 ) 



valid for all values of z, if we make the convention that 



li(2) = IjO), (0<-<<7). ... (11) 



As n(^) is meaningless so far as equation (6) is concerned 



for such values of z, there is no objection to this convention. 



It follows at once that the work done by the attractions 



of the slab when the molecule is brought from infinity to z is 



Zirvdft 



- 1 a[e J w — l)au 



2; 



it is convenient to have a notation for this expression, and 

 we shall call it 



27rvdf<cy(z). 



It is obvious from the symmetry that we must have 



«■(*)== «r(— z); 



just as much work is done by the attractions when the 

 molecule is brought from infinity to -{-- as when it is 

 brought right through the slab to —z. 



Consider a boundary surface of a body of gas, which may 

 be supposed to extend to infinity in the direction of the 

 positive axis of z. When a boundary field exists, the general 

 molecular density in any slab must be a function v{f) of/ 

 the distance from the boundary. The boundary of any 

 actual vessel may in general be regarded as plane since 

 the curvature will be negligible compared with the scale of 

 molecular sizes and distances with which we are concerned. 



