at Very Low Pressures. 13 



as limits of integration, the mass of the cylinder is 



= T^Wk {pz - z ° (p -P )/2} (30) 



Now if z is large enough to end in the main "body of the 

 gas, where surface-action is negligible, d$pz is <iB, where 

 B is an element of volume ; so the mass of the cylinder 

 becomes 



{ P dB-dSz s (p s -p)/-2}/(l-/3/k), 

 and total mass 



M = { P B-Sz> s -p)/2}/(l-/3/£). . . (31) 



Here, then, we have the surface condensation effect ex- 

 pressed by a surface-term in the expression for the mass in 

 addition to the pB, which would suffice if the density were 

 uniform; p s is given by (29a). 



Now, without going into details, we may be satisfied that 

 /3//c is small compared to unity ; for if k is expressed in c.G.s. 

 units, /3 is to be the force exerted by a long cylinder of 

 square centimetre base on a molecule of the gas at a centi- 

 metre from the base along the axis, which all experience 

 shows to be small compared to the kinetic energy of a molecule 

 at ordinary temperatures. Of course, if we artificially increase 

 the amount of surface enormously — as, for instance, by partially 

 filling a vessel with a powder or a porous material like char- 

 coal — we must remember that we cannot assume the pressure 

 in the centre of each little interspace or pore to be the same as 

 that in the free gas in communication with the manometer ; but 

 for each little interspace we can write an equation like (31), 

 and for the gas in the whole of the interspaces we can use 

 equation (31) if we change p to p e , the average density at the 

 centre of the interspaces. As /3/k is small, it follows from (31) 

 that the surface-term is always small compared to the volume- 

 term, and therefore the equation for a mass of gas in a vessel 

 which is partially occupied by a powder or porous material 

 will be 



M = P/ B /+A> B .> (32) 



where the suffix / connects with the free volume, and c with 

 that in the interspaces. The relation between p c and p f depends 

 on the average size of the interspaces and the attraction of the 

 solid for gas, as we can see if we follow in imagination the 

 course of a surface of constant pressure at the boundary 

 between the free region and the powder : if the pores are 



