12 Mr. W. Sutherland on Boyle's Law 



the walls of containing vessels is likely to produce apparent 

 departure from Boyle's law, becoming more conspicuous at 

 low densities, because the mass condensed is supposed to 

 become a larger fraction of the total mass the lower the 

 density. It is proposed to show in this paper that it is not 

 necessary that the effect of surface-condensation should be 

 more appreciable at low densities than at high, and that the 

 departures from Boyle's law in rare gases hitherto inves- 

 tigated are due to special circumstances and not to any 

 general failure of the laws of gases at very low pressures. 



In the paper on " Thermal Transpiration and Radiometer 

 Motion " * it was incidentally shown that in a gas approxi- 

 mately obeying Boyle's law the pressure p at a distance z 

 from a surface of a solid is connected with the pressure p a 

 at distance z a by the relation 



i°gW/>„ = ^i°g*A • • ■ • ( 2 °) 



where 3Am 1 m 2 /r 4: is the attraction between a molecule of 

 gas mi and of solid m 2 at distance r, p 2 being density of solid 

 and v 1 velocity of m x . This may be written 



P/P. = (.'j'f k , (29) 



denoting 6Am 1 irp 2 by /3, and m^* by k. 



When we wish to carry this expression right up to the 

 layer of molecules nearest to the solid wall, to find the 

 the pressure there, we have to take z as having a value z s 

 such that the attraction on a continuous normal cylinder 

 ending at z s from the surface will equal the attraction on the 

 discontinuous molecules in that cylinder ; thus z s will probably 

 not be much different from half the mean distance of a molecule 

 from its immediate neighbours near the solid surface. Now 

 the domain of a molecule near the surface is {mjp^ ; so that 

 z s is not much different from (mJp^/2, Then, if Boyle's 

 law holds, 



P Jp={Zzl( mi lp s fY lk (29a) 



is an equation specifying the density at the surface when that 

 at any distance z is known ; but in most cases p becomes 

 practically constant when z exceeds a certain small value, and 

 when it is determined the whole distribution of density in 

 the transition layer of variable density is specified. 



To determine the mass of gas in a vessel, take an element 

 of surface JS and erect a normal cylinder of height z starting 

 at z s /2 from the surface and reaching to z -f- z s /2 ; with these 



* Phil. Mag. [5] xlii. p. 389. 



