58 THE DYNAMICAL THEORY OF OASES. 



and for the second, 



(79). 



In all cases of quiet diffusion we may neglect the first term of each 

 equation. If we then put Pt+p,=p, and /, + />, = /, we find by adding, 



(80). 



If we also put p l ti l +p t u t =pu, then the volumes transferred in opposite direc- 

 tions across a plane moving with velocity u will be equal, so that 



Here p t (u, u) is the volume of the first gas transferred in unit of time 

 across unit of area of the plane reduced to pressure unity, and at the actual 

 temperature; and p,(u u,) is the equal volume of the second gas transferred 

 across the same area in the opposite direction. 



The external force X has very little effect on the quiet diffusion of gases 

 in vessels of moderate size. We may therefore leave it out in our definition 

 of the coefficient of diffusion of two gases. 



When two gases not acted on by gravity are placed in different parts of 

 a vessel at equal pressures and temperatures, there will be mechanical equi- 

 librium from the first, and u will always be zero. This will also be approxi- 

 mately true of heavy gases, provided the denser gas is placed below the lighter. 

 Mr Graham has described in his paper on the Mobility of Gases*, experiments 

 which were made under these conditions. A vertical tube had its lower tenth 

 part filled with a heavy gas, and the remaining nine-tenths with a lighter gas. 

 After the lapse of a known time the upper tenth part of the tube was shut 

 off, and the gas in it analyzed, so as to determine the quantity of the heavier 

 gas which had ascended into the upper tenth of the tube during the given time. 



In this case we have = .................................. (82), 



P>P* 1 fa /Q0\ 



pl pJcA>pdx- 



* Philosophical Transactions, 1863. 



