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LXI. On the Diffusion of Gases. — A simple case of Diffusion. 

 By S. H. Burbtjry*. 



1. T ET two reservoirs be connected by a uniform horizontal 



-jLJ tube. In the left-hand reservoir shall be a mixture of 

 two gases, gas I. and gas II., in certain proportions ; and in 

 the right-hand reservoir a mixture of the same two gases in 

 different proportions. The temperature and also the pressure 

 of the mixture shall be the same in either reservoir. Then a 

 stream of gas I. will flow through the tube, say from left to 

 right, and a stream of gas II. from right to left. 



We will suppose the proportions in which the gases are 

 mixed, as well as the total pressure and temperature, to be 

 maintained constant in each reservoir, as if, for instance, the 

 reservoirs be of infinite extent. Under these circumstances 

 the motion through the tube will become steady, and the tem- 

 perature and pressure of the combined gases will be the same 

 throughout. The problem of diffusion is to find what, under 

 these circumstances, the stream-motion of either gas will be 

 for given proportions of the mixture at the extremities of the 

 tube. 



It is assumed that the stream-velocity is very small com- 

 pared with the mean square velocity of either gas required by 

 the kinetic theory. This must be the case if the tube be long 

 enough. It is assumed, further, that in calculating the result 

 of encounters between the molecules they are to be regarded 

 as elastic spheres. 



If ?*! denote the number of molecules of gas I. in unit of 

 volume at any point, n 2 the same for gas II., then by Avo- 

 gadro's law ftj +n 2 is constant throughout the system. We 

 will take the axis of the tube for axis of x. Then at any point, 



dn x dn2 n 



dx dx 



2. Professor Tait has recently ("On the Foundations of the 

 Kinetic Theory of Gases," Transactions of the Royal Society 

 of Edinburgh, 1887) given what he considers to be the solu- 

 tion of the problem in a slightly more general form, assuming 

 the tube vertical. He assumes that the molecules of the 

 diffusing gas have, in addition to their ordinary velocities 

 required by the kinetic theory, a common velocity a of trans- 

 lation along the tube, very small compared- with the velocity 

 of mean square. In his view this common translation-velocity 



* Communicated by the Author. 



