FOUNDATIONS OF THE KINETIC THEORY OF GASES. 269 



which signifies that equal volumes of the two gases pass, in the same time, in 

 opposite directions through each section of the tube. This gives a general 

 description of the nature of the cases to which our investigations apply. 

 But, by (3) and (4), we have for the value of 



PjPjn^o!— « 2 ) 

 the expression 



or, by (9), (2), and (5) 



*(5-e2w^> 



Substituting this for the corresponding factors of R in the first of equations 

 (6), and neglecting the left-hand side, we have finally 



°~ 2J h da? + 3 S V ] h i h P 1 + P 2 1 It 3» li x j( n -n®i + n i&i> j 

 or 



dGi_( 3 p i + p 2 1,1, - , arMGti. 



~df~{l6? Mh+h)KK ' p + 3n> n ^ +7h ^ ) )dx 2 ' 



or, somewhat more elegantly, 



dG-, /3 /Jh+K-, I, ((r , -A^&i nn\ 



^- = (8^V iyif+S^x^+^A)]-^- ' • • (10,) 



50. This equation resembles that of Fourier for the linear motion of heat ; 

 but, as already stated in § 34, the quantities (^ which occur in it render it in 

 general intractable. The first part of what is usually called the diffusion- 

 coefficAent (the multiplier of dPGJdot? above) is constant ; but the second, as is 

 obvious from (5) and (8), is, except in the special case to which we proceed, a 

 function of dQJdx ; i.e. of the percentage composition of the gaseous mixture. 



51. In the special case of equality, both of mass and of diameter, between 

 the particles of the two systems, the diffusion-coefficient becomes 



D "8?is 2 V' 



2 , C, 



7rA 3»7TS 2 Jh ' 



or 



D _f3 /t , CA X X 



U ~ W 2 + 3 J 0-677 ,/A~ ^A ' 



where X is the mean free path in the system. Hence the diffusion- coefficient 

 among equal particles is directly as the mean free path, and as the square root 

 of the absolute temperature. Fourier's solutions of (10) are of course applic- 

 able in this special case. 



