ci)NsTiTrTKi OF SPIIKKH AI.I.Y SYMMETRICAL MOLECULI> 



Hence 



n ^" ',' it d T vv 



' - D ' '"' = ~ D "a^ ==D ^' 



by which tin- preceding equation may be reduced to 



dv , 8 mm' /Amm'V _,/,, / ,\ TJ n 9 " 



5 = + S - ;( - -.) IT " J 2A (v + v ) r u U u r . 



3x m+m'Vm+mv 3z 



Tliis gives us* as the expression for D u 



/oc\ itt/W + m'V /SI 1 



( 35 ) D '-' = 1 n *" 1 -- 7 / . /MV 



\ Amm / (v + v) P u 



By putting m = m', v = /, we get the following expression for the coefficient of 

 diffusion D,, of a gas into itself: 



/Ji \-7ft 

 D n = pT-- 



10. The Coefficient of Viscosity of a Compound Gas. 



As in dealing with the case of diffusion, we must now use an equation of transfer 

 for each system of molecules. Writing 



where (since the various systems of molecules are not supposed to be diffusing 

 through one another, so that u = u' u , &c.) E and F are the same for both systems of 

 molecules, by equations (ll) and (12) we have 



An* = 

 Ar = i^F, Att'r' = v'q'Y. 



In the expressions already obtained for A,,w s , A u v (viz., (25) and (29)) there occur 

 terms containing the coefficients a',. As we have already seen in discussing the 

 conduction of heat, these coefficients depend upon the existence of variations of 

 temperatures in the gas. We shall here suppose that the gas is at a uniform 

 temperature throughout, so that the said terms will disappear. 



* Since this paper was written I have found that the expression (35) had already been obtained by 

 L ANGEVIN (' Ann. de Chimie et de Physique,' (8), v., 245, 1905), who applied it to the motion of electrons 

 in an electric field. The present proof is shorter than LANOEVIX'S. ENSK<X; (' Phys. Zeitschrift,' xii., 

 533, July, 1911) has also published a simplified proof on lines not unlike those of the above proof. I am 

 indebted to Prof. I.AKMOK for the reference to ENSKOG'S paper (which appeared while this paper was in 

 the hands of tho Royal Society), whore I found the further reference to LANOEVIN'S theory. Note addrd 

 October, 1911. 



VOL. CCXI. A. 3 M 



