MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 107 
accurate expression. In the general case (13'06) is an approximation only, and the 
method used by Maxwell and the other writers just named does not afford a ready 
means of estimating the error involved. The present investigation makes it clear 
that in extreme cases this is far from small. 
(d) A Second Approximation to the Coefficient of Diffusion. 
Passing now to a second approximation, by means of (10'05) and (9'15) we obtain 
the result 
(13-07) 
p> — 1 3(m 1 +m 2 )PT 
1 e 0 i2 (o) 
(2nd approximation). 
The correction to (13’06) consists of a factor (l— e 0 ) -1 , e 0 being given by (9'14) and 
(9'09)-(9‘13) ; since for Maxwellian molecules = 1, it follows from (9’14) that 
e 0 = 0 in their case. In order to estimate the importance of e 0 in other cases we must 
consider some special typical molecular models, and determine the numerical values of 
e 0 for such gases. The most important models are those for which K' 12 (0), k t , etc., are 
given in § 9 (/). 
In paragraph (g) of this section we shall consider in detail the range in the values 
of e 0 calculated from these numbers, for various ratios of the molecular masses and 
diameters. Since e 0 only affords a second approximation to D 12 , however, and not the 
exact value, it is convenient first of all to examine certain particular cases of our 
formulae (cf §§ 7, 8) which throw some light on the accuracy of a second 
approximation in general. 
(e) The Coefficient of Diffusion when : m 2 and (tJ<t 2 are Very Large. 
In the special case when the mass and size of a molecule of the first kind are so 
great, compared with that of a molecule of the second kind, that mfm 1 is negligible 
(cf. § 7), we obtain from (10’05), (7’20) and (13’03) the result 
(13-08, 9) 
3KT D 0 = Do__3_ 
27n/ 0 m 2 K / 12 (0) D D 16^ 0 (<rj + o- 2 ) 2 (hirmf^ 
where D is a determinant (occupying only a quadrant of the infinite plane) whose 
general element is given by (7"21), while D 0 is its principal minor. As usual, for 
Maxwellian molecules D 0 = D. We proceed to make successive numerical approxi¬ 
mations to D 0 /D in the case of molecules of other types. 
For molecules which are rigid elastic spheres we have seen (9"32) that 
r. _ (^ + 2 )* 
t_ (*+IV 
(13-10) 
