MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 171 
This table well illustrates the general remarks on the convergence* of our formulae 
which were made in § 9 (a). 
if) The Coefficient of Self-Diffusion of a Gas. 
The next simplest case of a general character which we shall consider is that 
in which the two sets of molecules are alike in mass and dynamical properties ; 
a special case of this is that of a simple gas, the two sets of molecules being identical— 
the corresponding coefficient of diffusion D 12 will be written D n and termed the 
coefficient of self-diffusion. From (10'05), and (8‘9), the latter equation being the 
one appropriate to the case before us, we find that 
(13-20) 
D 3RT V' 0 
11 ™ 0 roK' u (o) V 0 ’ 
where we may now omit the distinguishing suffixes 1, 2 ; V' 0 is the principal minor 
of V 0 , whose general element is given by (8"10). We may note that the factor V' 0 /V 0 
is independent of v x and v 2 (§ 8). 
As far as the first two rows and columns, V 0 has the following form :— 
(13-21) 
• 1 H&i-l) 
2 (&i ~ 1 ) a\> ( 11 — 1 O&j + 7 k 2 ) + 
The first and second approximations to V' 0 /V 0 for a few typical molecular models 
are given in the subjoined table : the model chosen is the n th power centre of force, 
which is equivalent to a rigid elastic sphere when n — o°. 
Table III. 
Maxwellian 
Rigid elastic 
V 0 /V. 
gas, 
n = 9. 
n = 17. 
spheres, 
n = 5. 
71 = OO. 
1st approximation . . 
1-000 
1-000 
1-000 
1-000 
2nd approximation . 
1-000 
1-004 
1-008 
ffi = 1-015 
In calculating the approximations to V / 0 /V 0 for n — 9 and n — 17 we have adopted 
the values 0‘420 and 0‘390 respectively for I 2 (n)/Ii (n) ; it would be very troublesome 
* [Added June 2, 1916 .—It is interesting to notice that in all the cases in Table II. the error of the 
third approximation to D 0 /D is equal (to the order of accuracy of one unit in the last figure given) to the 
difference between the second and third approximations. 
After each step in the approximation the ratio of successive increments seems to become progressively 
larger, and from Table I. it would be difficult to judge whether D 0 /D converges to 1 • 12 or 1 • 13, if we did 
not know the correct value to be 1 • 1317.] 
2 B 
VOL. CCXVII.—-A. 
