MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 169 
effective in the particular case before us ; this solution is due to Lorentz, and may 
be expressed in our notation by # 
(13M3) 
d 12 
_ 2 
3tq7t (oq + <x 2 ) 3 (Jl‘7 rtW 2 ) 
This is identical with our own solution (13‘09) if 
(13-14) D 0 = 32 = ri317?t 
J U V7T 
and our approximations to D (l /D show how this numerical value is approached by the 
successive convergents to our infinite-determinantal solution. | Incidentally, we may 
notice that (13*14) affords an expression for x of a kind which, so far as I am aware, 
is quite new. 
If the molecules are n th power centres of force {cf. §9 {/)), our general formula 
(13*09) becomes (when mfm^ is negligible) 
(13*15) 
D 12 
D 0 3 X 
^ Si/Ji (n) ( hirm 2 ) 1/a T^3— 
5 
and the general term of the determinant D is given by 
(13*16) 
With this we may compare the exact formula obtained by Jeans ( loc. cit.), using 
the method of Lorentz, 
(13*17) 
2 
voli (n) (Awi 1 m 2 K ia ) w - 1 (/txra 2 ) 1/s 
* Cf. Lorentz, ‘ Archives Neerlandaises,’ 10, p. 336, 1905; ‘Theory of Electrons,’ p. 268. Also, for a 
more general theory along the same lines, cf. Jeans’ ‘Dynamical Theory of Gases’ (2nd ed.), §333 (654) 
•or §450 (890). 
PlDDUCK, ‘ Proc. Lond. Math. Soc.’ (2), 15, p. 112, 1915, has also deduced Lorentz’s result as a special 
case of the general method of solution by integral equations. 
t [I have now obtained a rigorous proof of this equation and of (13'18 ).—February 22, 1917 .] 
X Cf. the footnote to page 171. 
