128 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
§3. The Velocity-Distribution Function. 
(a) The Form of the Function. 
In the uniform undisturbed state of a gas, in which c 0 , \, h are constant, while c\ 
h' 0 , P are zero, the velocity-distribution functions assume Maxwell’s well-known 
form 
0 ) 
(301) 
7r 
(/ 3 )0 = (—) ~ e ~ M ’ 
The suffix 0 appended to f and f 2 is to indicate the special state to which these 
equations refer. They clearly satisfy the necessary conditions 
(3-02) Jjj (/Jo dU, dV, dW x = 1, jjj(/ 2 )aC 1 2 dU 1 cZV 1 c?W 1 = 
2 h 0 m 1 ’ 
and similar equations with su ffix 2. 
In the general slightly disturbed state considered in this paper, f( U, V, W) will 
differ from (f) 0 by an amount of the first order. From the equations of transfer (§ 2) 
it may be deduced* that f may be expressed as follows :— 
(3*03) /(If, V x , Wj) = {f) 0 
l-i2A 0 m 1 A 0 (U 1 £ , 0 + V^'o + W^'o) F, (Cf) 
—u, fj-f+v^+w, Gj (C, 2 ) 
-&2h omi C 0 (c„U ] 2 + c yy V 1 2 + c„W 1 3 + 2c yz V 1 W 1 + 2c„W 1 U 1 + 2c iy U 1 Vi) H, (C*) 
(3-04) / a (U a , Vj, W 8 ) = (/ a ) 0 
1 — -g2h 0 m 2 A Q (Ua^o-t V 3 »/ 0 + W a ^ 0 ) F 2 (C 2 2 ) 
-J2h ll m 3 B„ (u,f£ + V,g> +Wl G 3 (C/) 
-A2A 0 m a C 0 (<;„U 2 1 + c„V/+c„W i! 2 +2c J ,V 1 W J + 2c„W J U a +2c IJ ,U J V s )H J (C 1 J ) 
-D,^J S (C/) 
The constants A 0 , B 0 , C 0 , D 0 , and the functions F (C 2 ), G (C 2 ), H (C 2 ), J (C 2 ) 
remain to be determined. The latter involve ( x , y, z , t) only through the occurrence 
The argument is given in my second paper, loc. cit., §§ 2, 6, and will not be repeated here. 
