MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 149 
where D" is the determinant which is identical with D 7 except in its first two rows 
(for which cf. (5’38)), while D'fi is the minor of the second element in the first row 
of D". 
§ 8. The General Solution for the Case of Similar Molecules. 
Another instructive and specially simple particular case is that of a gas composed 
of two sets of molecules whose mechanical properties—mass and mode of inter-action 
during encounter—are identical. In this case all the symbols which we have 
distinguished by the suffixes 1 or 2, to indicate reference to one or other molecular 
group, now have the same value for either suffix, with the exception of v u v 2 or X u X 2 , 
which denote the numbers or proportions of the two molecular groups. Moreover 
(c/.(4-0l)-(4-04), (4-07)—(4T2), or, for a simpler and more general explanation, ‘ Phil. 
Trans.,’ A, vol. 216, § 7 (H), p. 309), we have 
(8-01) ^8 pn (n*i) = K P 22 (rtfa) = \p (r, s), 
l'l Vo V ti 
(8-02) Pl2 (r^) + Pl2 {r 2 s x ) = p 21 (■r 2 s 2 ) + p 2l (r^) = X ,\ 2 p (r, s) Pl2 {r 2 s x ) = p 21 (r x s 2 ), 
(8'03) “ 3 p'n i r lSl) = “j /) 22 (^ 2 ) = — 2 P (a $)» 
V\ V 2 V 0 
(8 04) P J 2 + p 12 (^*2®l) — P 21 (^Vb) T P 21 (^’ 1 ^ 2 ) XiX 2 p (I , s), 
where p(r, s ) and p (r, s) are defined by (8'0l) and (8‘03). 
By means of these relations we may reduce the expressions for a!' 0 and /3 f 0 to a 
much simpler form. Our operations may be performed on the actual determinants 
which express the general solution, but they could, of course, be equally well described 
as transformations of the general equations (5‘08)-(5'll). 
First considering V ($ rs a rs ), we add to the m th column on the right (m > 0) the 
corresponding column ( — m) on the left of the centre ; the new element on the right 
is now given by the equations 
(8’05) (m > 0, n>0) S mn (a mn + a_ mn ) = — A u S mn N mn \ Pn (m.n,) +p ia (m 1 n 1 ) + P 12 i , m 2 n 1 )}, 
"O 
= ~ •A-Ar.N™ (X^ + XAs) p ( m > n ) 
"0 
= X, — Ao<! mn N mnP (m, n), 
(m > 0, s < 0) S mn (ct mn + a_ mn ) = -X 2 — AJ mn N mnP (m, n ). 
"0 
Y 2 
(8‘06) 
