130 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
These yield the equations 
(3-101) 
2^ r = 0, 
0 
(3-102) 
2 S_ r = 0. 
0 
(3-103) 
iD 0 
^2 2(2r + 3R = - 
ot 0 
T'o 
XiT 0 ’ 
(3-104) 
00 
At 0 2 (2r + 3) S_ r = 
ot 0 
T' 0 
X 2 T 0 
(3-11) 
oo 00 
0 OX 0 
■ | = u o/Xi, 
(3'12) 
— 1 i A £’ 2 
9 1 o ^ 
l 0 
riT 1 00 
a_ r +B.^2'r-'/3_, 
OX 0 
j = -W'o A: 
In each of the pairs (3T03)-(3'12) we will multiply the first equation by Ai and the 
second by X 2 respectively, and add. We may separately equate the coefficients of 
3T 
and — (in the second resulting equation) to zero, since these quantities are quite 
ox 
independent of one another, and of their coefficients. We thus obtain the conditions 
(3‘121) Xi 2 (2?’ + 3) S r = -S 'o = -A 2 2(2r + 3)<L r5 
or, by (3-101), (3-102), 
(3-122) 
(313) 
(3'14) 
2Ai 'Zr S r = —S',o — — 2X„ 2 r S_ r . 
Xi2a r - — a'o = —X 2 2 a_ r , 
X t 2 'r-'/3 r = -ft'o = -X 2 2'r 1 /3_ r , 
0 0 
where also we have introduced a convenient notation for the separate sums involved. 
Expressed in terms of this (3-10l)-(3"12) are equivalent to 
(3-15) 
(3‘151) 
u'o — -y ( CL qA.o£'o + /3'oBo 
3T 
a xj ’ 
tv _ A TO T S' o 
1 0 — 3- L 'o i o c) o wy 
(W 
[Throughout the remainder of the paper we shall neglect —2, i. e ., we shall practically 
ot 
assume that the ratio of mixture is not varying with respect to time. The values 
