MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 133 
(411) p'n (n«x) = %v lVa jj e~ (zl+yi) xY 
(r+2, .s + 2) 
2 [ 0 i 2 * (?/){B 4 (r+2, s)+-|B*(r+l, 5 + l) + B*(r, 5 + 2)} 
k = 0 
+ Sfx 2 yYi 2 k {y){^ h {r+ l,s) + B*(r, 5 + 1)} 
- 16 /* 2 Yxi 2 k (y) B 4 (r, s )] 1212 c lx dy. 
(4+2) p'uir^) = % Vl v 2 Jj e-^xY 
(r+2, s+2) 
2 (-1 )* [ 012 * (y) {/*i 2 B 4 (r + 2 , s) + f B* (r + 1 , s + 1 ) 
* = 0 
+ y 2l W(r, s + 2) - 4 (/*i/* 2 ) -, V (mi 2 V ’B* (r + 1,5) + /£ 31 V> B* (r, 5 +1)) 
+ 4/xi/^B* (r, s)} - 8 (/*! p. 2 y k yY^ k {y) W /a B*( 7 - + 1, s) 
-2 (ft/i^YB* ( 7 =, s) + M 2 i V2 B A (r, 5+1)} 
-lG/x^Yx^* ( y) B k (r, s)] 2112 c lx dy. 
There are also six other equations, similar to the above, except that the suffixes 1 and 
2 are interchanged ; these need not be written down here. 
The limits of integration of x and y throughout the above expressions are 0 and 00 . 
The upper limits of the summations are in each case indicated by two numbers, which 
are not necessarily integers ; the upper limit is to be taken equal to the greatest 
integer which does not exceed either of these two numbers. The suffixes 1212 or 
2112 on the right-hand of the main square brackets of (4'08), (4*09), (4* 11), (4'12) are 
there placed only for convenience in printing : they should really be appended to each 
of the symbols B 4 (m , n ) contained within the brackets. These symbols are defined 
by the following equations :— 
(4‘13) B* 1212 (m, n) = m A 4 (2 / u 1 cc 2 , 2p. 2 y 2 ) • ”A k (2p. 1 x 2 , Zfof), 
B 4 2n2 (m, n) = m A k (2p. 2 x 2 , 2mi 2/ 2 ) • "A 4 (2 Ml rr 2 , 2 p. 2 y 2 ), B k (m, n) = m A /i (x 2 , if ) n A k (x 2 , y 2 ), 
where m A k (u, v) is a polynomial in powers of u,v defined thus :— 
(4+4) 
m A' c (u,v) = m A k (v,u) = 
fu\ ,2k y m t + 
\vj tZ t (t+i) t {t—k) ! 
u m ~ t v t 
k m. 
When k > 771 , m A k (u, v ) is zero. Also p. u y 2 , p 12 , p. 2l , have the following values :— 
(4* 15) = m 1 /(m 1 +'m 2 ) } y 2 — m 2 /(m 1 +m 2 ), y 12 = m ] /m 2 = +21 = W m i = /+/mu 
so that 
(416) 
+1+M2 = B 
u 2 
+12M21 — 
