THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 327 
deflecting effect of the forces alone, as above mentioned, and it will be omitted 
henceforward. Hence, corresponding to the equation (204) of § 9 (D), we have 
( 212 ) 
\tv ,2 (t +•§-)( k — 2 (4&+ l) <r 2 (2/m) F (t + 2) (1 + 
2 (4/)+l)(i+l)!o- 2 (2/m)- l/2 ( 1 + 
where we have written 
(213) 
Similarly we have 
(214) 
2 limb 2 
4(«+l) 
3S 
S = 
b 2 m 
12R 
(215) 
(216) 
K, 
K 0 , 1 = 64x-V(2Am)' V ‘(l+ f-). 
. (<+4 A 
3 S' 
T? _ 2 2 5 (2 hm)' k 1 
^0 — 256 1 
(* + DA H3T/’ 
25 ( 2 hm) 1 ' 2 
C„ = 
TrVi/ 1+S/T’ 64 7rVi/ 1+S/T 
(5 4 i/ 2 2 
7r <t 
It will be seen later that S is the well-known “Sutherland’s constant” (§11 (F)). 
§ 10. Numerical Calculations for Particular Molecular Models. 
Rigid Elastic Spheres. 
§ 10 (A) In the last section we determined the complete expression for the velocity- 
distribution function for a gas composed of Maxwellian molecules. In the other cases 
there considered we must be content to make numerical approximations, which can, 
of course, be carried to any desired degree of accuracy. We shall consider in most 
detail the case of rigid elastic spherical molecules, for which we shall calculate 
b rs and c rs for 0 = r = 3, 0 = s = 3. These are chosen for the fullest treatment partly 
because of their simplicity, and partly as representing the limit between which, and 
the case of Maxwellian molecules, the molecules of actual gases appear to lie. 
In making such numerical approximations the following table of expanded formulae 
for B A (r, s ) is useful:— 
Table I.—Expressions for B 4 (r, s). 
B°( 0 , 0 ) = 1 B 1 (1 , 1 ) = %xy B 2 ( 2 , 2 ) = t 8 5 xhf B 3 (3,3) = B<(4,4) = £B*V 
B°(l, 0 ) = x 2 -\-y 2 B x ( 2 , l)=f xy(x 2 + y 2 ) B 2 (3,2)=f xy(x 2 + y 2 ) 
B 3 (4, 3) = UxY {x 2 + y 2 ) B* (5, 4) = W*V (x 2 + y 2 ) 
B" ( 2 , 0 ) = x l + J J L x 2 y J + y l B 1 (3, l) = 2 xy (x 4 + J Sxbf + y 4 ) 
B 2 (4, 2 ) = i£-x 2 if (k 4 +^xV+ 2 / 4 ) 
B° (3, 0 ) = x 6 + 7x 4 if + 7 x 2 if + if B 1 (4, 1 ) = f xy (x 6 + ^-x 4 y 2 + --§-x 2 y 4 + y 6 ) 
B 2 (5, 2 ) =^x 2 y 2 (x 6 + + \*-x 2 y 4 + ty 6 ). 
2 Y 
VOL. CCXYI.-A. 
