THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 325 
however, it has not been found possible in the past to obtain any close numerical 
accuracy in calculations based on this molecular model, the errors resulting in previous 
theories (although these have been carefully constructed and closely scrutinized) 
ranging from 10 to 50 per cent. {cf. § 11 (F)). 
It is readily seen # that in the present case 
(201) x =° (P>2«r) sin |- x = p/2a (p=2o) 
so that 
p dp — 2a- 2 sin jx cos VX C ^X = 0-2 si n x ^X = d cos X- 
As p ranges from 0 to 2 <r, x ranges from 0 to 2-tt , and — cos x from —1 to 1 . 
Hence {cf. (ill)) 
( 202 ) f k {tij) = 2 (4&+ 1 ) C K <r 2 J ^{ 1 -P 2i . (cos x )} d cos x 
= 4 (4& +1) a- 2 {2hm)~' l ‘ l y, 
since 
P 2k {f) d/j. = 0 . Hence f k (ry) depends on k only as regards the numerical 
L 
factor (4&+1), and the present case is, analytically, the same as that considered in 
§ 8 (B) if we write {cf (183)) 
(203) 
--- - - ^ = l, or n — co, and n A k = 4 (4& + l) a- 2 , 
n — 1 
We may therefore quote from the formulae of § 8 (B) as follows without further 
discussion :— 
(204) 
(205) 
(206) 
(207) 
|tt i/2 (m + |)„,K M _ 2A . * = 2 (4&+1) rr 2 (2 hm) V T (m + 2) 
= 2 (4& +1) (m +1)! a- 2 (2 hm)~' 12 , 
Ko = K 0il = 647r _I/2 cr 2 (2/wi) -1/a , K (il = K 0il {t + 3)J{t+%)f 
p _ 225 { 2 hm) 
- L, 0 2 5 6 i o 2 > 
7 r "it v 
p 2 5 {2hm) ^ 
^0 61t 1 L 2 > 
7 T "<J V 
h = r = 9~ r y kj ~t 3)t — o-rp / _ r a 7 _ i \ 
t = o t\ p + fh 
15 
(208) ^„ = ^ = (- 2 )-^=-(-P (5? - Wr+1)(2r + 3)(2r+5) . 
As in the case of molecules which are point centres of force varying inversely as 
* Cf. §13, p. 453, of my former paper, ‘Phil. Trans.,’ A, 211 (1911). 
