THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 323 
As r tends to infinity, the last expression tends to zero more quick] y that 
2~v ^ n— 1 ) 
and also it is alternately of positive and negative sign, after the first two terms 
(both S 00 b r0 and S 10 b l0 being positive). 
Maxwellian Molecules: n — 5. 
§ 9 (C) It is now easy to see what are the special properties of the fifth-power law 
(n = 5), the law obeyed by the molecules which we term Maxwellian, which enabled 
Maxwell to work out the theory on this hypothesis with such great simplicity and 
accuracy. When n = 5, we have from (186) 
(189) K,, = S A„ 
which is independent of t. Hence, by (170), (171), (172), 
(190) i — K 0 1 — gAj, k t — 2 r C t K tj j — 2 r K 0il 2 r C f — K 0 1 — k 0 , b r0 — c r0 — 1 ; 
t =0 <=0 
(191) S r< o b r o = S rw0 c„ = (-2)- 2 (-iy r C t = ( — 2)~ r (l —l) r = 0, (r> 0); 
t = 0 
(192) B 0 = ^ C 0 - 25 (.A)- 1 . 
From (191) and the equation 5 00 = c 00 = 1 we deduce that in this case the principal 
minors of V ( S rs b rs ) and V (J rs c rs ) are equal to these determinants themselves, i.e., 
(193) 2 /3 r = 1 , 2 y r = 1 (Maxwellian molecules), 
r = 0 r = 0 
while from (190) it appears that all the elements of the first row and column of 
V (b rs ) and V (c rs ) are unity. Hence in V ( . (b rs ) and V,. (c„) the first column and 
column ( r) are identical, so that we have 
(194) 
(195) 
V (b„) = 0, V, (c„) = 0, r > 0 j 
V„(U'= V(6„), V ( c „) = V (c„) J 
(Maxwellian molecules), 
whence also, by (140), we have 
(196) /3 0 = 1 , yo — 1) ^r—y r — 0> (f> 0 ) (Maxwellian molecules), 
and also, by (148), 
(197) =-&=-! 
(Maxwellian molecules). 
