OF THE KINETIC THEORY TO DENSE GASES. 
13 
nT 
Also 
3 n 4- tc 
2h 1 + k 
D 1S 
' > &c 
[These results are easily obtained by considering the general determinant of n 2 
constituents 
2a b b b . | 
D = 6 2a b . . 
in which all the axial constituents are 2a, and all the non-axial constituents are b. 
It will be found for n — 2, n — 3, and thence by induction, that 
D = (2 a — b) u + nb (2 a — b) n ~ l . 
Replacing 2a by 1 + n — l/c/w, and b by — k/u, we get the result above stated.] 
Also v 2 and w l have the same value as u~. And the whole kinetic energy of the 
n spheres, or nT, is, on average, M —> or AT — yy ' 
Again, 
fC ^ 7Z 1 ^ K 
m ’' Tr = K_ 2V i ‘‘" 
— — WiW? — — MiWq — &C , 
n 1 - % 1 d 
I ^ 1 O ^ n 
-4- K — - Wo — -WoWo — &C., 
% 
2 ?i 
— &c. 
with similar expressions for the As and wfs. But 
Ml +K 
n — 1 
% 
a: 
u~ — - w n w., — &c. = -4- f 1 + k 
n n 
n - 1\ D 
n 
D 
IC 
n D 
— &c. = 3n/2hM 
by the properties of determinants. 
Therefore 
„ 3 n 3 n D u 
KUVr = 2h ~ 2 H) 
3 n 3 n + k 
2h ~ 2h 1 + K 
3 n — 1 k. 
Ill 1 T tc 
and 
wT,. = 
3 n — 1 
2h 1 + /c 
» T * = ,iT - nT '- = i (rh - hi) = 3M/2,t ’ 
and therefore 
