TRANSACTIONS OF SECTION A. 719 
it stationary in the medium of finite spheres is to write &+ & for &, n +n’ for n, 
¢+¢' for ¢, where &’ n’ ¢’ are three vectors for which positive and negative values 
are equally probable and for which &” n’ ¢ are very small compared with & &c. 
Further they are chosen at haphazard independently of & ny ¢,.so that ££ =nn’ 
=¢¢’=0 on average. The object is to find the ratio &” : &. 
The introduction of £ 7 ¢ does not directly affect w,w.on average, but it 
affects Sw. w-) as foundin Art. 3. In lieu of € in that article we must now 
write (€+ é’)’, that is, since £’=0 on average, €°+&”. Our equation II. now 
becomes 
dM —h(w,? + w,? +w.) 
dH ~2|| | drdydz| || dw, dwy dw: 
x {w w dak 2 hur eg 
Oe ba B25 ER? 
hw* chp ee SL 
+h 
pe wp ll 
Se ete 
The first line is zero by II. The second line is zero if &” =e Pe + &?) = 
ED 2 2 i = iy 
(B42), where k= Peclp. Or e?=* £_2 hs ie m2, 18, Be, but not k, bo 
negligible. Evidently ? +n? +¢?: &+7?+(::& : &; and as this ratio is inde- 
pendent of R and 2, it gives the solution for all values of R and x. 
8. When the chance that molecules within a sphere of radius R shall have 
velocities uw, ... u,+du, &. wy, .. w,+dw, is proportional to ——r++w, 
du, . . . dw, we know that the mean value of the energy of the motion of their 
common centre of gravity, or > (E47? +), is es 
If, therefore, the energy of this motion be “@ +n t+) + : (&2% +77 +0), 
as in the medium of finite spheres we now see it must be, that is iu 
4h 
+E +7 +), it is impossible that the above chance can any longer be 
represented by 
LECT he ed AW. 
The term containing ww’ + vv’ + ww’ necessarily appears in the index. 
The case is the same as if, the molecules being in motion according to the ordi- 
nary law, we gave to each of the spheres the additional component velocities 
€ 7’ (’, at. the same time maintaining / constant. It can then be proved that the 
above chance is proportional under those circumstances to e~"@du, . . . dwn, and 
Q = $3 (w+? +") — He +1? + (°)33 (uu! + vv’ + ww’). 
_ But we have seen that for small values of & in stationary motion &%+7n”"+¢? 
= Le +7 +0)= oe where » is the number of molecules within the R sphere, 
_and therefore the coefficient of (wu’+vv’+ww’) in Q is ~*. 
9. If now we write h,=h (147 — 1% , AQ becomes 
y n 
hy{(ad(w? + v7 + w?) + b SS (wu + vo’ + ww’)} 
with 
Qa-147—% 
7 
