718 REPORT—1896. 
plane of wy, and the other z= vc, \ » v being direction cosines of a diameter ec. For 
our present purpose we may take €=0 on plane of «y, and the value of € on the second 
plane is ues Consider two spheres, one on the plane of ay, the other on the 
da 
second plane, and suppose their relative velocity to be V, and its direction cosines | 
X pv. If the number per unit of volume of pairs of molecules having relative 
velocity V... V+dV be Ae~4” V2dV, the number having near P X p » for 
direction cosines of V is in excess of the normal by — Ac va vnvehv 2 
Let @ be the angle between V and the line of centres at collision. If we form 
the integral value of AvV* for all collisions taking place per unit of volume and 
time near P under the circumstances assumed, it is 
ae 7 pert 
—AvAe 3 Vd Viren VavchV! = | cos? 8 sin 646; 
. oO 
pee yt Ce Eee 
that is — Wer AL 2 VedVh & 
di 
6. Again, let X’ p’ v’ be the values of Ap vy after collision. Then we find 
easily j 
v= — vcos 26+ /1—r’* sin 26 cos d, 
NV = —A cos 26 ~— Ay _ sin 26 cos d, 
a‘ l—y 
$ being the angle between the plane containing \ » v and 2, and the plane con- 
taining A » v and the point of contact. Whence we find the integral value of 
’y’ for all collisions per unit of volume and time to bergreater than 
> q Pak sa Av : 
{2 sin 6 cos ofa —vcos26 + 4/1 —v*sin 26 cos ){ —Ac0s26 — ier sin26 cos), 
0 0 
44) 40 ’ nies Oo ed so ee AE 
which is zero, Let \V=V,,vV = V*. Hence if \’y’ =0, a (VeNe) = sais VvAV = 
3 
rep 1 yyaé 
5 dz 
79? because on average \?y? = rae 
3. 6° 
So> 
and changing the variable, we obtain 
Therefore, if 2 relate to the change due to collisions only, 
; [Jfox dy ae{|| e« A(wa? + Wy? + w,") dw, dwy dw; = = (w,w:) 
= 2 2 2 3 a 
= all dy All| € (wa? + wy" + wz") dw, dw, dw . = = « ha* ne by Art. 2. 
7. Wesee then that if . denote the whole time variation, the expression 
(w,W:); 
which was zero on average, has now, as the result of collisions, acquired a positive 
3 hw 3 & 
Inne 
ieee, oes oy 4. Re 
If we stop there a # O, and the motion is not stationary. The way to make 
