PROPERTIES OF MATTER IJST THE GASEOUS STATE. 
799 
That is, on arriving at A, the molecules will, in respect of G, enter the element as 
if from the resultant uniform gas at B, a point in the direction of the group, the distance 
s of which from A is a function of a, is inversely proportional to ^ and is independent 
of the variation of the gas and of the direction of the group. [Q. E. D. j 
Corollary to Theorem (II.).—The effect of a solid surface. 
If in the neighbourhood of A there is a solid surface such that, if B is a point on 
this surface, BA is of the same order of magnitude as s, then putting r=BA for the 
group arriving at A from the direction BA, equation (33) gives 
G a + I a —G b +I b 
T -dr 
V 
(35) 
and substituting for - from equation (32) and integrating 
dCr 
G A +I A =G E +I B -r^-C(e* +1), 
or since G B =G A +/ ,< b- and I B — C=s^~, therefore 
dr 
dr 
T p-T 
I ‘ = S *- CC ' 
(36) 
da 
C will be a function of /, m, n, and it may be written f(lmn)s —; therefore 
dr 
dG 
(37) 
The mean range. 
M 
81. The distance s, or —— (equation 30) is thus shown to be the distance at which 
jOp 
the elementary groups radiating outwards from a point have the mean value of G for 
the molecules which, in a unit of time, pass the central point. And hence it is 
proposed to call s the mean range of the quantity G. 
The mean range is thus seen to be approximately independent of the space variations 
of the gas, but since s involves fiff), which, as pointed out in assumption III., Art. 78, 
may, so far as is yet known, have different values for v and v 3 from its values for N 
and v 2 , which latter are equal, so the values of s for the mean velocity and mean cube 
5 K 
MDCCCLXXIX. 
