PROPERTIES OP MATTER IN THE GASEOUS STATE. 
797 
And from the dimensions of this equation it follows that ' represents a distance. 
Afp 
Therefore putting s for this distance 
d L 
dr 
Corollary to Theorem (/.). 
When is nearly constant, so that we may neglect s ~~ as compared with then 
|(G + I)8r=p 
. . . (31) 
[Q. E. D.] 
dr 
dr 
integrating equation (31) we have 
or 
I=s^+Ci‘ 
dr 
dG _I_C 
dr s s 
(32) 
J 
Near a solid surface. 
Equation (32) shows the nature of the inequalities as affected by discontinuity such 
as may arise at a solid surface. The last term on the right gives the effect of discon¬ 
tinuity for an element at a distance r from the surface, r being measured in the 
direction of the group. This effect diminishes as r increases. 
In the first of equations (32) we may obviously put iq yy for s <: . -\-Ce s , s 1 being a 
function of the position of the element and of the direction of the group. 
Theorem (II.). — When the variation in the condition of the gas is approximately constant, 
then in respect of any one of the quantities n, v, v 3 , &c., each elementary group of 
molecules entering a small element of volume at any point ivill enter approximately 
as if from the resultant uniform gas at a point in the direction from which the 
group arrives, the distance of which point from the element is a function of the 
mean velocity of a molecule and inversely proportional to the number of molecules 
within a unit of volume, and is independent of the variation of the gas and the 
direction of the elementary group. 
To illustrate this, supposing a small spherical element at A, and considering the 
group arriving in the direction BA, then if the gas varies in the direction BA the 
Fig. 11. 
resultant uniform gas for points along BA will differ, and if A were to be surrounded 
