791 
PROPERTIES OF MATTER IN THE GASEOUS STATE. 
O 
which will not be, neglecting u , the same as 2 u, as it would be if the gas were uniform 
and moving with the velocity u. 
The same thing may be shown for faces parallel to x, and for variations in the direc¬ 
tions y and z. 
In all the phenomena considered, the velocity 
c r^M-jt)— cr,.(MA) 
!'. + U— ^ 
is very small compared with the mean velocity of a molecule; but the relation is of 
the same order as that of the unhindered rate of thermal transpiration and the mean 
velocity of a molecule. 
78. The following limitations and definitions will tend to the simplification of 
subsequent expressions. 
The condition of the gas. 
All the assumptions and theorems, as indeed the entire investigation, with the 
exception of Arts. 108 a and 109, relate to a simple gas in which the diameters of the 
molecules may be neglected in comparison with the mean distance which separates them, 
the condition of which gas is at all points steady as regards time, and the molecules of 
which are subjected to no external forces, such as gravity and electric attractions ; and 
the term gas is to be understood in this sense unless otherwise defined. 
The small quantities neglected. 
As a first approximation, i.e., in theorems (I.) and (II.) no account is taken of varia¬ 
tions of the second order, such as are expressed by 
d~P To. 
&c - 
the effects of such variations being too small to make any difference in the results of 
the first approximation. 
Also throughout the investigation the velocity of the gas is assumed to be so small 
that such quantities as u and 
crgMit) 
\ er,.(M) — er /; (M) , 
may be neglected. 
Definitions. 
An elementary group of molecules .—In addition to the separation of the molecules 
into the groups A, B, C, D, E, F, G, H, as explained in Art. 67, a further subdivision 
is necessary in order to render the reasoning of this section definite. 
From any one of the eight groups are selected all the molecules having directions of 
MDCJCCLXXIX. 5 I 
