780 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
volume at the same instant. Thus £' 2 , rf, indicate the mean squares of £, rj, £ 
respectively for all the molecules in a unit of volume of uniform gas which is in the 
same mean condition as the gas at the point considered. 
Q is used to represent any quantity belonging to a molecule, such as its mass, 
momentum, energy, &c. 
S(Q) is used to represent the aggregate value of Q for a group of molecules as 
existing in a unit of volume; and when no further indication is given it will be 
understood that the aggregate is that of the entire group. 
cr(Q) indicates the aggregate value of Q carried across a unit of plane area in a 
unit of time by a group of molecules, which in the absence of further indication will 
be understood to be the entire group which crosses the plane. 
<x t -(Q), with the suffix, is used to express the direction of the plane as well as the 
aggregate value carried across it. 
u+ 
<x. r (Q), with the superimposed symbol, expresses the group over which the sum¬ 
mation extends : u-j- indicates that the summation is taken over all those molecules 
which are moving in the positive direction as regards the axis of x. By varying the 
superimposed symbol, the general symbol may be made to express the value of Q carried 
by a group of molecules having any particular motion across the plane indicated by 
the suffix. 
Fig. 10. 
67. As indicated by the signs of the component velocities, the molecules in a unit 
of volume or the molecules which cross a surface at a point in a unit of time will be 
divided into eight groups. 
These groups may be indicated by the eight corners of a cube, having its edges 
parallel to the axes, circumscribed about the point considered. Thus in fig. 10 the 
group which have u +. v-\~, w -f-, will approach O from the region indicated by the 
corner A, and similarly there will be a corner for each group. The particular groups, 
therefore, may be distinguished by the letters at the corners of the cube, fig. 10. And 
instead of 
