782 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
Gas in uniform condition. 
70. When the gas is uniform, whether at rest or in motion, the value of cr(Q) has 
already been determined by Professor Maxwell, but it is necessary to transform the 
expressions to the notation of this paper. 
We have by a well-known formula* 
A,=t{uQ), ] 
A,=S(*Q), i.(8) 
A : =2(«Q), j 
in which the suffixes x, y, z, indicate that it is the planes yz, zx, xy, that Q is being 
carried across, and the superimposed symbols a a a indicate the group of molecules 
over which the summation extends. 
We have also 
(9) 
and similar expressions for the values of Q carried across each of the other planes by 
all the other groups. 
In the equation (8) and similar equations we may obviously substitute for u, v, w 
their values 
w=f+-U ' 
V = y-\-\ > 
w=£+W J 
( 10 ) 
And since the gas is here supposed to be uniform, we shall have 
v=v >. 
W=w 
( 11 ) 
y, £ being identically the same as if the gas were at rest. 
71. For the purpose of this investigation it is necessary to express such quantities as 
u+ u— 
erf Q), o-.r(Q) in terms of the groups distinguished by the signs of £ y, £, instead of 
* “ On the Dynamical Theory of Gases,” Maxwell ; Phil. Trans. 1867, p. 69. 
