80 
MR. CLERK MAXWELL OX THE DYNAMICAL THEORY OE GASES. 
and at constant pressure 
7 p 
7-1 J 0’ 
( 117 ) 
where J is the mechanical equivalent of unit of heat. 
From these expressions Dr. RaNkine* has calculated the specific heat of air, and has 
found the result to agree with the value afterwards determined experimentally by 
M. Regnault|. 
Thermal Effects of Diffusion. 
If two gases are diffusing into one another, then, omitting the terms relating to heat 
generated by friction and to conduction of heat, the equation (94) gives 
1?, ^ft(B+*!+«)+te|fft(8+<+?»+p. (£+$+£) +*(£+$+£) j U8) 
= &§ig 2 Aj { («, ■ — u 2 y + (v, — v 2 y -j- {w l — wf } . j 
By comparison with equations (78), (79), the right-hand side of this equation becomes 
Xfe, u , + Si u 3 ) +Y(g 1 v 1 +g a v a ) + Z (gw + g a w a ) 
“ (tf“- + + tS) “ (t^H* *+ fz W ‘ 
dp<2 dp 2 
- If 1 +«?+ W?) - a ^(u! + vl - + w\) 
The equation (118) may now be written 
If i ^ {< +«i+w?+/3 1 (fj?+tf+ £*)) + (u\-\-vl + wl + (3 : 2 (g + n\ + Kt)) 
=^g l u l + Sa ii a )+Y( Sl v 1 +g a v a ) + Z (^+^+^)* 
. . (119) 
The whole increase of energy is therefore that due to the action of the external 
forces minus the cooling due to the expansion of the mixed gases. If the diffusion 
takes place without alteration of the volume of the mixture, the heat due to the mu- 
tual action of the gases in diffusion will be exactly neutralized by the cooling, of each 
gas as it expands in passing from places where it is dense to places where it is rare. 
Determination of the Inequality of Pressure in different directions due to the 
Motion of the Medium. 
Let us put 
Then by equation (52), 
fi^=Ti+2i and f2^2=i?2+!7 2 
j}= - 3i,%, - m^m; (2M,A,+3MA)s.2.-*(3A a -2A 1 ) m^m; f,2. 
M, 
jyp 2 2 2 2 
- h i&mxt m 2 ~ i A 0( 2 «i - u 2 -v x ~v 2 - w, - w 2 ), 
* Transactions of tlie Royal Society of Edinburgh, vol. xx. (1850). 
( 120 ) 
( 121 ) 
f Comptes Rendus, 1853. 
