72 
ME. CLEEK MAXWELL ON THE DYNAMICAL THEOEY OE GASES. 
where the last three terms are derived from equation (59) and two similar equations, and 
denote the quantity of Q which flows out of an element of volume, that element moving 
with the velocities u', v', no'. If we perform the differentiations and then make u'=u, 
v'=v, and w'=w, then the variation will be that in an element which moves with the 
actual mean velocity of the system of molecules, and the equation becomes 
^^+QN ^ 4-— ( 
d/ 
* ■ * ■ fi ;+s(WN)+^)+B(«W)=§ 
N. 
(73) 
Equation of Continuity. 
Put Q=M the mass of a molecule ; M is unalterable, and we have, putting MN=g, 
if +*(£+£+£) =°* (74) 
which is the ordinary equation of continuity in hydrodynamics, the element being sup- 
posed to move with the velocity of the fluid. Combining this equation with that from 
which it was obtained, we find 
N f+^+|^ N )+^ »)=*$ (75) 
a more convenient form of the general equation. 
Equations of Motion (a). 
To obtain the Equation of Motion in the direction of x, put Q=M 1 (M 1 -}-i 1 ), the mo- 
mentum of a molecule in the direction of x. 
We obtain the value of ^ from equation (51), and the equation may be written 
«.^+sfcB)+^fcU)+s( eSD=*A,f.*fc-«0+Xft- • • • (76) 
In this equation the first term denotes the efficient force per unit of volume, the 
second the variation of normal pressure, the third and fourth the variations of tangential 
pressure, the fifth the resistance due to the molecules of a different system, and the sixth 
the external force acting on the system. 
The investigation of the values of the second, third, and fourth terms must be deferred 
till we consider the variations of the second degree. 
Condition of Equilibrium of a Mixture of Gases. 
In a state of equilibrium u x and u 2 vanish, becomes and the tangential pressures 
vanish, so that the equation becomes 
£=*ft, (77) 
which is the equation of equilibrium in ordinary hydrostatics. 
This equation, being true of the system of molecules forming the first medium inde- 
