244 
PROFESSOR CLERK MAXWELL OX STRESSES IX RARIFIED 
b 
bt 
(Qp)+4£+£+5)+£wo+5(^)+|wo=4« 
(8.) Equation of Density. 
Let us first make Q=l, then, since the mass of a molecule is invariable, the 
equation becomes 
bp 
bt 
+P 
du , dv , dw , 
* + SS+a?.)=° 
(39) 
which is the ordinary “ equation of continuity.” 
Eliminating by means of this equation the second term of the general equation 
(38) we obtain the more convenient form— 
.(«> 
(9.) Equations of Motion. 
Putting Q=w+£> this equation becomes 
•.( 4i ) 
where any combination of the symbols £, y, £ is to be taken as the average value of 
that combination. 
Substituting their values as given in (28) 
bu 
V 
<l {p9^) + j y {pO*&) + f z (p 0a y) 
ddu 
= P X. 
(42) 
which is one of the three ordinary equations of motion of a medium in which stresses 
exist. 
(10.) Terms of Two Dimensions. 
Put Q= (c-j-c') : -. Since the resulting equation is true whatever be the values of 
u, v , iv, we may, after differentiation, put each of these quantities equal to zero. We 
shall thus obtain the same result which we might have obtained by elimination between 
this and the former equations. We find 
/ ^+^+2^+2 / ^+|( P n+|( P f«, ) +4( P f*i)=^ 
(43) 
or by substituting the mean values of these quantities from (29) 
