ME. CLEEK MAXWELL ON THE DYNAMICAL THEOEY OF GASES. 
81 
the last term depending on diffusion ; and if we omit in equation (75) terms of three 
dimensions in |, ??, £, which relate to conduction of heat, and neglect quantities of the 
form and g>£ 2 — p, when not multiplied by the large coefficients Jc, , and Jc 2 , we get 
2 (du dv dw\ 8 q /-,oo\ 
+ 2 i , &-3i'(«s+^+&j=r ( ( 122 ) 
If the motion is not subject to any very rapid changes, as in all cases except that of 
the propagation of sound, we may neglect In a single system of molecules 
3/rA, 
(123) 
whence 
3kA 9 g(dx 3 \dx'dii'dz)( v ' 
dy 
11 p 
If we make 
3 /cA 2 § 
yj will be the coefficient of viscosity, and we shall have by equation (120), 
r du 
l i 
( da dv div\ i 
\dx' 
“3-1 
ftx'dy^ dz J J 
f dv 
1 , 
' du dv du A ] 
w 
“ 3 I 
fix'd ‘ dz) J 
[■ > 
(dw 
1, 
(du dv dw\ ] 
V 
(te+dj+fe) j 
(125) 
(126) 
and by transformation of coordinates we obtain 
(127) 
These are the values of the normal and tangential stresses in a simple gas when the 
variation of motion is not very rapid, and when p, the coefficient of viscosity, is so small 
that its square may be neglected. 
Equations of Motion corrected for Viscosity. 
Substituting these values in the equation of motion (76), we find 
"du 
[d 2 u d?u d^u] 1 dfdu dv dw 
^ J \dx tl 'd]/' 2 'dz z \ 3 ^ dx\dx'dy' d. 
s )= Xt 
(128) 
with two other equations which may be written down from symmetry. The form of 
these equations is identical with that of those deduced by Poisson* from the theory of 
* Journal cle l’Ecole Polytechnique, 1829, tom. xiii. cah. xx. p. 139. 
M 
MDCCCLXVII. 
