GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 
247 
(14.) Stresses in the Gas. 
Subtracting one-third of the sum of the three equations from (44), we obtain 
0 du 2 (du dv du A /A dr 6 3 p? (d : 6 dr 6 dr- 6 
=- 2^- + -q- +-+-j+3^ ^ s +^ 2 +^+- rf? 
.(53) 
This equation gives the excess of the normal pressure in x above the mean hydro¬ 
static pressure p. The first two terms of the second member represent the effect of 
viscosity in a moving fluid, and are identical with those given by Professor Stokes 
(Cambridge Transactions, vol. viii., 1845, p. 297). The last two terms represent the 
part of the stress which arises from inequality of temperature, which is the special 
subject of this paper. 
There are two other equations of similar form for the normal stresses in y and z. 
The tangential stress in the plane xy is given by the equation 
(du f ddd_ 
' dx)' 6 p6 dxdy ‘ 
There are two other equations of similar form for the tangential stresses in the 
planes of yz and zx. 
(15.) Final Equations of Motion. 
We are now prepared to complete the equations of motion by inserting in (42) the 
values of the quantities a 3 , a/3, ay, and we find for the equation in x 
bu dp /d 2 u dhi d 2 u\ 1 d (die dv did 
bt + Yx~^ + ff + df) + ^7x\dx + Fy + 'd 
9 f d (d~e d~e d-e. 
l./,. 2 +xi+ )—P x 
If we write 
+ 2 pd dx\d.v 2 ' dy' 
, , 1 [du , dv , dw\ , 9 f(d 2 d , ddd , d 2 d 
9 /i bd 23 y bp 
^ 5 d bt 15 p bt 
or, if the pressureis constant, so that pbO-\-6dp=0 
, 10 /x bd 
'P=p+Jeu 
then the equation (55) may be written 
(55) 
(5tf) 
(57) 
(51 
