GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 
245 
/>^+4( fe2 )+ 2 ^ I + 2 ^(4‘+<+^l' 
+R* 
dy 
dx 
KpW 
with two other equations of similar form. 
Similarly we obtain by putting Q = («-|-£)(?>+ 7 ?) 
6 /. , J dv , cfot 
p^(0afi)+p0(j x +-^ 
M4 *+<+“>!+«*!+<+*£ 
+K^ 
d -(p6'a?[$) +|(p^)+|(pfll«^) 
efof r ' dy xr 7 d. 
with two other equations of like form for /3y and ya. 
Ep 3 fl 
- 1 -a 
/* 
/3 ■ 
(44) 
(48) 
(11.) Terms of Three Dimensions. 
Putting Q = (« + £) 3 and in the final equation making u=v=w= 0 and eliminating 
bu 
— by (41) we find 
^ 4-0 1 c.ndU t#r» dU r. PLXi 
^+ 3 P^+8p^+3p^ 
or 
d 
dx 
+sW‘)+|wS)+sW0 
-( 
fife 
-3^ 
£(pe)+|(^)+f>fa]=4? 3 
which gives 
Pdp-((9 ? a : ) + 3p(B0) f ( a 3 —+ a 2 ^-+a 3 y— 
jJm 
du 
dx 
JO 
dx 
— 3 IP da 2 
de 
d6 
dy 
dff 
clz 
+ 3 RV^+ 3 E V^( a 2 ^+ a fe+ a r ^)+ 3 ll V^-( a ^) 
dy 
<fe 
(46) 
rf ,(pto»)+| ; (pfc / 3)+|(pfe y )j=p(RS)^(-2^+^+ a /) . (47) 
dx 
Since the combinations of a/3y represent small numerical quantities, we may at this 
stage of the calculation, when we are dealing with terms of the third order, neglect 
terms involving them, except when they are multiplied by the large coefficient p/pi. 
The equation may then be written approximately :—- 
