PROPERTIES OP MATTER IN' TIIE GASEOUS STATE. 
829 
By equation (48) we have 
pu- 
or since pa 2 is constant 
S (1 pOL 
y/ TT dx’ 
s da 
U = 
dx 
(124) 
which it may be noticed is of the same form as results from the equation of transpira¬ 
tion through a tube when p is constant. 
Thermal Impulsion. 
112. In this case there is no motion, therefore 
u— 0, 
whence from equations (48) 
s dpu 
pVj ~^r~chx • - 
. (125) 
This satisfies equation (120). 
Substituting from equation (125) in equations (121) and (122), and remembering 
o ^ ^ (Jj 
that p x —~ - - — (paU), Art. 82, we find that these equations lead to the same 
7 T ClX V 
result if pa 2 is constant. 
per 
Putting p y — we have from equation (122) 
d t doc\ 
ivmj x )= o, 
dx 
whence integrating 
_ y/ 7rII 1 
dx 11 r y r z sp l 
( 120 ) 
where H has the same value as in Art. 111. 
dr y _ chp 
dx dx 
civ (It 
Remembering that ~=—= 1, also considering s constant, we have differentiating 
_ \/ir H. 1 A ■ 1 
djx 11 sp l r y r\r y ' r 2 
r y +r z da. 
r y r z dx 
(127) 
Also putting r v —r z , cl— a.' when r= go and cl—cl c when r—c, and integrating 
equation (126), we have 
