PROPERTIES OF MATTER IN THE GASEOUS STATE. 
807 
taken for the axis of the tube, and it is assumed that all perpendicular sections of the 
tube are surfaces of equal pressure and temperature, the variation of temperature and 
pressure being in the direction x. 
The equations to the surfaces of the tube are taken 
z=±c .. (65) 
90. From equation (57) we have for steady momentum 
£{<■-,(M«)H-|{<7.(M«)}=0 ..... 
. . . (66) 
for steady density 
|{<r,(M)R4{ov(M)J = 0 . . .' . 
. . . (67) 
and for steady pressure 
~{aM[u z +v z +w^)}+j{o-M{u 2 +v z -\-w z )}=:0 . . 
. . . (68) 
Steady pressure not important. 
.91. In a tube, since heat may he communicated from the surface to the gas, the 
temperature may be maintained constant; and if the density be steady the pressure 
will also be steady, hence the condition of steady pressure ceases to be important. The 
law of variation of temperature is determined by the sides of the tube. 
Transpiration when s is small as compared with c. 
92. If 5 is so small that it is unnecessary to consider the layer of gas throughout 
which the direct influence arising from the discontinuity at the surface extends, 
clp d 
substituting in equation (66) from equations (46), and putting - = - (<x,(Mw)), which 
we may do within the limits of our approximation, we have for steady momentum, 
since W = 0 in the tube 
dp _ 1 d ( dpa. U 
dx 7T dz\ d 
(69) 
And from equations (43) and (67), since p and a do not vary across the tube, we have 
for steady density 
jiUr£)= J> u >.. • < 70 > 
Since pu—pXJ ■ 
s dp 
\/ r- d. 
we have from equation (70) 
5 L 
MDCCCLXXTX. 
