PROPERTIES OE MATTER IN' THE GASEOUS STATE. 
827 
cPf(pa)^ 1 df(pa)' 
cly 3 r y dx 
#/(p«) _1 df(pu) 
dz 2 r z dx 
( 119 ) 
The equations of steady condition. 
110. Equations (118) and (119), together with equations (43) to (47), enable us to 
obtain from equation (57) the equations of steady condition. 
For steady density 
d_ 
dx 
r y ri P Y- 
= 0 
( 120 ) 
For steady momentum putting, as before, 
dp 
dx 
dp 
dx 
= 0 
( 121 ) 
For steady pressure 
C L 
dx 
iy 
3 d P 'J \ 
y' n t dx ) 
= 0 
( 122 ) 
These equations (120), (121), (122), might be treated in a manner similar to that in 
which the corresponding equations for the case of the tube were treated in Section IX., 
but for various reasons another method commends itself. 
In the first place we cannot in this case ignore the condition of steady pressure, for 
there can be no lateral adjustment of temperature as in the case of the tube. (See 
Art. 91.) The physical meaning of this is, that in this case the condition of the gas 
cannot be supposed to vary uniformly even along the lines of flow. It must vary after 
a fixed law, and this fact restricts the conditions under which the equations can be 
considered to hold to points where - is so small that (- j may be neglected. So that 
any general result obtained from these equations would only apply to points at 
considerable distances from the foci C and C'. 
Again, these equations as they stand include the case in which the flow of the gas 
may be caused by a considerable difference of pressure, as, for example, transpiration 
through a small aperture under pressure, whereas if we exclude this case we may, 
by neglecting such terms as - 2 -A 3 very greatly simplify the equations without affecting 
their application to the cases which it is our principal object to explain. 
