PROPERTIES OF MATTER IN THE GASEOUS STATE. 
839 
Fig. 14 shows the inequality of pressure which may exist over a surface, itself at 
uniform temperature, but differing from the temperature of the gas. 
On the convex side the lines diverge much more rapidly than ou the concave side, 
and hence the inequality of pressure due to the communication of heat will be greater 
on the convex side. 
Stability of the equilibrium. 
122. The figures give the lines of flow ou the supposition that the gas is at rest and 
the surfaces all rigidly fixed. The condition would then be one of equilibrium. But 
in order that such a condition might be maintained, it would be necessary that the 
condition should be one of stable equilibrium. This is a point on which the foregoing 
reasoning furnishes us with no information. 
It is satisfactory, therefore, to be able to see what must happen if the equilibrium is 
unstable. This is shown by equation (124), which gives the motion of the gas, so that 
there may be no forces. 
If either the surface A B, or the containing vessel, be perfectly free to move, then no 
inequality of pressure will be possible, but motion must ensue. Equation (124) shows 
the law of such motion. 
The motion. 
123. The motion is given by 
s da 
U vA r dx 
If we suppose the containing vessel to be fixed, then, to allow of the motion of the 
gas, the plate must move with the gas. On the other hand, if the plate be held, the 
vessel will be carried by the gas in the opposite direction. Such is the phenomena of 
the radiometer. The vanes are as nearly as possible free to move in the vessel, so that 
their motion merely indicates the motion of the gas caused by the inequality of tem¬ 
perature in the gas, which inequality is maintained by the unequal temperature of the 
two sides of the vanes arising from their different power of absorbing light, or, in the 
case of curved vanes, by the greater temperature of the vanes as compared with the 
vessel. 
The constraint which is put upon the vanes in a rotatory manner necessarily dis¬ 
turbs somewdiat the free motion of the gas, as must also the friction of the pivot and 
other resistances. Therefore the condition of the gas within the vessel cannot be one 
of absolutely equal pressure; and when either the size of the vanes or the density of 
the gas are too great, the utmost inequality of pressure is insufficient to overcome 
these resistances, and there is no motion. If, then, exhaustion proceeds, the inequality 
of pressure increases, and motion ensues—the rate of which, if the vanes were abso¬ 
lutely free, would increase as the density diminished, until the mean range was limited 
MDCCCLXXIX. 5 P 
