■ 
28 THERMODYNAMICS OF RADIATION 
reflected waves. It makes no difference whether the waves are travelling involv< 
towards or away from the screen, because on reversing the direction of pressu: 
conveyance of momentum we also reverse the sign of the momentum that Th< 
is being conveyed; so that a wave-train conveying positive momentum withor 
away from the screen gives the same pressure as a wave-train conveying screen, 
negative momentum into the screen. A pressure system cannot be repre- in the 
sented by a vector; it may be associated with an axis but not with a positfv 
direction. from t 
The rule that of negi 
pressure = energy-density defines 
applies only to radiation travelling normal to the surface; oblique incidence accour 
must be considered separately. region 
23 
22 . Consider as in the last section a column of radiation travelling in ‘ 
a fixed direction, and place in its track a screen of area S inclined so that ^ . 
the angle of incidence is 9. The cross-section of the column obstructed by 
the screen is S cos 6, and accordingly the force, which would be ES for ^ 
normal incidence, is ES cos 9 for oblique incidence. This force is in the 
direction of the momentum of the beam; resolving it into components 
normal and tangential to the screen the force is for ms 
ES cos 2 9 normal, ES cos 9 sin 9 tangential. kinetic 
a • . , pressu 
An important case is when the radiation is isotropic, i.e. consists of .^ g ^ 
waves of equal intensity in all directions. Since the average value of cos 2 9 
over a sphere is ^ and of cos 9 sin 9 is zero the force becomes in this case render 
ES normal to the surface. Thus we have the important law— moleci 
The pressure of isotropic radiation is | of its energy-density . elemer 
This pressure is exerted normally on any surface exposed to the radia sharin; 
tion and is entirely analogous to the hydrostatic pressure of a fluid. In degree 
a gas the momentum is conveyed by the molecules; and a gas at rest, in a § as 1 
which the velocities of the molecules are symmetrical as regards direction ratio c 
so that the momentum is being conveyed at the same rate in all directions, 
is analogous to isotropic radiation. In non-isotropic radiation or in a later, 
disturbed gas with unsymmetrical distribution of molecular velocities pressic 
there is no longer a simple hydrostatic pressure; a stress-system with six calculi 
different components is involved. P ass ^ 
When the radiation is not isotropic the normal pressure on a surface su ^ 
is given by using the weighted mean of cos 2 9 instead of the factor |. mater. 
It is to be noted that an increase of flow in a particular direction 9 at the throu^ 
expense of flow in the opposite direction does not alter the pressure. In approi 
the interior of a star we have often to consider radiation which is nearly mstea 
isotropic but with a slight preponderant outward flow; this kind of 
asymmetry does not in itself affect the pressure, though it is likely to