444 Lord Rayleigh on the 
makes no difference in respect of the energy passing any 
element of the spherical area. But this supposition does 
not correspond to a constant temperature of the source, in 
consequence of the energy received back from the cloud by 
reflection. ‘Tio keep the total emission of energy constant, 
we should have to suppose a rise of temperature increasing 
indefinitely with the size and density of the cloud. 
Let us now suppose that the region under consideration 
is bounded upon all sides by a distant envelope of perfect 
reflecting-power. Then, whatever the density of the clouds 
which may wholly or partially occupy the enclosure, we know, 
by the second law of thermodynamics, that at every internal 
point there is radiation in every direction of the full amount 
corresponding to the temperature of the source. In one sense 
this conclusion holds good, even although the matter com- 
posing the cloud has the power of absorption. But in that 
case equilibrium would not be attained until the clouds them- 
selves to the remotest parts had acquired the temperature of 
the source; whereas under the supposition of perfect trans- 
parency the temperature of the cloud is a matter of indiffer- 
ence; and equilibrium is attained in a time dependent upon 
that required by light to traverse the enclosure. So far we 
have made no supposition as to the distribution of the cloud ; 
but we will now imagine a layer of such thickness as to allow 
only a very small fraction of the incident radiation to pene- 
trate it, to line the interior of the reflecting envelope. This 
layer itself plays the part of a practically perfect reflector; and 
it is not difficult to see that the reflecting envelope hitherto 
conceived to lie beyond it may be removed without interfering 
with the state of things on the inner side of the layer of cloud. 
We thus arrive at the rather startling conclusion that at any 
distance from the source, and whatever the distribution of 
clouds, there is always in every direction the full radiation due 
to the temperature of the source, provided only that there lie 
outside a complete shell of cloud sufficiently thick to be im- 
pervious. And this state of things is maintained without (on 
the whole) emission of energy from the source. 
Even if the material composing the cloud possesses absorb- 
ing-power for some kinds of radiation, e. g. for dark radiation, 
but is perfectly transparent to other kinds, e. g. luminous 
radiation, the general theorem holds good as respects the latter 
kinds; so that in the case supposed the light would still be 
everywhere the same as in a clear enclosure whose walls 
have throughout the same luminosity as the source. But in 
order to compensate the absorption of dark rays, the source 
must now be supplied with energy. 
