61.

For the following we imagine a perfectly evacuated hollow cylinder with an absolutely tight-fitting piston free to move in a vertical direction with no friction. A part of the walls of the cylinder, say the rigid bottom, should consist of a black body, whose temperature $T$ may be regulated arbitrarily from the outside. The rest of the walls including the inner surface of the piston may be assumed as totally reflecting. Then, if the piston remains stationary and the temperature, $T$, constant, the radiation in the vacuum will, after a certain time, assume the character of black radiation ([sect:50.] Sec. 50) uniform in all directions. The specific intensity, $K$, and the volume density, $u$, depend only on the temperature, $T$, and are independent of the volume, $V$, of the vacuum and hence of the position of the piston.

If now the piston is moved downward, the radiation is compressed into a smaller space; if it is moved upward the radiation expands into a larger space. At the same time the temperature of the black body forming the bottom may be arbitrarily changed by adding or removing heat from the outside. This always causes certain disturbances of the stationary state. If, however, the arbitrary changes in $V$ and $T$ are made sufficiently slowly, the departure from the conditions of a stationary state may always be kept just as small as we please. Hence the state of radiation in the vacuum may, without appreciable error, be regarded as a state of thermodynamic equilibrium, just as is done in the thermodynamics of ordinary matter in the case of so-called infinitely slow processes, where, at any instant, the divergence from the state of equilibrium may be neglected, compared with the changes which the total system considered undergoes as a result of the entire process.

If, e.g., we keep the temperature $T$ of the black body forming the bottom constant, as can be done by a suitable connection

between it and a heat reservoir of large capacity, then, on raising the piston, the black body will emit more than it absorbs, until the newly made space is filled with the same density of radiation as was the original one. Vice versa, on lowering the piston the black body will absorb the superfluous radiation until the original radiation corresponding to the temperature $T$ is again established. Similarly, on raising the temperature $T$ of the black body, as can be done by heat conduction from a heat reservoir which is slightly warmer, the density of radiation in the vacuum will be correspondingly increased by a larger emission, etc. To accelerate the establishment of radiation equilibrium the reflecting mantle of the hollow cylinder may be assumed white ([sect:10.] Sec. 10), since by diffuse reflection the predominant directions of radiation that may, perhaps, be produced by the direction of the motion of the piston, are more quickly neutralized. The reflecting surface of the piston, however, should be chosen for the present as a perfect metallic reflector, to make sure that the radiation pressure [eqn:(66)] (66) on the piston is Maxwell's. Then, in order to produce mechanical equilibrium, the piston must be loaded by a weight equal to the product of the radiation pressure $p$ and the cross-section of the piston. An exceedingly small difference of the loading weight will then produce a correspondingly slow motion of the piston in one or the other direction.

Since the effects produced from the outside on the system in question, the cavity through which the radiation travels, during the processes we are considering, are partly of a mechanical nature (displacement of the loaded piston), partly of a thermal nature (heat conduction away from and toward the reservoir), they show a certain similarity to the processes usually considered in thermodynamics, with the difference that the