RADIOMETER. It had been remarked at various times, amongst others by Fresnel, that bodies delicately suspended within a partial vacuum are subject to apparent repulsion by radiation. The question was definitely investigated by Sir W. Crookes, who had found that some delicate weightings in vacuo were vitiated by this cause. It appeared that a surface blackened so as to absorb the radiant energy directed on it was repelled relatively to a polished surface. He constructed an apparatus in illustration, which he called a radiometer or light-mill, by pivoting a vertical axle carrying equidistant vertical vanes inside an exhausted glass bulb, one side of each vane being blackened and the other side bright, the blackened sides all pointing the same way round the axle. When the rays of the sun or a candle, or dark radiation from a warm body, are incident on the vanes, the dark side of each vane is repelled more than the bright side, and thus the vanes are set into rotation with accelerated speed, which becomes uniform when the forces produced by the radiation are balanced by the friction of the pivot and of the residual air in the globe. The name radiometer arose from an idea that the final steady speed of rotation might be utilized as a rough measure of the intensity of the exciting radiation.
The problem of the cause of these striking and novel phenomena at first produced considerable perplexity. A preliminary question was whether the mechanical impulsion was a direct effect of the light, or whether the radiation only set up internal stresses, acting in and through the residual air, between the vanes and the walls of the enclosure. The answer to this was found experimentally by Arthur Schuster, who suspended the whole instrument in delicate equilibrium, and observed the effect of introducing the radiation. If the light exerted direct impulsion on the vanes, their motion would gradually drag the case round after them, by reason of the friction of the residual air in the bulb and of the pivot. On the other hand, if the effects arose from balanced stresses set up inside the globe by the radiation, the effects on the vanes and on the case would be of the nature of action and reaction, so that the establishment of motion of the vanes in one direction would involve impulsion of the case in the opposite direction; but when the motion became steady there would no longer be any torque either on the vanes or on the case, and the latter would therefore come back to its previous position of equilibrium; finally, when the light was turned off, the decay of the motion of the vanes would involve impulsion of the case in the direction of their motion until the moment of the restoring torque arising from the suspension of the case had absorbed the angular momentum in the system. Experiment showed that the latter prediction was what happened. The important part played by the residual air in the globe had also been deduced by Osborne Reynolds from observing that on turning off the light, the vanes came to rest very much sooner than the friction of the pivot alone would account for; in fact, the rapid subsidence is an illustration of Maxwell's great theoretical discovery that viscosity in a gas (as also diffusion both of heat and of the gas itself) is sensibly independent of the density. Some phenomena of retardation in the production of the effect had led Sir G. G. Stokes and Sir W. Crookes to the same general conclusion.
The origin of these phenomena was recognized, among the first by O. Reynolds, and by P. G. Tait and J. Dewar, as a consequence of the kinetic theory of the constitution of gaseous media. The temperature of a gas is measured by the mean energy of translation of its molecules, which are independent of each other except during the brief intervals of collision; and collision of the separate molecules with the blackened surface of a vane, warmed by the radiation, imparts heat to them, so that they rebound from it with greater velocity than they approached. This increase of velocity implies an increase of the reaction on the surface, the black side of a vane being thus pressed with greater force than the bright side. In air of considerable density the mean free path of a molecule, between its collisions with other molecules, is exceedingly small, and any such increase of gaseous pressure in front of the black surface would be immediately neutralized by flow of the gas from places of high to places of low pressure. But at high exhaustions the free path becomes comparable with the dimensions of the glass bulb, and this equalization proceeds slowly. The general nature of the phenomena is thus easily understood; but it is at a maximum at pressures comparable with a millimetre of mercury, at which the free path is still small, the greater number of molecules operating in intensifying the result. The problem of the stresses in rarefied gaseous media arising from inequalities of temperature, which is thereby opened out, involves some of the most delicate considerations in molecular physics. It remains practically as it was left in 1879 by two memoirs communicated to the Phil. Trans. by Osborne Reynolds and by Clerk Maxwell. The method of the latter investigator was purely a priori. He assumed that the distribution of molecules and of their velocities, at each point, was slightly modified, from the exponential law belonging to a uniform condition, by the gradient of temperature in the gas (see Diffusion). The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities. As far as the order to which he carried the approximations—which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart—the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions. If, therefore, the walls of the enclosure held the gas that is directly in contact with them, this equilibrium would be the actual state of affairs; and it would follow from the principle of Archimedes that, when extraneous forces such as gravity are not considered, the gas would exert no resultant force on any body immersed in it. On this ground Maxwell inferred that the forces acting in the radiometer are connected with gliding of the gas along the unequally heated boundaries; and as the laws of this slipping, as well as the constitution of the adjacent layer, are uncertain, the problem becomes very intricate. Such slipping had shown itself at high exhaustions in the experiments of A. A. Kundt and E. G. Warburg in 1875 on the viscosity of gases; its effects would be corrected for, in general, by a slight effective addition to the thickness of the gaseous layer.
Reynolds, in his investigation, introducing no new form of law of distribution of velocities, uses a linear quantity, proportional to the mean free path of the gaseous molecules, which he takes to represent (somewhat roughly) the average distance from which molecules directly affect, by their convection, the state of the medium; the gas not being uniform on account of the gradient of temperature, the change going on at each point is calculated from the elements contributed by the parts at this particular distance in all directions. He, lays stress on the dimensional relations of the problem, pointing out that the phenomena which occur with large vanes in highly rarefied gas could also occur with proportionally smaller vanes in gas at higher pressure. The results coincide with Maxwell’s so far as above stated, though the numerical coefficients do not agree. According to Maxwell, priority in showing the necessity for slipping over the boundary rests with Reynolds, who also discovered the cognate fact of thermal transpiration, meaning thereby that gas travels up the gradient of temperature in a capillary tube, owing to surface-actions, until it establishes such a gradient of pressure (extremely minute) as will prevent further flow. In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the momentum and the energy at an element of volume of the molecular medium, with the precision necessary in order that the dynamical equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid-a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved.
Of late years the peculiarities of the radiometer at higher gas-pressures have been very completely studied by E. F. Nichols and G. F. Hull, with the result that there is a certain pressure at which the molecular effect of the gas on a pair of nearly vertical vanes is balanced by that of convection currents in it. By thus controlling and partially eliminating the aggregate gas-effect, they succeeded in making a small radiometer, horizontally suspended, into a delicate and reliable measurer of the intensity of the radiation incident on it. With the experience thus gained in manipulating the vacuum, the achievement of thoroughly verifying the pressure of radiation on both opaque and transparent bodies, in accordance with Clerk Maxwell’s formula, has been effected (Physical Review, 1901, and later papers) by E. F. Nichols and G. F. Hull; some months earlier Lebédew had published in the Annalen der Physik a verification for metallic vanes so thin as to avoid the gas-action, by preventing the production of sensible difference of temperature between the two faces by the incident radiation. (See Radiation.)
More recently J. H. Poynting has separated the two effects experimentally on the principle that the radiometer pressure acts along the normal, while the radiation pressure acts along the ray which may be directed obliquely. (J. L.*)