Instead of allowing free rotation of the vane system on a pivot, it may be suspended by a quartz fibre. Radiation falling on the black face of the vane will then cause the system to turn round until the restoring couple, due to the torsion of the suspension, balances the deflecting couple due to the radiometer action. A small mirror, attached to the vane system and reflecting a beam of light on to a scale, enables very small deflections to be observed. Pringsheim in 1883 constructed such an instrument and used it for spectrographic investigations in the infra-red. In 1893 Nichols constructed a radiometer in which the mica vanes, one at each end of a horizontal arm, and each blackened on its front surface, were suspended by a quartz fibre. Radiation falling on both vanes would tend to turn them in opposite directions, and if they were correctly adjusted the system would not move under the influence of general stray radiation. The radiation to be measured was allowed to fall on one only of the vanes, and the resulting de flection of a spot of light reflected by a small mirror was observed. In 1901 Nichols improved his radiometer, by making it smaller, to such an extent that he was able to measure with it the radiation from individual stars.
The radiometer has been applied to measurements of ultra violet radiation and to that of short Hertzian waves (wave length I to 2 MM.).
0. Reynolds in 1874 had shown, on the kinetic theory of gases, that communication of heat from a solid to a gas would involve a reactionary force on the surface of the solid. On the same theory Sir W. Crookes in 1876 gave an explanation of the action of his light-mill; this was as follows: The temperature of a gas is, on the kinetic theory, proportional to the mean kinetic energy of translation of the molecules, and the pressure exerted by a gas on the surface of a solid is due to the bombardment of the surface by the molecules. If the solid and the gas are at the same tem perature, the molecules, after striking the surface, will rebound with the component of their velocity normal, the surface merely reversed. If the surface of the solid is warmed, as in the case of the light-mill by radiation, heat will be imparted to the molecules which strike the surface, and they will rebound with greater velocity than they approach.
Vanes, black on one side and bright on the other, on which radiation falls, will be warmer on the black surface, and molecules striking them will rebound with a greater reactionary kick from the warm sides than from the cool sides, and thus produce a greater pressure on the warm sides; it is this extra pressure which sets the mill in rotation.
In this explanation it is assumed that the molecules do not very often collide with each other, that is to say that their mean free path is comparable with the dimensions of the vane. When this is the case the force is proportional to the pressure of the residual gas. If the pressure is higher, and the mean free path is small compared with the size of the vanes, the molecules after rebounding from the warm surface of the vane collide with other molecules imparting their increased energy to them, and the general temperature of the gas in the neighbourhood of the surface is raised; but this involves a reduction of the density of the gas, so that fewer molecules now strike the vane in unit time, and this reduction in the number of rebounding molecules compensates for the greater contribution of each to the pressure on the vane, so that over the central portion of the vane the pressures on both sides become equal. However, near the edge of the vane, mole cules from the hot side can collide with molecules from the cold side and the temperature will be the mean of the temperatures on the two sides ; the density near the edge will thus tend to be the same on the black as on the bright side. The greater reactionary kick of the molecules hitting the warm side is thus uncompensated by a reduction in the number of collisions. Thus when the mean free path is small, the excess pressure is confined to a narrow region round the edge of the vane, and the resultant force de pends on the length of the edge and not on the area of the vane.
The calculation of the pressure on a warm surface formed the subject of another paper by 0. Reynolds in 1876; in this he takes into account the Maxwell-Boltzman law for the partition of the energy among the degrees of freedom of the molecule. (See KINETIC THEORY.) He assumes that it has the three degrees of freedom corresponding to three mutually orthogonal directions in space, that is to say, he neglects the possibility of spin of a mole cule or of any internal vibratory motion. He shows the close con nection between thermal transpiration and the radiometer effect, and proves that slip of the gas over the surface of the vane must play an important part in the action of the radiometer. Such slipping had been observed by A. A. Kundt and E. G. Warburg in 1875 in their work on the viscosity of gases. He concluded that the pressure was proportional to the rate of divergence of the lines of heat flow : if these are parallel there is no excess pressure ; where they diverge there is an excess pressure.