The validity of an equation of the form I) with A, a and b constants and a comparable with unity is well established experimentally. In the case of tungsten it has been shown to be valid over a range of variation by I o" in the current and a corresponding range in the temperature. An earlier theoretical formula put a =1 and from an empirical point of view there is little to choose between a =-1- and a= 2 on account of the insensitivity of the factor Ta compared with the exponential term, but the formula with a= 2 is definitely required by theo retical considerations. This brings us back to equation (8), viz. : = AP , in which form A/a should have the absolute value expressed by (9). There is no doubt that for a considerable number of metals A is comparable with Whether such deviations as appear are due to the neglect of elec tron reflection I) or to other refinements which have been disregarded is at present under experimental investigation. There is, however, no reason to doubt that the major part of A is given by equation (9).
The remaining constant in equation (8), which is the only constant in the equation involving the specific properties of the material concerned, is directly related to other important physical properties of the substance. If we consider an enclosure con taining two different substances in contact and imagine an electron taken along a closed path passing through the area of contact and also outside both substances the law of conservation of energy requires that where 4)1 and /2 are the values of 4) (the quantity in equations (4) and (5) above) for each substance, V is the contact potential difference between them, P is the Peltier electromotive force at the junction and e the electronic charge. In general P is small compared with V in (io), so that if we neglect the thermoelectric terms as small compared with the others it follows from (5) that the contact potential difference (Volta effect) between two sub i2 and being the saturation current densities from the two substances at temperature T. The quantity 4o is also equal to where is least frequency of light which is able to eject electrons from the material under consideration. For all metals (ko is of the order of magnitude 4 in equivalent volts the values ranging from about 2 for the most electropositive to about 6 for the most electronegative metals.
When a current of electrons is drawn away from the surface of a hot body, each electron has to do an amount of work 4 in escaping. This involves a cooling effect of equivalent amount at the surface of the wire. There is also an equal heating effect at the surface when a stream of electrons flows into a body. These effects are precisely analogous to the cooling and heating effects caused by the more familiar evaporation and condensation of vapours. Their magnitudes have been measured and are in agree
ment with the values of 4 got from the variation of the emission with temperature.
It has been mentioned that with small retarding fields there is an electron current from hot bodies, so that the current flows in a direction opposite to that of the applied electromotive force. This is due to the fact that the electrons are emitted with defi nite initial velocities. By measuring the currents which will flow against various retarding potentials the number which have a velocity exceeding any assigned value can be ascertained. In this way it has been found that the emitted electrons have the same distribution of velocity as would have the molecules of a gas of the same molecular weight at the same temperature in accord ance with Maxwell's Law. To be precise, out of any number N emitted, the number with velocity components between 21 and u+du perpendicular to the surface is For practical purposes a thermionic source of electrons should be very refractory and preferably have a low value of 4. The refractoriness is required to ensure durability and to withstand the somewhat drastic preliminary heating treatment which is re quired to establish the necessary degree of vacuum. The best material on the score of refractoriness is tungsten, but it has a rather high 4 (about 4.5 volts). This can be reduced by mixing a small quantity of thoria with the tungsten during manufacture which by an appropriate technical treatment produces a layer of thorium over the tungsten surface. Similar effects are got by coating suitable metals with mixtures of the oxides of the alkaline earths or with the products of the decomposition of barium azide. In these cases also it is believed that the effects are due to a layer of the alkaline earth metal which develops on the surface of the supporting metal. It has also been found that tungsten, and especially oxidized tungsten, can be coated with layers of alkali metals such as potassium and caesium which are stable below a certain limiting temperature. These bodies admit of quantitative study and it is found that the effective work function 4 has a minimum value when the layer of alkali metal is approximately one atom thick. There is perhaps still some uncertainty as to the values of the work function for the pure alkali metals, but it is probable that they are higher than this minimum value. This conclusion is supported by the existence of an exactly parallel displacement of the photo-electric threshold with the compo sition of the surfaces in which the minimum value is less than that for the pure alkali metal.