The limit of resolving power which can be used in the investigation of the fine structure of a spectral line depends upon the half-value width of the components. In the absence of electric fields, magnetic fields or pressure broadening, the half-value width of a line is a function of the temperature and the molecular (or atomic) weight of the radiating gas. The molecules possess velocities in random directions, and, as a result of the Doppler effect, small variations occur in the wave-length of the radiation according to the velocity and direction of the radiating molecule, or atom. It can be shown by the gas kinetic theory that owing to this random Doppler effect the half-value width of a line is equal to approximately λ x 10-6 x √θ/M, where M is the molecular, or atomic weight of the radiating substance and θ is its absolute temperature. The greatest resolving power which can be achieved is therefore equal to 106 x √M/θ. For a given substance M is constant and θ alone can be varied; and in order to resolve the finest separations it is necessary to make θ as small as possible. By making use of the sputtering of metals in the neighbourhood of a hollow cathode, Schueler was able to observe the spectra of atoms at the temperature of liquid air, the spectra obtained being of very great intensity although the vapour pressures of the metals at that temperature are vanishingly small. By this method he was able to resolve the resonance lines of sodium, finding each line to consist of two extremely close hyperfine structure components; the half width of the lines was rather less than half of that which it would be if the spectrum of sodium vapour, at very l;ow pressure, were observed. By this method it is therefore possible to reduce the half-value of lines of the more volatile metals by a factor of two, and of the less volatile metals by a factor of three. Unfortunately this appears to be the limit of the method. On account of the heat generated by the discharge and the losses due to heat conduction, a very great quantity of liquid air is consumed so that it is improbable that the temperature could be further reduced by cooling with liquid hydrogen. Moreover, even if this were possible, the Doppler width of the lines would only be reduced by an additional factor of two, the mean velocity of molecules decreasing as the square root of the temperature.