While the band spectra with a spectroscope of high resolving power can be more or less completely resolved into lines, this is not the case with the _continuous spectra_. They are emitted not only by glowing solids (cf. p. 54), but also by many gaseous substances. When such gases are exposed to electric discharges they emit, in addition to the line spectra and band spectra, continuous spectra which in certain parts of the spectrum furnish a background for bright lines which come out more strongly. It might seem impossible to correlate these with the Bohr theory; but in reality a spectrum does not always have to consist of sharp lines. This can at once be seen from the correspondence principle. If the motions in the stationary states are of such nature that they can be resolved into a number of discrete harmonic oscillations each with its own period (for instance the orbit of an electron in a rotating ellipse; cf. p. 149), then, according to the correspondence principle, in the transition between two such stationary states there are produced sharp spectral lines “corresponding” to these harmonic components. But not all motions of atomic systems can be thus resolved into a number of definite harmonic oscillations. When this cannot be done, the stationary states cannot be expected to be such that transitions between them produce radiation which can be resolved into sharp lines. A simple example, where it is easily intelligible that the Bohr theory will not lead to sharp lines, is obtained in a simple consideration of the hydrogen atom. Let us examine the lines belonging to the Balmer series which are produced when an electron passes to the No. 2 orbit from an orbit with higher orbit number, which is farther from the nucleus. As has been said, we obtain here an upper limit for the frequency corresponding to a value of the outer orbit number which is infinite; this means, in reality, that the electron in one jump comes in from a distance so great that the attraction of the nucleus is infinitely small. The energy released by such a jump is the same as the ionizing energy A₂ which is required to eject the electron from the orbit No. 2 and drive it from the atom. It is here assumed, however, that the electron out in the distance was practically at rest. If the captured electron has a certain initial velocity outside, it will have a corresponding kinetic energy A. When in one jump this electron comes from the outside into orbit No. 2, the energy lost by the electron and emitted in the form of radiation will be the sum of the ionizing energy A₂ and the original kinetic energy A. The frequency ν will then become greater than that corresponding to A₂; and since the velocity of the electron before it is captured is not restricted to certain definite values, neither is the value of ν. The radiation from a great quantity of hydrogen atoms which are binding electrons in this way will, in the spectrum, not be concentrated in certain lines, but will