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ON  THE  WIDENING  OF  SPECTEUM  LINES                           297
widely held this cause should be more potent than (i). The transverse vibrations emitted from a luminous source cannot be uniform in all directions, and the effect perceived in a fixed direction from a rotating source cannot in general be simple harmonic. In illustration it may suffice to mention the case of a bell vibrating in four segments and rotating about the axis of symmetry. The sound received by a stationary observer is intermittent and therefore not homogeneous. On the principle of equipartition of energy between translatory and rotatory motions, and from the circumstance that the dimensions of molecules are much less than optical wave-lengths, it followed that the loss of homogeneity from (ii) was much greater than from (i). I had in view diatomic molecules  for at that time mercury vapour was the only known exception ; and the specific heats at ordinary temperatures showed that two of the possible three rotations actually occurred in accordance with equipartition of energy. It is now abundantly clear that the widening of spectrum lines at present under consideration does not in fact occur ; and the difficulty that might be felt is largely met when we accept Schonrock's supposition that the radiating centres are in all cases monatomic. Still there are questions remaining behind. Do the atoms rotate, and if not, why not ? I suppose that the quantum theory would help here, but it may be noticed that the question is not merely of acquiring rotation. A permanent rotation, not susceptible of alteration, should apparently make itself felt. These are problems relating to the constitution of the atom and the nature of radiation, which I do not venture further to touch upon.
The third cause of widening is the disturbance of free vibration due to encounters with other bodies. That something of this kind is to be expected has long been recognized, and it would seem that the widening of the D lines when more than a very little soda is present in a Bunsen flame can hardly be accounted for otherwise. The simplest supposition open to us is that an entirely fresh start is made at each collision, so that we have to deal with a series of regular vibrations limited at both ends. The problem thus arising has been treated by Godfrey* and by Schonrockf. The Fourier analysis of the limited train of waves of length r gives for the intensity of various parts of the spectrum line
.............................. (19)
where k is the reciprocal of the wave-length, measured from the centre of the line. In the application to radiating vapours, integrations are required with respect to r.
Calculations of this kind serve as illustrations ; but it is not to be supposed that they can represent the facts at all completely.    There must surely
* Phil. Trans. A. Vol. oxcv. p. 346 (1899). See also Proc. Roy. Soc. Vol. LXXVI. A. p. 440 (1905) ; Scientific Papers, Vol. v. p. 257.
h Ann. der Physik, Vol. xxft. p. 209 (1907).chemical questions involved are very obscure. The coloration with soda ap to require the presence of oxygen (Mitcherlich, Smithells).