﻿Widening of Spectrum Lines. 281 



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 trans- 

 latory 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 tempe- 

 ratures 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 ail 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 re- 

 lating 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 some- 

 thing 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 Schonrock j\ The 

 Fourier analysis of the limited train of waves of length r 

 gives for the intensity of various parts of the spectrum line 



£- 2 sin 2 (7rr£), (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. 



* Phil. Trans. A. vol. cxcv. p. 346 (1899). See also Proc, Roy, Soc. 



vol. lxxvi, A. p. 440 (1905) ; Scientific Tapers, vol. v. p. lY>7. 

 f Ann. der Phrjsik, vol. xxii. p. 209 (1907). ' 



