202 Proceedings of the Royal Society of Edinburgh. [Sess. 
question as to whether a Fraunhofer diffraction pattern can be produced 
having the structure of the line. This will be best solved by trial, by fixing 
an arrangement of slits on the table of a spectrometer so that the rays 
from the collimator fall on them normally, and examining the appearance 
seen in the telescope. As bright a sodium flame as possible should be used 
as source, and there should be some means of setting the slits accurately 
parallel to the slit of the collimator. 
The question arises as to how the broadening of the line due to the 
train being limited is related to the other causes of broadening of a spectral 
line. The whole question of the widening of spectral lines has been recently 
considered by Lord Rayleigh.* He comes to the conclusion that at low 
pressures, when the line is narrow, its width is due solely to the Doppler 
effect, but at high pressures the influence of impacts becomes apparent. The 
impacts produce sudden changes in the phase and intensity of the vibrations, 
and the method of taking account of such changes is to represent the 
vibration by a Fourier integral, as has been done here. To explain the 
occurrence of satellites, however, we cannot rely on the random impacts of 
molecules or atoms. The change of phase postulated must be due to some- 
thing in the atom itself, something inseparable from the process of radiation 
from the atom. For example, in the third case considered above, after the 
oscillator has acted for time l , it must rest for k and then act again for l. 
It next rests for an interval which must be determined by chance, and then 
goes through its cycle again. Superimposed on the cycle of changes there 
are of course irregular changes due possibly to impact, and these cause the 
widening of the line at high pressures. Lord Rayleigh considers that, 
although it is certain that damping of the vibrations must operate as a 
cause of widening, we cannot at the present time point to any experimental 
verification of its influence. 
The objection that may be urged against the suggestion put forward in 
this paper is, that it is incompatible with the high path difference at which 
interference can be observed in the case of monochromatic radiations. 
Michelson obtained interference with the green line of mercury when there 
was a path difference of 540,000 wave-lengths. This seems to require no 
change of phase for 540,000 periods, a number that would bring the 
attendant lines much closer in than is required for the satellites, i.e. if we 
use the result for the first of our three cases. I do not consider that the 
objection is a fatal one. 
In any case, the possibility of successive stages in the emission of an 
* “On the Widening of Spectrum Lines,” Phil. Mag., xxix, p. 274, 1915. 
