1915-1916.] Explanation of the Satellites of Spectral Lines. 199 
X.— On a Possible Explanation of the Satellites of Spectral Lines. 
By R. A. Houstoun, M.A., Ph.D., D.Sc., Lecturer on Physical 
Optics in the University of Glasgow. 
It is well known that, when examined with a modern high-power spectro- 
scope, the bright lines in the spectra of the different elements exhibit an 
individual character. Some are diffuse, some are sharp, some are diffuse 
on the one side and sharp on the other, and some are accompanied by 
fainter lines in their neighbourhood. To the latter the name of satellites 
has been given. The most celebrated satellites are those of the green line of 
mercury, which have been investigated very often owing to the ease with 
which the mercury spectrum can be produced. They are much fainter 
than the main line, and at least six can be seen. But there are cases 
occurring in which a satellite is so strong that it is hardly possible to say 
which is the main line. Thus the red line of hydrogen is a close doublet 
with a separation of T4 A.U., the two components of the doublet being of 
approximately equal brightness. 
The purpose of this short paper is to suggest that satellites may in 
some cases be caused by sudden changes of amplitude or phase in an 
oscillator of one definite period. The explanation is interesting principally 
on account of the use it makes of certain well-known diffraction formulae. 
Let us suppose that an oscillator is emitting a wave given by cos /3t, 
and that the wave starts suddenly when t = 0 , and stops suddenly when t = l. 
Then, expanding the wave in a Fourier integral, we have 
typical unlimited wave being given by 2ir/a. It is clear, however, from 
the denominator of the first term, that in the integration the only waves of 
(MS. received April 24, 1916. Read May 15, 1916.) 
I da I [cos{(a -/3)g-atj + COs{(a + fil)g - at}]dg 
1 f°° sill |(a — /3)/cos{J(a — /3)l— at) sin |(a + /3)l cosj |(a + [3)1 - aG 
Thus the orginal limited cosine wave of period 2i rj/3 is equal to the super- 
position of an infinite number of unlimited cosine waves, the period of the 
