524 Proceedings of Royal Society of Edinburgh. [sess. 
of cooling by expansion, are at a lower temperature than the 
photosphere, absorption-lines, characteristic of the substances of 
the atmosphere, appear in the otherwise continuous photospheric 
spectrum. But since all these atmospheric particles move towards 
us, their lines must be displaced towards the more refrangible side 
of the spectrum, in accordance with Doppler’s principle. Now, 
it will be noticed that, in whatever direction we may look at 
the star, i.e. in whatever part of space the observer may be 
stationed, the phenomenon will always be the same. The dis- 
placement of the absorption-lines towards the more refrangible 
side of the spectrum is therefore a general feature peculiar to all 
stars possessing expanding atmospheres. 
There are two reasons why these absorption-lines, instead of 
being narrow and sharply defined, as in normal star spectra, 
should be broad and hazy. Firstly, the motions of the gaseous 
particles towards us are not uniform. We may take it for certain 
that considerable differences must exist in the amount and 
direction of these motions which would tend to broaden the 
lines. Secondly, the density of the atmosphere near the surface 
may be considerable, especially during the first stages of the 
star’s development. We know that from this cause, too, a 
broadening of the lines may be expected. Considering the 
doubtless violent character of the catastrophe, we may also safely 
conclude that the broadening due to the causes mentioned must 
have been considerable. 
We now turn our attention to the radiations emanating 
from those parts of the expanding atmosphere lying inside the 
segments D B C and D' B' C'. Obviously the spectrum produced 
by these radiations must show bright lines, characteristic of the 
same substances which cause the absorption spectrum in front of 
the star. But since in this case there are as many motions towards 
as from us, the centres of these lines — which are also broad and 
hazy, owing to the effects of density and divergence of directions 
— must appear in their normal positions. 
In consequence of the great distance of the star, the two spectra 
are superimposed upon one another in the spectroscope. We see, 
therefore, a double spectrum, consisting of broad bright lines in 
approximately normal positions, edged on their more refrangible 
