( 587 ) 
fore, originate not, it is true, from the most luminous centre, but 
yet from pretty intensely radiating parts of the sun. They yield the 
white light of the umbra and of the penumbra, which though stan- 
ding out dark against the other parts of the sun, yet are relatively 
bright enough. 
Slight irregularities in the distribution of density around P render 
it possible that parallel to PA there emerge rays that have followed 
other paths which, nevertheless, will essentially be included in the 
solid angle Ps. 
But rays which have undergone anomalous dispersion and yet 
reach our eye in a direction parallel to PA, must have proceeded 
from a much greater diversity of directions and need not, therefore, 
have been emitted in such numbers by the intensely luminous 
central part of the sun. 
We may also put the matter thus: Of all the light, coming from 
the intensely radiating nucleus of the sun (to which may be reckoned 
all that lies within the sphere N) and emerging from the vicinity 
of P, those rays, whose refractive index is abnormally high or low, 
will be more effectually dispersed in all directions, owing to the 
local differences of density, than rays with a normal index. 
The consequence is that the observer looking in a given direction 
towards P, will see less of those abnormally refracted rays than of 
the other light. Those rays will, therefore, seem absent in the 
spectrum of the spot: the FRAUNHOFER line is seen broadened. 
Whereas our considerations concerning the chromosphere light 
were made independent of any theory of the nature of the photo- 
sphere, the present broadly outlined explanation of the phenomenon 
of the sun-spots is to a certain extent based on the theory of 
SCHMIDT — with which, in fact, it stands or falls. 
If subsequent investigations should prove the lines that mostly 
appear broadened in the spectra of the spots, and those which call 
forth strong anomalous dispersion, to be identical, this would support 
SCHMIDT's solar theory. 
For the rest it is easy to see that henceforth the principle of 
anomalous refraction will have to be considered side by side with 
that of DoPPLER in every instance when an explanation is required 
of the many irreguiarities that have been observed in certain 
FRAUNHOFER lines both near the sun’s limb and in faculae and 
spots; cf. the illustrations in LockyeEr’s Chemistry of the Sun 
pp. 122 and 123. Youne, The Sun, pp. 157 and 210. ScurrineR 
“Die Spectralanalyse der Gestirne’, p. 349, 
