( 269 ) 
must be very small near te edge m„ from whence only rays, not 
coming from 'the photosphere, can reach the observer. 
Our rarefied region, though perfectly transparent, thus looks like 
an object emitting at the left side less, at the right more light than 
the back-ground. , 
If in those parts of the atmosphere, which surround our rarefac¬ 
tion, the density were not perfectly uniform, the distribution of the 
brightness within the region considered would be modified, to be sure, 
but not so much as to change the main character of our result. 
From case A we deduce as a general rule: 
A relatively small region in the solar atmosphere, where the density 
passes through a minimum, and which, as seen from the earth, is 
projected excentrically on the solar disk, will show darker than the 
surroundings on the side opposite the centre of the disk, and may be 
brighter than the surroundings on the side facing the centre, the latter 
peculiarity however requiring, that the distance from the centre be not 
too small. V‘ " 
If the rarefaction is projected near the centre of the disk, it will 
show a dark rim on all sides. 
Let us now consider the course of the light through a small 
region, enclosing a maximum of density (case B, fig. 2). Again the 
rays bend in such a way that their concave side is turned toward 
the places of greater optical density, that is, now, towards M. x ) 
Examined from N, the region round M gives the impression as it 
there were an object, emitting at the left side more, at the right 
side less light than the back-ground. 
From case B we deduce the rule: 
A relatively small region in the solar atmosphere, where the den¬ 
sity passes through a maximum, and which is seen excentrical on the 
solar disk, will show darker than the surroundings on the side facing 
the centre of the disk, and may be brighter than the surroundings 
on the side opposite the centre, provided the distance from the centre 
be not too small. 
If the condensation is projected near the centre of the disk, it will 
show a dark rim on all sides. 
In our scheme we supposed the region of smaller or of greater 
optical density to be approximately spherical. In order to make sure 
whether the above rules always represent the main character of the 
H If in both cases A and B the density gradients had the same absolute values, 
the rays would generally change their direction more in B than in A, because in 
B they are curved in the same sense as the levels of equal density, and therefore 
havel a longer way through the non-homogeneous region. 
