( 268 ) 
0,5, and therefore, even if that gas occupies only a small percentage, 
in the mixture, so that its density gradients too are hut a small 
percentage of those of the atmosphere, even then the light in question 
will be more strongly curved than normally refracted rays. Its radii 
of curvature will be very small indeed as compared with the radius 
of the photosphere; and much lesser gradients than the one assumed 
would already suffice to produce very marked refraction effects with 
such waves. 
On the influence of a local rarefaction or condensation in the 
solar atmosphere on the distribution of the transmitted, light. 
In fig. 1 (PI. I) SS' represents a part of a central section of the 
photospheric surface. Whether in that surface we meet with a 
physical discontinuity in the condition of matter, or not, is of little 
consequence in the following argument. Perfectly opaque it is not 
likely to be; so we may safely presume that an external point M 
receives more light along the direction ah than along other directions 
cd, efl gh. x ) Let an observer be stationed at a great distance in iV. 
We imagine the atmosphere SQQ'S' to have a uniform density 
throughout, except in the neighbourhood of M. At that point the 
density may be a minimum (case A) or a maximum (case B), and 
from there gradually pass to the uniform value on all sides. Let us 
suppose the gradient to be greatest in the space between the two 
little circles. Fig. 1 refers to case A. Rays leaving the surroundings 
of M in the direction MJSf have suffered an incurvation there, the 
concave side of which faces the regions of greater optical density, 
and, therefore, is turned away from M. From a distant point iV 
one will observe a certain distribution of brightness, determined 
I- by direction and magnitude of the density gradients, and 2. by 
direction and intensity of the light entering our region of unequal 
density. A rigorous solution would require a knowledge of the 
density in each point, and of the intensity corresponding to each 
direction of incidence; but it is not difficult to discern, that the main 
result must always be ae follows: In the middle the rarefied region 
siows the intensity of the back-ground as seen in the direction/?; 
towards the edge m t the brightness will first increase, because we 
meet with rays emerging radially from the photosphere (direction ab);~ 
uil leron it will perhaps decrease (direction cd)-, but it certainly 
\' Th t ' S presum ption is supported by eonsiderations to be stated afterwards (cf. 
the foot note oil p. 280 ). 
