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differences of density dependent on strong vertical currents or, accord- 
ing to Fays, on vortex movements in the atmosphere. The pheno- 
menon is commonly localized in the level of the fotosphere, at all 
events, not far above or below it. Now if the total body situated 
within the photosphere, actually forms a sharp contrast with the outer 
atmosphere and if its surface radiates to every side an almost equally 
intense light with a continuous spectrum, the broadening of the 
FRAUNHOFER lines and the darkness of the spots cannot be accounted 
for by merely attributing the spots to differences of density. The 
phenomenon must then be set down to differences of temperature, 
smaller radiating power, condensation, stronger absorption, ete. 
Matters are different, however, if A. Scumipt’s view is taken to 
be the correct one, according to which the sun’s limb is an optical 
illusion caused by regular refraction in a gradually dispersing, 
nowhere sharply bounded mass of gas. In this theory the apparent 
surface of the photosphere is merely a critical sphere, characterized 
by its radius being equal to the radius of curvature of rays of light 
travelling along its surface horizontally; there is not the least 
question of any discontinuity in the distribution of matter on either 
side of this spherical surface; inside as well as outside the critical 
sphere the average density of 
matter and its radiating power 
increase gradually towards the 
centre and it is only at great 
depths that the condition of matter 
need be such as to emit a con- 
tinuous spectrum. 
Let the circle ZZ' in the dia- 
gram be the section of the critical 
sphere with the ecliptic, and let 
the earth be in the direction MA. 
Suppose a spot visible in the centre 
of the sun’s disc; it is seen projected 
on the critical sphere in P. Now let 
us suppose that the density increases 
all around from the centre P of 
the spot, locally producing there 
cylindrical, rather coaxial layers 
with the line of vision for basis. 
Rays pA and qA suffering nor- 
Fig. 5. mal refraction, may, as is easily 
seen, have traversed in the sun the paths rp, sq and may, there- 
