270 



deviated by irregular gradients of' optical density be about 9 times 



greater in Q than in P. (Even a smaller ratio would probably 



suffice). There will then appear a circular boundary between P and 



Q, lying in a plane through the sun's centre perpendicular to the 



line of sight, but there is no particular "solar surface" corresponding 



to it. ^) 



In a level P just inside the apparent photosphere the average 



value of o may still be of the order of magnitude 10^" cm. We 



can easily show that to such curvatures of rays correspond quite 



reasonable density gradients. F'or if we suppose hydrogen to be a 



principal constituent of the visible layers, the average refraction- 



'* — 1 

 constant /i? = — — ot the medium may be estimated at 1.5. Putting 



this value, and o =i iO'", into the relation *) 



./A_ 1 



(is Rq » 



we obtain the density -gradient 6 X 10-", which means that in two 

 points one kilometer (10* cm.) distant from each other the density 

 OJily differs 0,000006, i.e. 0,5 7o of the density of our terrestrial 

 atmosphere. It would be very remarkable indeed, if the general 

 circulation in the sun did not bring along local differences of tempe- 

 rature and of composition sufficient to account for density gradients 



M At first sight one might bo inclined to think that tlie boundary llius defined 

 lias tlic same radius as Schmidt's critical sphere would have. On closer examina- 

 tion, however, the two notions appear to be entirely different. This is clearly 

 brought out with the aid of l)>e following analogous conception. Imagine a 

 spherical mass of liquid (radius R) of constant average optical density, and, as a 

 source of light in the middle of it, an incandescent lump provided with a big globe 

 of milky glass. As there is no radial density-gradient, a critical sphere in the 

 sense of Sch[MDt's theory could not appear in that medium. Let llie liquid be a 

 mixture of a solution of common salt and a solution of glycerine in water, both 

 solutions having the same specific weight but difïerent refracting power (cf. Physik. 

 Zeilschr. 11, 59, 1910). If we now suppose that only in the outer spherical shell 

 (radii R and -^^ R) the solutions are completely mixed, whereas in the inner 

 shell, surrounding the luminous globe, ths liquids are only stirred, but still 

 honeycombed with irregular gradients of optical density — the average optical 

 density of the shells being the same — then the inner shell will seem to be a 

 self-luminous body. Tb.e origin of its boundary is comparable with that of the 

 solar limb according to our theory. 



The above interpretation of the photosphere evidently involves an explanation 

 of the reversing layer and the chromosphere as soon as we take account of 

 anomalous dispersion. On this subject, however, we shall not expatiate in the 

 present paper. 



2) Cf. these Proceedings IX, p. 352, 1907. 



