268 



of' gravitation, prevails tlirontiliout the visible layers of the siin, is 

 certainly not less plausible, therefore, than the exclusive hypothesis, 

 usually admitted, which maizes gravitation the only effective agent 

 in determining the radial gradient ^). 



^ 2. We must now endeavour to concei\e the appearance of the 

 sun's edge in a transparent gaseous medium where the pressure 

 varies but slowly along the radius. 



As already remarked, Schmidt's ingenious optical explanation 

 cannot be adhered to. Nevertheless the jtrinciple of ray-cur\ing 

 introduced by that author is extremely suggestive; it leads to the 

 following interpretation of the solar liml), which appears not to 

 encounter similar difficulties. 



Let fig. 2 represent an equatorial, section of the sun. It can hardly 

 be doubted that besides the gradual, perhaps slow variation of oi)lical 

 density corresponding te the outward decretise of pressure, there are 

 many irre^/ular optical density yradients connected not only with the 

 local differences of pressure that accompany the convection cuirents 

 and solar vortices, but also with the diflerences of temperature and 

 of composition occurring in the gaseous mixture. 



Now, the average magnitude of those irregular gradients of optical 

 density will very probably decrease as we proceed from a le\el P 

 toward a level Q. 



Let us imagine the "'irradiation surfaces" to be constructed for a 

 point Pj of the level P and for a point Q^^ of Q. At the level Q the 

 irregular gradients may in general be so small that rays, leaving it 

 along a tangent Q^E in the direction of the earth, are hardly ever 

 sufficiently curved to be the continuation of rays coming from within 

 the irradiation surface of Q^ . This condition will obtain if the average 

 radius of curvature of ravs tangent to the level Q is more tlian, 



1) In the Asti-ophysical Journal 31, p. Iü6 (1010) Mr. J. A. Andersüx has 

 criticized the conclusions arrived at in my paper ''Regular Consequences ot Irregular 

 Refraction in the Sun" (Proe. Koy. Acad. Amst. Oct. 28, 1909). His refutation of 

 the idea that i-efraction miglit be very momentous in solar physics is entirely 

 founded on the following two assumptions: 1. the photosphere may be represented 

 by a perfectly uniform self-luminous surface, radiating approximately according to 

 the cosine law, and 2. on the sun tlie weight of a gas is 27.3 times as great as 

 on the earth. I think, we may now safely slate that the first assumption is con- 

 trary to observed facts, and that the second assumption is an unproved dogma, 

 subject to well-founded doubts. 



Moreover, a very important point, overlooked by Mr. Axdeesox is, that consi- 

 derable optical density gradients may result from differences of temperature or of 

 composition, even at uniform pressure. 



