( ■■^5'! ) 



to the radius of curvature of luminous rays whose patii is horizontal 

 at a point of its surface. Tliis radius of curvature is. consequently 

 Q = 7 X lO'o cms., a value which we may introduce into the expres- 

 sion for the density gradient -. 



dA _ 1 

 ds Rq 

 The refractive equivalent R for rays that undergo no anomalous 

 dispersion varies with different substances, to be sure; hut in an 

 approximate calculation we may put R = 0,5. Then at the height of 

 the critical sphere we shall have : 



dL 1 



0.29 X lO-'o, 



ds 0.5 X 7 X lO'o 

 (this is 50 times less than the density gradient in our atmosphere). 

 All arguments supporting Schmidt's explanation of the sun's limb, 

 are at the same time in favour of this estimate of the radial density 

 gradient in the gaseous mixture. 



Let us now consider rays that do undergo anomalous dispersion. 

 In order that e.g. light, the wave-length of which differs but very 

 little from that of one of the sodium lines, may seem to come from 

 points situated some arc seconds outside the sun's limb, the radius 

 of curvature of such anomalously bent rays need only be slightly 

 smaller than 7 x 10'*^ cms. Let us e.g. put 



9' = 6 X iOio cm. 



If we further assume that of the kind of light under consideration 

 the wave-length is (\4 Angstrom-units greater than that of JJ^, then 

 for this kind of light R'=:^QOO, as may be derived from the obser- 

 vations of Wool) and of Jewett ^) ; we thus find for the density 

 gradient of the sodium vapour 



— = — — = 0.0001 X 10-10, 



ds R'q' 1600 X 6 X l<->'^ 



a quantity, 2900 times smaller than the density gradient of the 



gaseous mixture. 



Hence if only part of the caseous mixture consists of sodium 



" 3000 



vapour, then, on account of the radial density gradient, the critical 



sphere will already seem to be surrounded by a "chromosphere" of 



light, this light having a striking resemblance with sodium light. This 



kind of light has, so to say, its own critical sphere which is larger 



than the critical sphere of the not anomalously refracted light. If the 



1) See page 352. 



