273 



At the center of the disk (<9 =r 0) we liave between the intensities 

 of red and violet light the [)ropoi'tion 



Jr Jo,r ^ + S^,Z 



Po '1' ~r • 9 ' 



in which, according to Rayleigh's formula, s„ ]> .sv (if cases of ano- 

 malous dispersion be excluded, so that the disparity between n,. and 

 iir may be neglected). 



At a point, corresponding to the angle 6, we have 



Jo,r 2 4- Si,z sec 6 

 Jo^y 2i -{- s,-z sec 6 



The second factor of p^ is greater than unity, and pf^ is greater 

 than Po- This means, that the longer waves preponderate as we move 

 from the center of the disk tOAvard the limb. With increasing values 

 of sec 0, pg approaches the limit 



*^o,r Sy '^ o,r ^r 



this proportion, however, will be more or less modified by irre- 

 gular refraction. 



§ 4. Taking all in all, the above theory of the photosphere thus 

 appears to account for the sun's edge, and for the principal features 

 of the results of Vogkl's well-known spectrophotometric measurements. 



It implies at the same time an interpretation of the granular 

 structure of the solar disk as an effect of refraction. If Anderson ^) 

 and other astrophysicists were right in assuming the irradiation 

 surface of a point M near the photospheric level to be a hemisphere 

 sps^ (Fig. J p. 266), irregular gradients of optical density could not 

 produce any sensible disturbance in the uniform brightness of the 

 disk, except in special cases. But their assumption certainly is 

 erroneous ; the average intensity of the light passing through M varies 

 considerably with the value of the angle 6 ; so the irregular refraction 

 of the light must necessarily result in variegation of luminosity. 



Waves that undergo anomalous refraction will of course be deviated 

 to a higher degree in the same gradients. Following out this line 

 of thought, we arrive at explanations of spectroheliograph results ^), 

 on which we shall not now insist. 



A few remarks may be added in connection with the sun-spot 



1) Astroph. Journal 31, 166 (1910). 



2) Gf. Astroph. Journal, 21, 278, 1905; 28, 360, 1908; 31, 419, 1910. 



18 

 Proceedings Royal Acad Amsteidam. Vol. XVI 



