Physics. — ''The Scntterin(] of Light hij Irreipdav Refraction in the 

 Sun". By Prof. L. S. Ounstkin ami Dr. F. Zkrnikk. 

 (Communicated by Prof. W. H. Julius). 



(Communicated in the meeting of April 27, 1917). 



By the investigation of Di-. J. Spijkkrbof.k in his dissertation 

 "Scattering of Light, and Distribntion of Intensity over the Disc of 

 the Sim", the supposition of Julius '), that besides the scattering- by 

 the action of the molecules also the scattering by irregular bending 

 of rajs owing to accidental gradients of the optical density must 

 play a parr in the origin of the distribntion of light over the disc 

 of the sun, has been corroborated. 



In this paper it is our object to show, that a mathematical 

 treatment of the problem of the scattering of light by curving of rays 

 is possible. For it is possible to put up an integral-equatiou for this 

 phenomenon and to transform this with suitable and plausible 

 suppositions into a difTerential equation with boundary conditions. 



The problem treated here is the counterpart of the problem of 

 molecular ditfusion in a tlat layer of gas, which was solved by 

 ScHWARZSCHiLD. The deduction of the integral equation resembles Iiis 

 train of thoughts, but in our case we have the advantage, that the 

 peculiar nature of the problem allows that a ditFerential equation 

 can be deduced from it, whicli makes mathematical discussion so 

 much easier. It seems to us, that the irregular reflection and the 

 irregular double refraction may be treated in an analogous way, 

 which is important for the theory of the extinction of liquid crystals. 



In a medium, in which accidental gradients of the index of 

 refraction arise, a ray of light will be curved in an irregular 

 fashion. If a broad bundle of parallel rays runs through the medium, 

 the different rays will be curved in ditferent ways. And so, if the 

 bundle is broad with regard to regions of a constant index of 

 refraction, a bundle of initially parallel rays will be spread |)lume- 

 shape. Now we fix our attention on the action of a volume-element 

 on a ray, which goes in a given direction, and imagine that the 

 nature of the irregularity of the index of refraction in the medium 



1) W. H. Julius. Verslag Kon. Akacl. v. Wet. 18, 195 (1909) and 22, 04—75 (1913). 



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