( 218 ) 



The comparison, however, is entirely misleading, because, so far, 

 an essential relation between absolute size and density gradients is 

 overlooked in it. But if carried through properly, it will lead us 

 to the opposite conclusion, namely that refraction in the solar 

 atmosphere must alter the distribution of the light on the disk 

 entirely. 



If we wish to form an image, on a reduced scale, of the sun 

 considered as a refracting body, we have to reduce the radii of 

 curvature of the rays in the same proportion as we do the diameter, 

 for instance 10 10 times (so as to make the diameter of the photos- 

 phere 14 cm.). By the general equation ! ) 



dL _ 1 

 ds Rq 

 we know that, for a given value of the refraction constant R, the 

 radius of curvature q of a beam of light is in reverse proportion 



dL 

 to the density gradient — in the direction toward the centre of 



ds 



curvature. In our image, therefore, the density gradients have to 



be taken 10 10 times as great as they are in the sun. 



Let us suppose that at a certain level in the solar atmosphere 



irregular density gradients occur, which are of the same order of 



magnitude as the radial (vertical) density gradient in our earth's 



atmosphere, viz. 16 X I** 10 *)■ At the corresponding points in our 



dL 

 image we then have to put — = 16. If the layer of "varnish" 



ds 



were really traversed by many density gradients of this order of 



magnitude, it would be very different from ordinary transparent 



varnish, and certainly be able to disturb the uniform brightness 



of the background, like a layer of glass beads or swollen sago 



grains. Even normally refracted waves would perceptibly deviate 



in an envelope of this kind. For if in our equation (1) we put 



n— 1 dL 



== R = 0,5 and — =16, we get o = 0.125 cm., so that the 



A ds 6 N 



average curvature of such rays is already sufficient for producing 

 sensible changes in the divergence of beams on their way through 

 a shell not thicker than 0.1 cm. 



!) Proc. Roy. Acad. Amsterdam, IX, p. 352. (1906). 



2 ) The frequent occurrence of density gradients nearly perpendicular to the 

 radii of the sun is rendered more probable still, since increasing evidence has 

 been obtained by Prof. Hale of the existence of solar vortices, in which the con- 

 vection currents (especially in sun-spots) are sufficiently strong to produce magnetic 

 splitting of absorption lines. (Gf. Nature, Vol. 78, p. 368—370, Aug. 1908), 



