'2n 



We are aware that this formuLa does not hold exactl}'' for iion- 

 homogeiieous media, nor for oblique directions when simply replacing 

 c by z sec 6 ; but as a first approximation we shall put 



9 



2 -\- sz sec 6 



where J and ,/„ now bear on units of surface located in the layers 

 PP' and CC' respectively, and taken perpendicular to the direction 

 considered. Supposing ./„ to be independent of direction, we find 

 that ./ decreases as 6 increases, in agreement with the characteristic 

 of the iri'adiation surface ^). 



One of the causes whj- the latter equation cannot be expected 

 to represent the conditions completely is, that it does not allow for 

 possible incurvation of the direct beams passing tlirough the medium. 

 If S appi'oaches the value 90°, our formula makes .7 tend toward 

 zero, whereas in reality the brightness at the limb only falls to values 

 between 0,13 Jo = o and 0,30 ./(/ = o with ditferent colours. 



Now, it is evident that refraction by the irregular density gradients 

 at once accounts for the discrepancy ; indeed, a beam reaching M 

 along NM [6 nearly = 90°) might have been turned into that 

 direction out of another direction F' W for which 6 has a smaller 

 value, so that ./ will have a greater value than the one corresponding 

 to the formula. It is exactly this process on which our explanation 

 of the sun's edge was based. 



If, therefore, Ave consider both scattering and irregular refraction 

 effects, the conclusion!-; to which the Iheoi-y leads are compatible 

 \\'\\\\ the observed shape of the irradiation surface, or with the law 

 according to which the average intensity of a given kind of light 

 decreases from the centre toward the limb of the solar disk. 



The agreement also prevails wheii kinds of light of different, 

 wave-lengths are considei'ed. Let us distinguish between, e.g., red 

 and violet, by introducing the subscripts r and v. 



') A full comparison of tlie llieorelicnl wilii Ihc ol)servalioni»l Jnadialion sur- 

 faces for different wave lengths will be piil)lislie(l at a later dale. If 2 cos © may 

 be neglected as compared willi «2, the expression Ijccomes 



2 

 J—J^^cosS , 



BZ 



the equation of a sphere, tangent to the photoplieric level in Ji. The irridiation- 

 surface, as constructed with the values for violet light taken from H. G. Vogel's 

 well-known table (Ber. der Berl. Akad. 1877, p. 104), is in its main part strikingly 

 similar to such a sphere. 



