118 



df df df . . u'/cosO-df ÖV' 1 öy\ 



^ cos if 4- ^ shi if cos (f: 4- -- sin ih sm (f =^ - - t^ + ;^ — ,+ .'rz:^r~i 



bx öy ' bz ' U\siniybd- di>' sirï'd'bcpy 



For the case important iii practice that ƒ only depends on x 

 and I'J consequently : 



sin i> cos v> -'- = — cos i> V- sin d^ — -^ I ') • 



For this case the boundary conditions are, if we have at x =: 

 a layer, which radiates according to tlie cosinus law and at d a 

 plane layer through which no inward-radiation takes place: 



f=c for: X = cos ih ^ 



ƒ = for : X — d cos i'> < 0. 



For »>=0 and all values of .(;: / and r^ continuous, -^=0; tor 



cos{)=zl or— 1 i-=^- 



It is worth observing that the diffusion is determined by the 



«^ 

 quantity —, i. e. the average square of diffusion per length- 

 unity. This magnitude is specific for the i)roblem, does not depend 

 upon the length, as «* is doubled in doubling the length /. The 

 magnitude is related to the nature of the irregularities. It is a 

 constant which still may be different for different layers of the sun. 

 The study of the distribution of inlensity over the disc of the sun 

 will bo able to supply us with the knowledge of the average value 

 of the char0,cteristic constant of the sun. 



Utrecht, April 1917. Institute for Theoretkud Physics. 



1) For the two dimensional problem : 



0/ «^ dV 



cos »>--=:-— - — ~ 



d.f U dd-' 



