339 



middle-point becotiies tlie zei'o in out' scale of /-values. If the 

 distance between the lines is 2A, we have in the new notation: 

 I, =^ A for the line on the red side, /, ^ — A for the line on the 

 violet side, and we get, in analogy with (2), the relation 



»-'=iéi+rb + <»■-■' c) 



For each of the lines we may again define two "/:/-bonndaries", 

 to be found by taking (6) eqnal to ± H, wherein H has the value 

 fixed by the relation (5). 



We consider the red-facing line of the pair. Its //-bonndaries 

 Ir and /[' are foimd by snbstituting in (6; H for n — 1, /« or ly 

 for /. We thus obtain, according as the -|- sign or the — sign is 

 chosen : 



Ijt or lv= h / 1 A' = SR-ir Tii 



or Sv+Ty. (7) 

 Similarly it follows, that the violet-facing component of our pair 

 has for its //-boundaries 



Ir or ly=SR—TR or Sy—Ty (7a) 



^ 2. Refraction lines in the spectrum of the limb of the solar disk. 



Seen in the light of the dispersion theory, the widening of the 

 Fraunhofer lines in the specti-nin of the limb is due to the fact, 

 that near the limb smaller values ± H' of ?t — 1 are already suffi- 

 cient for producing the same relative darkening, which in the central 

 parts of the disk is only produced by the greater values ± H. 

 The //'-width, shown by the line at the limb, will be called B' . 

 As a counterpart of (5) we now obtain the relation 



k I y k' 



and, in the case of two limb-lines, as counterparts of (7) and {7a) : 



k I y p 



in or ry= h / 1- ^' = S'r + T'r 



±//'-(n.-l)^l/ l±H'-in-\)y^ H-r H 



or S'y+T'y (9) 

 I'r OT l'y= S'r- T'u or S'y-T'^' .... (9a) 



^ 3. Theoretical possibility of a general solution of our problem. 



In principle, the formulae (5), (7), (8), and (9) embody a rather 



complete answer to Ihe queslion how, on the basis of the dispersion 



