341 



their greater darkness remain almost stationary. The point midway 

 between the boundaries will, therefore, by its position depict all 

 asymmetrical distortions of the dispersion line somewhat exaggerated 

 in comparison with the "centre of gravity" instinctively used by 

 the observer to identity the place of the line. If, therefore, we 

 calcniate the displacements of that mldivay jwint, we are sure to 

 find upper limits for the displacements which, according to the 

 dispersion theory, ma^' be expected as tlio result of measurements. 



§ 5. The difference in mutual infiitence of refraction lines at the 

 limb and in the centre of the disk. 



It is easily seen that the midway point Mjj between the H- 

 boundaries of the red-facing displaced refraction line is determined 

 by the absciss 



Im=^^I^{Ir-[-Iv)^'U{Sr-\-Sv-^Tr^T\') in the centre-spectrum, 

 and by (10) 



l'il^'IAi'R+lv) = 'IASR + S'v-\-T'H-\-ry) in the limb-spectrum, 



so that the amount of its displacement, when passing from centre 

 to limb, is: 



l'ii-f^t=^l^(S'R-^S'v-SR-Sv + rR+ T'y - Tr-Tv) . (11) 



This expression contains side by side all the various systematic 

 displacements of Frai;nhofer lines which the dispersion theory fore- 

 sees as consequences of irregular ray -curving. The first two terms 

 give the general displacement of limb-lines against arc-lines; the 

 third and fourth the general displacement of centre-lines against 

 arc-lines'); the fifth and sixth term show the ap[>arent repulsion 

 of neighbouring lines in the limb-spectrum; the seventh and eighth 

 the apparent repulsion in the centre-spectrum. 



At present we are especially interested in the increase which the 

 apparent repulsions must undergo when passing from the centre to 

 the limb, because we are in possession of a good many observational 

 data concerning this phenomenon '). 



For each component of a pair the said increase is represented by : 

 ^I,{Tr + Tv-Tr-Tv) 

 which expression, after substituting the quantities determined b}' 

 (9), (8), (7) and '5), becomes 



') Here are, of course, not included those displacements which the core-lines or 

 true absorption lines may perhaps be subjected to as a result of radial velocities, 

 pressure, or fields of force. Such displacements will simply have to be added to 

 the phenomena we are considering. 



*) Cf.: W. H. Julius, Mutual Influence etc., Astroph. Journ. 54, 92, 1921, and 

 VV. H. Julius and M. Minnaert, Ann. d Phys. 71, 50, KxYSER-Festheft, 1923. 



