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common spectroscopical investigations undertaken with entirely diffe- 

 rent purposes. 



We remark in the first place that curiously shaped diaphragm 

 openings are not absolutely essential for the production of phenomena 

 as those described above. If e.g. our source of light had a constant, 

 say circular shape; if on the other hand the direction and magnitude 

 of the density gradient in our tube had not been so regular, but 

 very different in various j)laces of the field reproduced by the lens F, 

 then the i>>-lines would also have shown all sorts of excrescences, 

 now determined by the configuration of the density distribution. 



In the second place we will try to form some idea of the quan- 

 titative relations. 



The radius of curvature 9 of the path of the most deviated rays, 

 occurring in our photographs, may be easily estimated from the 

 distance d of the diaphragm to the middle of the furnace, the 

 distance ö of the most distant diaphragm openings to the optical 

 axis, and the length / of the space in which the incurvation of the 

 rays is brought about. For : 



Q il z=. d : Ö. 



Putting d=l cm., cZ=110 cms., /=27 cms. this gives: (►=3000 cms. 

 The average density L of the sodium vapour was in this case about 



of that of the atmospheric air. 



1000 ^ 



Let us see how" 9 changes with the density gradient. 



We always have : 



n 



n ^ ' 



if n represents the local index of refraction of the medium for the 



. dii 



ray under consideration and n = — the change of this index per cm. 



in the direction of the centre of curvature. Approximately we have, 

 for a given kind of light: 



n—\ 



From this follows: 



