( 295 ) 



In all these series we clearly see an increasing deepening of colour 

 with decreasing brightness. We have tried to represent the colour as 

 a linear function of the magnitude; and by a graphical method 

 we found : 



CI. Ill— VI c = 2.15 + 0.35 (771 — 3) 

 „ VII— VIII 2.27 + 0.36 

 „ IX— XII 3.17 + 0.39 



„ XIII— XIV 4.45 + 0.42 

 „ XV 5.47 + 0.39 



„ XVI— XVIII 6.60 -I- 0.20 



Thus we find about the same coefficient in all groups except in 

 the last. The value of the coetTicients is chiefly determined by the 

 difference between the observed colours of the very bright stars of 

 the 1^* magnitude and of the greater number of those of the 3^ and 

 4^*^ magnitudes. In order to make the coefficient of the last group 

 agree with the others, it is necessary to assume for the apparent 

 colour of a Tauri and a Orionis 5.6 instead of the real estimates 

 6,4 and 6,5. It does not do, however, to assume such a large error 

 for these bright and often observed stars; therefore we must for 

 the present accept the discordant coefficient of the red stars as real, 

 although it is difficult at the present to account for it. 



If now we combine the results of the five first groups by arranging 

 the deviation of each observed value of c from the constant for the 

 group (the value of c for m = 3), according to brightness and deriving 

 thence mean values we find : 



—0.91 



—0.47 



0.02 



-fO.27 

 +0.39 

 +0.60 



A linear relation c = c, -\- 0,34 (m — 3) yields the computed values 

 given under C, and the differences obs.-comp. — C,. These are 

 distributed systematically and show the existence of a non-linear 

 relation. A curve, which represents as well as possible the mean 

 values, gives the computed values C^ and the diiferences, obs.-comp. 

 — 6\. Fora greater brightness the curve gives a greater variation of 

 the colour with the luminosity and for fainter stars a smaller one. In 

 all the six groups, except the fifth and the sixth, we remark that 



