42 



C. V. L. Oharlier 



from the earth, which distance T shall call a Siriometer and denote with 8. If a 

 denotes the mean distance of the sun from the earth and the distance r of the 

 star is expressed in Siriometers we have 



a 



sm 71 == — ^ = 



rS 

 1 



1 



0"206 265 



so that 



(70) 7r= — . _ 

 ^ ' r.lO^sml r 



If r = 1, we have % = 0."206. 



The relation between the apparent brightness, Ä, and the luminosity, H, of a 



star may be as before 



(71) H=hr^, so that for r=l we have li = H. 

 Introducing magnitudes instead of the brightness we have 



Jf = m + 2,5 (log h — log R) 



or according to (71) 



(72) M =m — 5 log r. (log r = — 0.686B7487 — log tt) 

 If here ir is introduced instead of r w^e have (from (70)) 



(72*) M=m-Yb log + 3'".428 



through which formula we shall compute the absolute magnitude, M, when n is known. 



For 51 stars, the parallaxes of which may be considered as rather accurately 

 known, I have in this manner computed M. The resulting values are shown from 

 table 9. Regarding the names or coordinates of the stars I refer to Meddel. N:o 34. 



The absolute magnitudes var}^ between — 2"*. B and + 10'".4. For abridging 

 the computation the stars are distributed into classes, each having a breadth of one 

 magnitude. The midth of each class is given in the first column. In the third 

 column, designed F(x), are given the number of stars belonging to each class. The 

 other give the details of the computation of the mean and the dispersion of the 

 observed frequency-curve. 



Absolute magnitude of the stars. 



M 



X 



F{x) 



xF{x) 



x'F{x) 



(a;+l)^ Fix) 



Check 



— y.l 





- 6 



2 



-12 



+ 72 



50 



+ 479 



— 1.1 





- 5 



3 



- 15 



+ 75 



48 



— 14 



— Ü.1 





- 4 



3 



— 12 



+ 48 



27 



+ 51 



+ 0.9 





-3 



3 



- 9 



+ 27 



12 





+ 1,9 





- 2 



6 



— 12 



+ 24 



6 



+ 516 



+ 2.9 





- 1 



6 



- 6 



+ 6 



0 





+ 3.9 





0 



6 



0 



0 



6 





+ 4.9 





h 1 



9 



+ 9 



+ 9 



36 





+ 5.9 





- 2 



3 



+ Ö 



+ 12 



27 





+ 6.9 





-3 



3 



+ 9 



+ 27 



48 





+ 7.9 





-4 



2 



+ 8 



+ 32 



50 





+ 8.9 





-5 



3 



+ 15 



+ 75 



108 





+ 9.9 





-6 



2 



+ 12 



+ 72 



98 









Sum 51 



— 7 



+ 479 



516 





