studies in Stellav Statistics 51 



For the three vakies of here to be considered the equations for and are 



Xj = Vs : Wj = — SVs — Vs^'o + ^-0512 



Xj = Va : »?i = — 2 Vs — Vâ w,, + 0.0576 /c^ ; 



= : m^ = — 1 V.1 — Vs Wo + Û.0512 h\ 



Applying these formulae as well as (82) to our results found for the square 

 (Tab. 8) we have 



iV^ = 30 000 000 ; Ä;=+3.119; »Wq = + 20.07 



and hence 



X. = V3 



Xi = V. 



Xi = Vs 



Ol = + 1.801 1.788 





= + 2.205 





= + 2.547 



02 = + 2-547 





= -|- 2.205 





= + 1-801 1-788 



»il = — 9.52 





= — 11.98 



Wl 



= — 14,55 



»?2 = + 10.56 



'»h 



= + 8.10 





= + 5.52 



»Wj = — 5.04 



m s 



= — 5.26 





= — 5.59 



mum of density h 



ence 



occurs for 







1/ = — 5.04 



y 



= — 5.26 





y — — 5.59 



respectively, corresponding — according to the formula y = — 51og r — to 



r=-\- 10.2 r = + 11.2 r = + 13.2 



for the distances. From that value of r the density is continually decreasing, when 

 r increases. It is remarkable that, whereas and Wg vary greatly with X^, the 

 value of is nearly constant for the three values of X, considered. 



The rate of decline of the density, from the maximum value, is very dependent 

 of Xj and increases with diminishing values of Xj, as is seem from the values of Oj. 



The variations of the dispersions and are in inverse order. Small values 

 of Xj correspond to values of 'pearly equal to k. Large values of X^ correspond 

 to small values ot a^. 



The mean value — — of the obsolute magnitudes decreases with increasing 

 values of X^. 



We have deduced in tab. 9 the mean value and the dispersion of the ab- 

 solute magnitudes and found them to be respectively ilf=-|- 3 76; a = -f 3.06. 

 The value thus obtained for Ml^rn.^) agrees best with the value of m.^ for X = Vs, 

 whereas the dispersion better agrees with the value of for X = Va . 



27. It remains to compute the density at different distances. We have 

 according to (83*) 



(83**) log Do = log N — log h — log a, — log w + 0.6 + 0.9 b a^^ , 



where co = 4;r : 48 = tt : 12. 



