52 



C. V. L. Charlier 



For the square we now derive 



for X = Vs X = Vs 



Do = 5916 



Do = 760.3 ' 



X^ = Vs 

 Do = 88.7 



(it may be observed that Dq :]/27: = 0.4 Do = maximum density). 



Using now (83), which is easy to calculate with the help of Sheppard's table 

 of the probability function, we get the following values of D(r) giving the number 

 of stars per cub. siriometer at different distances for the three values of Xj con- 

 cidered. I have added also the values of D(r) for the square corresponding to 

 the value X^ = ^/a. The table is interrupted where the number of stars sinks below 

 0.01 star per cub. siriometer. 



Tab. 12. Number of stars per cuh. siriometer 



//^•^ Curiae o/~ C3fe?2£ùéy 



in 



100 - 



r 







\ = Vs 





X, = '1^ 





10 



2855 



301 



34.4 



31.4 



50 



396 



107 



18.9 



4.7 



100 



58.8 



30.1 



7.9 



0.90 



150 



14,2 



11.7 



4.2 



0.28 



200 



3.7 



5.6 



2.4 



0,11 



250 



1.4 



2.9 



1.5 



0,05 



300 



060 



1.7 



1.03 



0.03 



350 



0.27 



l.no 



0.70 



0,02 



400 



0.34 



0.64 



0.51 





450 



0.06 



0.42 



0.37 





500 



0.04 



0.28 



0.29 





550 



0.02 



0.20 



0.23 





600 



0.01 



0.14 



0.18 





650 





O.U 



0.J3 





700 





0,08 



0.11 





750 





0.06 



0.09 





800 





0.04 



0.08 





850 





0.04 



0.06 





900 





0.03 



0.05 





950 





0.02 



0.04 





1000 





0.02 



0.04 





1050 





0.01 



0.03 





1100 





0.01 



0.03 





1150 







0.02 





1200 







0.02 





1400 







0.01 





/oo 



zoo 



300 



