studies in Stellar Statisticy 



39 



Tab. 7. 6',. 



RD 







Observed 



4.9 



4.6G 



12 



19 



5.9 



5.64 



56 



56 



(5.9 



6 62 



243 



211 



7.9 



7.72 



1 100 



816 



8.9 



8.95 



5 500 



4 207 



9.0 



9.07 



6 300 



5 801 



9.1 



9.16 



7 000 



6 655 



9.2 



9.25 



8 200 



8180 



9.3 



9.49 



10 400 



10 589 





13.89 



694 000 



717 000 



As to the numbers in the last line (from C. du C.) a full agreement can 

 evidently be reached by a rather small correction of JV (amounting to some 3 % of N). 

 Regarding the other numbers the following remarks may be made. 



19. Though the observed and the calculated values of A{m), in the main 

 points, do agree, it must be noted that a systematic difference, occurring also in 

 other squares, is manifested for values of m between 7'"^ and 9™. This difference 

 may be accounted for in three different ways : 1) There may be a systematic error 

 in the magnitudes of the Harvard Durchmusterung. Though such systematic errors 

 are not excluded (compare the discussion of Messrs Müller and Kemppp on the 

 Harvard measurements, where an error in HD depending on the colour of the star 

 is made probable), I am inclined to estimate these errors as too small to account 

 for the observed difference. In any case it is impossible, as yet, to discuss these 

 systematic errors. 



2) Considering the a[m) to be a frequency curve of type A), the adopted form 

 (63) is only the first term in the equation of this curve, the general form being 



(68) a[m) ^ a,{m) + Çi, a,"'(m) + ß, a.'^m) + . . ., 



where 



(68*) a,{m)=---=e 2^^-. 



Through an appropriate determination of the parameters ßj and the syste- 

 matic differences in Tab. 7 can evidently be made to vanish. For the present I 

 shall not pursue this matter. It is desirable to procure first a count of the number 

 of stars belonging to magnitudes between 9^.2 and 13™.89. It will suffice to make 

 such counts for some selected areas of the heaven. 



3) Though there is little doubt, as far as I have examined the subject, that 

 the observed a{m) may be represented through the formula (68) with any degree of 

 accuracy, it is not impossible that even other functions can sucessfully be used to 

 represent the observations. I will discuss in a subsequent lecture the main alternative 

 solution that here is to be taken into consideration. 



