studies in Stellar Statistics 

 Tlie equation for (ieterniining N hence is 



(66) 0 



N 

 N 



1 , m.^, Err ^ 

 1,»?3, Err (l 



= im„ — Err 1 — 



+ — »/,) Kit 1 



2^ 



N , 



4" {m^ — Err ( 1 

 (where J., = Alm^) etc 



35 



N j 



N 



This equation can be solved through trials, giving to N a series of increasing 

 values till the right member of (66) changes its sign and then proceeding according 

 to known methods. Any two of the equations (65*) then give the values of x and y. 



1 give in Tab. 4 a table of Err (u) for values of u between ti = O.oo and 

 « = 0.999 999 999. It has been computed by tlie assistent of the observatory Cand. 

 Åkesson from the table of the probability integral given by Sheppakd in Bio- 

 mefrica. The mode of calculation has necessitated a somewhat irregular repartition 

 of the number of decimalplaces. 



It is to be observed that Err (u) is an odd function of u, so that 



Err («) = — Err('w). 



17. Before applying these formulae we have still to determine the limiting 

 magnitude of the C. du C. To this purpose I have proceeded in the following 

 manner. Father Hagen in Rome has edited a very beautiful collection of charts 

 giving the comparison stars of known variables. For some of these stars Pickering 

 and Wendell have given the magnitude according to the Harvard Scale (US) in 

 Vol. 37 of Harv. Ann.*) All those charts, for which the magnitudes have been 

 determined in Harvard were now compared with the maps of the C. du C, as far 

 as these maps were available at the observatory of Lund. With a sole exception 

 all stars on the charts of Hagen (photometrically determined in Harvard) were seen 

 on the C. du C. Moreover even fainter stars are shown, sometimes evidently as 

 much as one or two magnitudes fainter. The excess of the limiting magnitude 

 over the magnitude of the faintest stars in Hagen were each time estimated, inde- 

 pendently by the assistent mr. Åkesson and by myself. The resulting limiting- 

 magnitude for each map is seen from the following table : 



*) The charts of Hagen combined with the photometric measurements at Harvard have 

 been used by Kapteyn (Publ. of the astr Lab. at Groningen N:r 18) for determining the number 

 of faint stars from the G. du C. It has not been possible, for my aim, to apply the method of 

 Kapteyn, as it should then have been necessary to me to confine me to a very limited number 

 of the C. du C. In the squares Cj to C^.^ there are, as can be found from the tables 13 to 24, 

 942 charts already edited and for only 10 of them (given in Tab. 5) the magnitudes can be found 

 from the measures at Harvard. 



