36 



C. V. L. Charlier 

 Tab. 5. Limiting magnitude of C. du C. 



Var. star 



a (1900) 



3 (1900) 



R Piscinm 



1".25'».5 



+ 2°.21'.9 



R Arietis 



2 .10 .4 



+24 .35 .5 



R and S Tauri 



4 .22 .8 



+ 9 .56 A 



S Hydrœ 



8 .28 .3 



+ 3 .26 .7 



E, Herculis 



16 . 1 .7 



+18 .38 .4 



S 



16 .47 .3 



+15 . 6 .6 



R Delphini 



20 .10 .5 



+ 8 .47 .1 



R Vulp. 



20 .59 .9 



+23 .25 .5 



S Pegasi 



23 .14 .5 



+ 8 .22 .3 



N:o 



Number 

 of stars 



Lim. 

 nia^^n . 



+ S".!! 



364 



13"". 5 



+24 .17 



1049 



14 .3 



+ 9 .33 



1241 



13 .5 



+ 3 .66 



7761 



13 .4 



and 67 



381) 



+18°.m 



526 



(13 .7) 



+16 .127 



957 



13 .6 



+ 9 .152 



2954 



14 ,1 



+24 .158 



16041 



14 .3 



and 159 



2662 f 



+ 9M75 



1422 



14 .4 



Remarks 



All stars visible and some more 

 d:o and much fainter 

 d:o and some few more 



some i Hagen not visible 



exposed only 20 min. 

 all visible and very much fainter 

 d:o and much fainter 



d:o and very much fainter 



d:o and much fainter 



+0"'.2 



+1 .0 



+0 .1 



0 .0 



+ 1 .5 



+1 .0 



+1 .5 



+1 .2 



The 1st Column gives the name of the variable star for which Hagen has 

 given a map of stars of comparison. The 5th col. gives the number of stars on 

 the map of C. du G. on which was star occurs. The 6th col. gives the concluded 

 value of the magnitude of the faintest stars visible on the map (= »limiting magni- 

 tude»). In the last col. is giveu the estimated ditïerence of magnitude between 

 C. du C and the faintest stars in Hagen. 



The mean value is: 



Limiting magnitude of the C. du. C, = 13'".89 + 0™.17. 



Though there may seem to be many objections against the manner of estimating 

 Aw, the concluded value of the limiting magnitude will probably not exceed three 

 times the mean error (= ± 0™.5i). It is of interest to compare the magnitudes 

 given by Hagen (not reproduced here) with the Harvard scale (= HS). The influence 

 of the stardensity — which was so well illustrated in tab. 3 for the BD magnitudes 

 — is very pronounced. Taking this influence into consideration it should not be 

 impossible to make use also of these charts of Hagen for which the magnitudes 

 are not determined in Harvard. 



18. For determining the parameters of our formula (63) for the number of 

 stars of a given apparent magnitude, according to the method of § 16, we have 

 now to issue from three values of m combined with the corresponding three 

 numbers A(m). For m I shall take the following values 



= 5.9 BD 

 = 9.2 BD 

 = 13.89 (C. du C). 



The values of and must be reduced to the HS with the help of the numbers 

 given in Tab. 3. Moreover we must observe that only tenths of magnitude are 

 given in BD so that for instance 5.9 in BD embraces all stars between 5.85 and 

 5.95. Hence we have to give to the magnitudes in BD a correction = + 0'".05 

 (= 1st correction). Hence our values of m and A(m) for the two squares 

 and C,^ are: 



