MOUNT WILSON OBSERVATORY. 197 



STELLAR PHOTOMETRY. 

 Photographic Magnitudes in the Selected Areas. 



With the exception of three fields, the catalogue of magnitudes for Areas 

 1 to 139 has been practically completed by Scares, with the assistance of Miss 

 Joyner and Miss Richmond. The stars have been counted for half -magnitude 

 intervals, both for the fields measured at Groningen and at Mount Wilson. 

 These fields overlap but do not coincide, and since the limiting magnitudes 

 differ for the two series, it has been necessary to segregate the counts in order 

 that the results may be homogeneous. The totals are subject to some revi- 

 sion, but stand approximately as follows: Mount Wilson, 60,000; Groningen, 

 40,000. 



A detailed statement of the whole investigation, which has extended over 

 several years, has been prepared by Scares. This has appeared as an appendix 

 to the report by Dr. van Rhijn on the status of investigations in the Selected 

 Areas. 



The Luminosity Function. 



The constants of the luminosity function depend on the formula for mean 

 parallax expressed as a function of proper motion and apparent magnitude. 

 Since the mean-parallax formula has been based in part on the parallactic 

 motions of stars as faint as the eleventh magnitude, it is of interest to know 

 how accurately the luminosity function represents the accumulated data for 

 the stars of the brighter apparent magnitudes whose distances have been 

 measured individually. The density function is also involved, but this 

 depends only on the luminosity function and the observed number of stars in 

 each interval of apparent magnitude, which is subject to no great uncertainty. 

 Scares has made the calculations necessary for a comparison. For the stars 

 brighter than the fifth apparent magnitude the calculated distribution of 

 absolute magnitudes agrees with the observed distribution as well as can be 

 expected in view of the numerous disturbing factors. The chief divergence is 

 an excess in the calculated number of stars of very high luminosity, which may 

 be interpreted as a systematic difference between mean parallaxes and paral- 

 laxes measured directly by trigonometric methods. This difference is of the 

 same sign and approximately of the same amount as that brought to light 

 through the recent discussion by van Rhijn. 



Unfortunately, the comparison can not be extended satisfactorily to the 

 stars of fainter apparent magnitude, because of the selection in favor of large 

 proper motions and low luminosities, which affects the data on parallaxes of 

 individual stars. This leaves an important point unsettled. It is known that 

 the observed number of stars of low luminosity among those near the sun is in 

 excess of the number calculated from the luminosity function, but the total 

 numbers involved are so small that the divergence can scarcely be accepted 

 as proof of error in the luminosity curve. The comparison in question re- 

 produces the evidence on this point, but does not greatly extend it. 



Since important questions depend on the form of the luminosity function, 

 an attempt has been made by another method to test the applicability of the 

 gaussian error curve. It can be shown analytically on the basis of the adopted 

 distribution functions for luminosity, density, and tangential velocity that, 

 very approximately, 



M—H = si linear function of H, where H = m-\-5\og n 

 and M is the mean absolute magnitude of the stars having the apparent mag- 



