198 CARNEGIE INSTITUTION OF WASHINGTON. 



nitude m and the proper motion n. This presupposes that the luminosity 

 function has the form of an error curve. If, however, the observed data for 

 stars of known parallax be grouped according to magnitude and proper motion, 



the following result is found: The differences M—H are approximately a 

 linear function of H for M less than the sixth absolute magnitude. Beyond 

 M = 8 the relation seems again to be linear. Between these two points the 

 functional relation is more complicated. Beyond the eighth magnitude the 

 linear character is uncertain, but this at least seems definite: about 75 stars 

 of low average luminosity show a definite departure from the linear relation 

 which satisfactorily represents the stars of higher luminosity. This indicates 

 that for stars on the ascending branch of the curve the gaussian curve of 

 Kapteyn and van Rhijn is applicable. For stars on the descending branch, 

 however, another curve is required, which will be gaussian or not according 



as the differences ilf—// for the fainter stars do or do not bear a linear relation 

 to H. 



The method used has the advantage that the data combined are selected and 

 grouped on the basis of proper motion, so that all stars of large proper motion 

 and known parallax can be utilized. The results indicate that the luminosity 

 function is a skew curve with a descending branch that is relatively flat, and 

 that the total number of intrinsically faint stars is much greater than hitherto 

 supposed. At the same time, it must be noted that the conclusion turns on 

 the characteristics of a small number of stars. 



STELLAR SPECTROSCOPY. 



A three-prism stellar spectrograph designed primarily for photographing 

 the yellow and red portions of the spectrum has been completed during the 

 year and has been used by Merrill in his studies of Me and S type stars. We 

 have also secured a two-prism spectrograph by Hilger, with an optical ratio of 

 1 to 5, for use at the primary focus of the reflectors in work on the ultra- 

 violet part of the spectrum. These instruments, together with two new 

 camera lenses, an 18-inch triplet by McDowell and a 10-inch lens designed by 

 Moffett, represent the additions made to the instrumental equipment of this 

 department. The low-dispersion spectrograph for use in the plate-holder 

 frame at the Cassegrain focus of the 100-inch reflector, which was referred to 

 in last year's report, has proved to be most useful for work on very faint stars. 



A total of 1,366 spectrograms has been obtained during the year with the 

 large Cassegrain spectrographs, 567 with the 100-inch reflector, and 799 with 

 the 60-inch. About 100 others have been secured with the smaller spectro- 

 graphs, mainly at the primary focus of the two reflectors. The observing 

 program has remained much the same as in recent years, the stars observed 

 with the 100-inch telescope being mainly dwarf stars of large proper motion, 

 faint variables, and the companions of visual binaries, while the list for the 

 60-inch reflector is made up principally of the stars from the Preliminary 

 General Catalogue of Boss and numerous double stars taken from Russell's 

 list of dynamical parallaxes. 



Radial Velocitie8. 

 The catalogue of the radial velocities of 1,013 stars by Adams and Joy, 

 to which reference has already been made, constitutes the most extensive 

 publication of this character so far issued by the Observatory. The list 



