stellar clusters 



43 



results with those of Müller and Kempf he fiuds a very satisfactory agreement 

 with the visual scale, for different magnitudes as well as for different spectral types. 

 A comparison with the Harvard visual magnitudes shows on the other side a 

 systematic difference depending on the spectral type, amounting to about one- 

 quarter of a magnitude for the reddest stars. This difference may be due to the 

 circunistances pointed out by Müller and Kempp in their discussion (1. c. p. XXII ff.), 

 where the systematic difference, depending on color, between Potsdam and Harvard 

 is explained by a Purkinje effect acting on the Harvard observations. Peihaps 

 this explanation may also count for the systematic différence between the color- 

 indices of Parkhurst and King (at Harvard) sliown in Parkhurst's Table V. 



The color-index is intimately correlated to the spectral type of a star. A 

 discussion of the former involves therefore a simultaneous determination of the 

 latter. The spectral types are now generally defined according to the Harvard 

 system. Some obscurities are perhaps still to be elucidated (compare Parkhurst 

 p. 188 on the definition of GÖ) and some difficulties to be overcome (e. g. regarding 

 the true order of the subclasses in the system as well as regarding the rigorous 

 definition of these subclasses), and it seems probable that these difficulties and 

 these obscurities are best treated with the help of the color-indices which, indeed, 

 seem to be admirably suited to give a satisfactory definition of the different spectral 

 subclasses of the stars. I come back to this question below. 



The spectral type of the stars are determiued by Parkhurst with the same 

 instrument which is used for the photometric observations. The dimensions of the 

 instrument being rather small (objective prism of 15" refracting angle, mounted on 

 a Zeiss doublet lens of 145 mm aperture and 814 mm focal length) the determination 

 of the spectral type must be rather uncertain, which constitutes a feeble point in 

 the investigation of Parkhurst. 



Parkhurst makes a thorough discussion of his material, comparing these 

 results in different points with the results of other observers. He especially gives 

 the color-index corresponding to different spectral types. There are, however, 

 some points which deserve a further investigation, which I intend to consider here. 



This relates mainly to the correlation between spectral type and color-index. 

 It is of interest to know the correlation coefficient between these important attri- 

 butes of a star and moreover we ought to know not only the color-index corres- 

 ponding to each spectral type but also the spectral type corresponding to the diffe- 

 rent color-indices, questions which — as well known from the theory of correlation 

 — are often essentially diff'erent. 



For performing this discussion it is necessary * to substitute for the spectral- 

 classes a continuous scale expressing the spectral character of a star. Such a scale 

 lies, indeed, implicitly in the Harvard classification of the spectra. 



* The theory of contingency developed by Pkarson allows to make such a discussion even 

 for non graduated attributes. A. graduation, when possible, is, liowever, always to be preferred. 



