( 146 ) 



3 log II -{- 4 log P — 6 log a = const. -}- 3 log X — 2 log ó 

 m — ^"/j log P -|- ^ log a z=z m^ 

 then we have iiir = const. — 2,5 log X -{- Ys log ö. 



If we arrange the values of vir after the spectra according to the 

 Draper Catalogue (for the Southern stars taking CannoxN; according 

 to the brightest component a Centauri was reckoned to belong to 

 class G), we find as mean values : 



Class A — 2.92 (9 stars — 4.60 to — 1.09) 



„ F —1.32(19 „ — 3.6J „ +0.14) 



„ GandE — 0.49(11 „ —1.60 ,,+1.28) 



The 3 stars of the type K (with H) give — 4.88 (y-Leonis), 

 — 1.05 and +0,87, hence diifer so widely that no valuable result is 

 to be derived from them. To the extraordinarily high value for 

 X'^/ö^ given by y Leonis attention has repeatedly been drawn. 

 While for a great number of stars of the other classes the extreme 

 values of iiir differ by 3.5 magnitudes we fmd that y Leonis differs 

 by 5 magnitudes from the mean of the two other values, that is to 

 say : its radiating power is a hundred times as large, or its density 

 is a thousand timq^ as small as for these other stars. For the classes 

 A and F we fmd that X^/ö^ is 640 and 8 times respectively as large 

 as for class G; conclusions about class K as a whole, such as are especially 

 wanted here, cannot be derived from it. It may be that an investi- 

 gation of binary systems with partially known orbit motion (for which 

 we should require auxiliary hypotheses) would yield more results. 



About the mass itself, however, something may be derived from 

 the spectroscopic binary systems. The elements derived from obser- 

 vation asi?ii and F directly yield M sin^i; as it is improbable that 

 there should be any relation between the type of spectrum and the 

 angle between the orbit and the line of sight we may accept the 

 mean of ahiH to be equal for all groups. For systems of which only 

 one component is visible, the element derived from observation 

 contains another unknown quantity, viz. the relation /? of the mass 

 of the invisible to that of the visible star. If a is the semi major 

 axis of the orbit of the visible star round the common centre of 

 gravity, we have 



a' sin '* ,r /^' . «. 



P» (1+/?)' 



It is not perfectly certain, of course, that on an average /:? is the 



same for all classes of spectrum; if this is not the case the M'^ 



a' sin ^i 

 may behave somewhat different from the values of — =^^ — computed 



here. 



