460 MASSES OF VISUAL BINARY STARS. 



globes out of the solar orb — the niagnitiide would no longer be 

 0.0, because the light emitting surface has now been increased. 

 The increase in magnitude is = — 5/6 log. 2 = — 0.25, or each 

 Star would have the magnitude of 0.50, whilst, as before, the 

 semiaxis would be i" and the period one year. 



This would be a model system resembling oiu" Sun in sur- 

 face brilliancy and gravitative power. 



The magnitude, ])eriod, and semiaxis of any double star in 

 themselves tell us nothing about its distance because of spatial 

 relations. Let us consider two systems of equal emissive bril- 

 liancy })er luiit area, but one twice as far from us as the other. 

 If the further one has eight times the mass (or gravitative 

 power ) , it will have four times the area, and therefore the same 

 apparent Ijrightness. Hence, as seen in the sky, these tw^o sys- 

 tems would appear to be identical in every respect. Because we 

 know the parallax of a Centaurus, we have learnt that its mass 

 is 1.90 (nearly twice the gravitative power of the Sunj. If its 

 parallax had been half what it is, then its visual appearance 

 would have been the same if its mass had been 15.2 O. And 

 generally, as the distance increases p times, the mass increases 

 /i" times, if the visual appearance remains unchanged. 



In this argimient an assumption has crei)t in, namely, that 

 the spectral type is independent of the mass. We have no proof 

 that stars eight times the mass of a Centaurus could exhibit its 

 spectrum. At the same time we cannot assert that a star's spec- 

 trinn alters with its mass. It has also been assumed, and will 

 be maintained, that that stars of similar s])ectra have equal 

 emissive power or brilliancy per unit area. 



In all the cases where we have both good determinations of 

 the orbits and parallaxes of double stars we find that their gravi- 

 tative power does not differ greatly from that of the Sun ; let 

 us take tlie most reliable results from Table I. 



T(j find out 



betneen mass, magnitude and distance,- Table I\' has been pre- 

 pared. The right-hand portion of Table T\' within leaded lines 

 may be omitted, as no known double stars fall within it. 



Excei)ting the columns " Radial for (iiven Masses," the table 

 i,s to be interpreted as actual experience. Thus, if there was in 

 the heavens a double star with equal-sized components, whose 

 magnitude is 3.75, and whose angular separation is 9". if it is 



