462 ' MASSES OF VISUAL lilNARV STARS. 



a solar typo star, the annual change of position angle would be 

 about o''.S4, but its distance and mass are indeterminate. It 

 might be any of the following : — 



Mass Distance 



(Sun Unity). (in Radials). 



1,000 63 



512 50 



216 ..~ 38 



64 25 



8 13 



I 6.3 



y^ 3-2 



1/64 1.6 



so far as the table goes. It can be continued further by the 

 factors at the foot of the hrst eight columns, which will furnish 

 the 'inverse or reciprocal masses ; thus, if we read the first 

 column, not as 1,000 times the Sun's mass, but as i/ioooth of 

 it. we must multiply the radial distance by i/'iooth. and so on. 

 yielding the example — 



Mass Distance 



(Sun Unity). (in Radials). 



i/iooo 0.63 



1/512 0.78 



1/216 I.I 



1/64 1.6 



1/8 3.2 



coming again in the last two cases to figures already tabulated. 

 Intermediate numbers can be found from the relation — 



Mass/ (Radial)" =r Constant, 



but the table need onl}- be used for qualitative inspection. As 

 already stated, Table I\', in the columns headed Magnitudes and 

 Distances., covers all our observational experience ; that is, we 

 know nothing of double stars fainter than loth magnitude (cor- 

 responding to about 9.3 in the B.D. scale of magnitudes), the 

 case of unequal pairs such as, say, 10. i and 12. i, or of 9.75 in 

 the case of equal pairs, and as regards distances, we know little 

 or nothing of pairs under o".25 apart. 



The table can perhaps best be interpreted negatively. \\"e 

 know that a Centaurus at 17". 7 moves over ^°.35 a year. Is 

 there any similar pair, nearer or further away ? It is unlikely 

 that any are nearer, but within a space covered by 100 radials 

 we might expect to find 1,000,000 stich pairs, ranging to the 9.75 

 magnitude if of the mass of the Sun or of (1,000") if of 1,000 

 times the mass of the sun. because for such stars the limiting 

 radial is 1,000. There are about six such pairs. Hence stars 

 of the size of a Centaurus are very few indeed — they are excep- 

 tional stars. 



Then, we know of several pairs of stars revolving in about 



