OF ARTS AND SCIENCES. 13 



then the star has the same density as the Sun, the square of (7 will 

 give its briglitness. Again, if the star has the same brightness as the 

 Sun, its density will equal one divided by the cube of G. 



The product of the semi-axis major by the sine of the inclination 

 and divided by the period is given in the last column but one. It 

 serves as a measure of the annual approach or recession of the two 

 components. Neglecting the eccentricity, the maximum motion in sec- 

 onds will equal this quantity multiplied by 2 tt = 6.28. 



The last column gives the name of the astronomer by whom the 

 orbit was computed, which is adopted in this discussion. 



An inspection of the last column but one shows that the value of 

 -^ — in several cases amounts to 0''.03 or even more. Neglecting 



the eccentricity, the maximum motion would therefore equal 2 tt times 

 this quantity, or nearly 0".2. The eccentricity in some cases would 

 diminish the motion, but in other cases it would increase it. An ec- 

 centricity of 0.5 might vary it from 0".l to 0".4, according to the 



position of the peri-astron. This value of ■ would probably be 



even larger for some of the recently discovered stars, in which P is 

 still smaller than in the stars given in the table. It is commonly 

 supposed that the parallax of an average first-magnitude star does 

 not much exceed 0".l. That of a sixth-magnitude star would then 

 be about 0".01 unless the fainter stars are really smaller than the 

 brighter, or unless there is a perceptible absorption of light in space. 

 Substituting the values dz^=. 0".2, p = 0".01, in the formula for the 



inline, » = — -, given on page 9, we deduce Z= — ~— = 1.5. Ac- 



13/ ^ 13 /J 



ccordingly the difference in the positions of the F line would be 

 1.5 times as great as the deviation observed in the case of Sirius. 

 As the spectra of the two components could be observed in turn (or 

 perhaps simultaneously) without disturbing the spectroscope, many 

 of the causes of uncertainty present in similar measures of single 

 stars would be removed. 



In any case, if the F line could be seen in both components, we 

 could assign a limit within which we could be certain that it was the 

 same for both, and this would give a value of the parallax which 

 must be less than the true parallax. A determination of the outside 

 limit of distance of a star would appear to have nearly the same im- 

 portance as the inside limit of distance found by micrometric distance. 

 Moreover it does not seem probable that a star will be found whose 

 parallax is very large, or previous observation might have detected it. 



