OP ARTS AND SCIENCES. 6 



When the parallax of a star is known, these principles may be 

 applied to determining its linear diameter. If the San was removed 

 to the distance of the star its diameter would have the same ratio to 

 the parallax that the chord of the Sun's diameter, as seen from the 

 Earth, has to unity. It would therefore equal 



Ij) sin 16' 2"=: 0.00933 j9. 



Table III. gives the light in stellar magnitudes which would be emit- 

 ted by the Sun if removed to such a distance that its parallax would 

 have the value given in the first column. 



TABLE III. — Parallax. 



If the parallax of « Centauri is assumed to be 0".9, the Sun as seen 

 from it will appear as a star of the 1.3 magnitude. The light of 

 a Centauri is not known with much certainty, as we have to depend 

 upon eye estimates. Assuming the magnitude of the two components 

 to equal 0.0 and 3.0, we find that if ^= 1 for both of them, their diam- 

 eters will be 1.82 and 0.46 times that of the Sun. The parallax of 

 61 Cygni may in like manner be assumed to be 0".3, and the magnitude 

 of its components 5.0 and 6.0. The Sun would then appear, from this 

 distance, as a star of the 3.7 magnitude, and the diameter of the two 

 components, compared with that of the Sun, if their emissive powers 

 are the same, will be 0.55 and 0.35. 



I. Binary Stars. 



In the case of a binary star, another equation of condition may be 

 introduced from Kepler's third law. Let iV denote the mass of the 

 binary in terms of that of the Sun, P the period of revolution in years, 

 a the semi-axis major, or mean distance of the components, and b the 

 equivalent diameter, or the diameter of a star having the same mass 

 as the binary, and the same density and intrinsic brightness as the Sun. 



Comparing the binary with the system formed by the Sun and Earth 

 seen at the same distance, we see that the two systems have masses in 



