OF ARTS AND SCIENCES. 11 



of a star having the same mass as the binary will therefore have a 

 magnitude 2.0 — 0.2 = 1.8. 



]\Iost of the binary stars whose orbits have been computed are com 

 pared in Table V. The successive columns give a current number, 

 the name of the star, the number of the Dorpat Catalogue, the right 

 ascension and declination for 1880, the semi-axis major in seconds, the 

 eccentricity, the period in years, and the inclination of the plane of the 

 orbit in degrees. The next two columns give the magnitudes of the 

 components as estimated by Struve. Three of the stars are not con- 

 tained in the Dorpat Catalogue, and for them the mngnitudes given 

 have been assumed. The next column gives the equivalent diameter 

 0.00933 a P"', or the magnitude of a star having the mass of the 

 binary and the density and brightness of the Sun. From the magni- 

 tudes of the components we may compute, by the third column of 

 Table IV., the brightness of a star having the same mass as the binary 

 and the same brightness and density as its components. Subtracting 

 from this quantity that given in the preceding column gives the next 

 column. If these quantities were small, we might assume that they 

 were due to errors in the assumed magnitudes of the stars. Their 

 variations are, however, far too large to be explained in this way. As 

 they are almost all negative, we may hifer that the assumed light of 

 the Sun is too small, or that a larger value should have been given on 

 page 2 to S. A great part of the difference must be ascribed to 

 variations in the density or brightness of the stars. We have at present 

 no way of discriminating between these causes. Such a method as 

 has been proposed on page 3 for determining I would serve to distin- 

 guish them. Until then, it will be convenient to reduce this differ- 

 ence fi-om magnitudes to the relative diameters of two stars of equal 

 density and brightness, one having a mass, the other emitting a lio-ht 

 equal to that of the binary. Assuming the diameter of the first of these 

 stars as a unit, the diameter of the other is given in the next column, 

 and may be denoted by G. In almost all cases this quantity is greater 

 than unity, from which we should infer that most of the stars enumer- 

 ated are either much brighter or much less dense than the Sun, unless, 

 as suggested above, the measurements of the light of the Sun are 

 largely in error. Let d denote the density, b the brightness of the 

 components of the binary, and D the equivalent diameter of the 

 binary in terms of the same unit as C. Then D^ : C^ =: 1 : b, and 



D^ : V = 1 : d ; eliminating D, C = ^, or the brightness is propor- 



tioual to the square of C and the density inversely as its cube. If 



