6 PROCEEDINGS OF THE AMERICAN ACADEMY 



the ratio of iVto 1, mean distances in the proportion of a to p, and 

 periods of revolution as P to 1. Accordingly, by Kepler's law, 



N:l={:,:i,o.N= ^. But N= ^^^^^ , since 0.00933;. 



will equal the diameter of the Sun at the distance of the binary. 

 Hence, equating these two values of N, p is eliminated, and we have 

 J=: 0.00933 a P~"^ The stellar magnitude corresponding to the di- 

 ameter, b, may now be found from Tables I. and II. So far, no 

 hypothesis has been introduced, and the errors in these quantities will 

 depend only on the errors in the photometric measurements and in the 

 micrometric determination of the elements of the orbit. 



If now we could find the value of / for each of the components, as 

 suggested above, we could determine the true diameter of the two 

 stars, and from their orbits, and the mass of the binary, deduce their 

 average densities. Until these measures are made, we can do no 

 better than assume that both stars have the same density, and that 

 /= 1 for each. On this hypothesis, if h^, h., are the equivalent diame- 

 ters of the two components, and b the equivalent diameter of the 

 binary as computed from the time of revolution and mean distance, 



the density will equal . 



•' ^ 6j8 -i- i^3 



Since the value of the parallax is eliminated, it follows that these 

 considerations will not aid the determination of the distance of a 

 binary. The time of revolution of a binary would remain unchanged 

 if removed to double the distance, provided that the linear distance of 

 the components and their diameters were increased in the same propor- 

 tion, or that the angular dimensions of the system remained unchanged. 

 In other words, the observed time of revolution of a binary system is 

 wholly independent of its distance from the observer. 



The relative masses of the two components could be determined 

 micrometrically and independently of the above methods, by measuring 

 the position of each component from the adjacent stars. If tliis was 

 repeated at intervals during an entire revolution of the binary, the 

 components would be found to have described similar ellipses whose 

 dimensions would be inversely proportioned to the masses. From the 

 Proc. Roy. Astron. Soc, x\. 235, it would appear that INIr. Gill will 

 apply this test to the components of a Centanri. If the difference in 

 light is three magnitudes, and the intrinsic brightness and densities the 

 same for the two components, the ratio of the masses would be as 63 

 to 1. The semi-axis major of the ellipse described by the larger 

 star would therefore be, according to the elements given by Hind, 



