G-ORE — A Catalogue of Binary/ Stars, 8fc. 
573 
where I = mean motion of the earth in miles per second, and 0 the true 
anomaly at any time. 
In Column 20 I have given the relative brilliancy of each binary 
star (on the assumption that all the stars in question are spheres of 
equal density) computed in accordance with Mr. Monck's formula 
{" Observatory,'' Eeb. 1887), viz. :— 
where k represents the brilliancy per unit of surface (on the above- 
mentioned assumption), /, the intensity of the light, as measured by 
the photometer, F, the period of the star's revolution, and a, the 
angular radius (semi-axis major) of the orbit. 
Adopting Mr. Monck's standard star (7^=1), viz. $ Ursse majoris, 
with Duner's orbit, and the Oxford determination of its magnitude, 
this formula for any other binary star becomes 
where m is the magnitude of the star according to the Oxford measures 
{Uranometria Nova Oxoniensis), P being expressed in years and a in 
seconds of arc. 
This formula is strictly correct only if the mass of the smaller 
star of the pair may be neglected ; but in the extreme case of equality 
in the masses of the components the effect will only be to reduce h 
Por the fainter binaries (which have not yet been measured with 
the photometer) I have adopted the magnitudes of Argelander's 
Burchmusterung, or those given by Struve, and for the southern 
binaries, the estimates of the Uranometria Argentina. In the case of 
^ Sagittarii I have taken the magnitude as given in the Harvard 
Fhotometry . 
Column 21 contains a reference to the publications in which the 
given elements of the orbit orginally appeared. 
The position angle and distance of a binary pair at any time t 
may be computed from the elements of the orbit by means of the 
to 
y2 1-2599 
