38 
The N.Z. Journal of Science and Technology. 
[Jan 
ASTRONOMICAL NOTES. * 
The Combined Magnitude of Double or Multiple Stars. 
If we know the magnitudes of the components of a double or multiple 
star it is convenient to have a quick wav of determining the magnitude of the 
whole regarded as a single point of light. The work may be reduced to a 
minimum either by the use of the table below or by the use of the graph. 
If we take the brightness of a star of any particular magnitude as unity, 
then the brightness of another n magnitudes brighter is given by the 
formula b — r n where log. r = -4. 
The values of b corresponding to values of n from T to 10 are given in 
the table. 
To find the combined magnitude of any number of stars which appear 
as a single point of light : Read off from the table the brightness of each, 
MAGNITUDEThe tenth magnitude being standard. 
add all these numbers together, then read off from the table the magnitude 
which corresponds to the aggregate brightness. If the magnitudes do not 
differ too widely the calculation may conveniently be made graphically. 
Example 1 .—Two components of a double star are of magnitudes 9-5 
and 8*7 respectively : what is the combined magnitude ? 
Take the brightness of a 10th magnitude star as unity. Then for the 
fainter n = -5 and for the brighter n — 1-3. From the table—Mag. 9-5 
('n = -5), brightness 1-5849 ; mag. 8-7 (n = T3), brightness 3-3113 ; 
combined brightness, 4-8962 . therefore n = 1*72, and combined magni¬ 
tude = 8-28. 
Or, reading from the graph, the brightness of star mag. 9-5 is repre¬ 
sented by MP, that of the star mag. 8-7 by NQ. Adding these we get SR, 
which corresponds to mag. 8-28. 
