58 
Sidereal Astronomy. 
[January, 
H 
Proportion. 
Simple stars ...... 
222 
074 
Really multiple stars . . . 
78 
0*26 
300 
1*00 
The numerical proportion between the multiple stars and the 
simple stars is 26 per cent — that is to say, one-fourth of the 
300 selected stars. 
Is the proportion the same for those of inferior magni- 
tude ? To ascertain this I have examined separately 2615 
multiple stars described in the great catalogue of Dorpat, 
and 770 from the catalogue of Pulkowa : they extend from 
the first to the ninth magnitude. I have found that below 
the eighth magnitude the progression diminishes, and that 
to obtain comparable results we ought to stop at the seventh. 
Deducting those optically double, we find that 2340 physical 
couples have been noticed in the celestial sphere from the 
north pole to 150° of southern declination, from the first to 
the seventh magnitude. In the same extent of the celestial 
sphere there are the following number of stars : — 
1st magnitude 
2nd 
3rd 
4th 
5th 
6th 
7th 
>> 
? ) 
}> 
11 
34 
106 
325 
1000 
3800 
12500 
Total 17776 
The proportion of these numbers should give us about 
two double stars to every fifteen stars. It is certain that 
this proportion is too low, because the most brilliant stars 
have been observed more frequently and examined with 
more care than the less brilliant ones (although at Dorpat 
and Pulkowa they have scrutinised the heavens with the 
express aim of finding double stars. Without the perseve- 
rance which was devoted to scrutinising so attentively the 
neighbourhood of Sirius and Procyon, we should not have 
discovered their satellites. The diminution of the multiple 
stars below the fourth magnitude may also be due to the 
increasing feebleness of the satellites, in proportion as the 
primary ones are themselves smaller or farther off. If we 
consider the stars of the entire heavens, in order of bright- 
ness, we arrive at the following proportion : — 
