Dr. Herschel's Catalogue 
484 
many more I have since collected, should be of that kind. Such 
an inquiry, though not very material to our present purpose, 
will hereafter be of use to us, when we come to consider more 
complicated systems. For, if it can be shown that the odds are 
very much against the casual production of double stars, the 
same argument will be still more forcible, when applied to treble, 
quadruple, or multiple compositions. 
Let us take f Aquarii, for an instance of computation. This 
star is admitted, by Flamsteed, De la Caille, Bradley, and 
Mayer, to be of the 4th magnitude. The two stars that com- 
pose it being equal in brightness, each of them may be supposed 
to shine with half the light of the whole lustre. This, according 
to our way of reckoning magnitudes,* would make them 4m 
x s /2, — 5yin ; that is, of between the 6th and 5th magnitude 
each. Now, the light we receive from a star being as the square 
of its diameter directly, and as the square of its distance in- 
versely, if one of the stars of £ Aquarii be farther off than the 
stars of between the 6th and 5th magnitude are from us, it must 
be so much larger in diameter, in order to give us an equal 
quantity of light. Let it be at the distance of the stars of the 
7th magnitude; then its diameter will be to the diameter of 
the star which is nearest to us as 7 to 5j, and its bulk as 1,885 
to 1 ; which is almost double that of the nearest star. Then, 
putting the number of stars we call of between the 6th and 
5th magnitude at 450, we shall have 686 of the 7th magnitude 
to combine with them, so that they may make up a double star 
of the first class, that is to say, that the two stars may not be 
more than 5" asunder. The surface of the globe contains 
* The expressions zm, 3m, 4m, &c. stand for stars at the distance of z, 3, 4, &c. 
times that of Sirius, supposed unity. 
