of 500 new Nebula , atm? Clusters of Stars. 485 
34036131547 circular spaces, each of 5" in diameter; so that 
each of the 686 stars will have 49615357 of these circles in 
which it might be placed ; but, of all that number, a single one 
would only be the proper situation in which it could make up a 
double star with one of the 450 given stars. But these odds, 
which are above 75—- millions to one against the composition of 
£ Aquarii, are extremely increased by our foregoing calculation 
of the required size of the star, which must contain nearly 
double the mass allotted to other stars of the 7th magnitude ; 
of which, therefore, none but this one can be proper for making 
up the required double star. If the stars of the 8th and 9th 
magnitudes, of which there will be 896 and 1134, should be 
taken in, by way of increasing the chance in favour of the sup- 
posed composition of our double star, the advantage intended to 
be obtained by the addition of numbers, will be completely 
counteracted by the requisite uncommon bulk of the star which 
is to serve the purpose for, one of the 8th magnitude, ought 
to be more than 2^ times bigger than the rest ; and, if the 
composition were made by a star of the 9th magnitude, no less 
than four times the bulk of the other star which is to enter the 
composition of the double star would answer the purpose of its 
required brightness. Hence therefore it is evident, that casual 
situations will not account for the multiplied phenomena of 
double stars, and that consequently their existence must be 
owing to the influence of some general law of nature ; now, as 
the mutual gravitation of bodies towards each other is quite suf- 
ficient to account for the union of two stars, we are authorised 
to ascribe such combinations to that principle. 
It will not be necessary to insist any further -on arguments 
drawn from calculation, as I shall soon communicate a series of 
MDCCCII. 3 R 
