30 ON THE CONSTRUCTION Of THE HEAVENS. 



infulated, it cannot be improper to confult calculation, in or- 

 der to fee whether it be likely that the 700 double ftars I have 

 given in two catalogues, as well as many more I have fince 

 collected, fliould be of that kind. Such an inquiry, though 

 not very material to our prefent purpofe, will hereafter be of 

 ufe to us, when we come to confider more complicated fyf- 

 tems. For, if it can be fhovvn that the odds are very much 

 againft the cafual production of double ftars, the fame argu- 

 ment will be ftill more forcible, when applied to treble, qua- 

 druple, or multiple compofitions. 

 Computation Let us take zz Aquarii, for an inftance of computation. 



probability 116 This ftar is admitted, by Flamfteed, De la Caille, Bradley, 

 that the remoter and Mayer, to be of the 4th magnitude. The two ftars that 

 ftar fliould be « com p f e jt being equal in brightnefs, each of them may be 



much larger than 



the mean lize as fuppofed to thine with half the light of the whole luftre. This, 



is reouiiite } according to our way of reckoning magnitudes *, would make 

 them 4m x \/ 2 = 5y m ; that is, of between the 6th and 5th 

 magnitude each. Now, the light we receive from a ftar be- 

 ing as the fquare of its diameter direclly, and as the fquare of 

 its diftance inverfely, if one of the ftars of zz Aquarii be farther 

 off than the ftars of between the 6th and 5th magnitude are 

 from us, it muft be fo much larger in diameter, in order to 

 give us an equal quantity of light. Let it be at the diftance 

 of the ftars of the 7 th maguitude; then its diameter will be to 

 the diameter of the ftar which is neareft to us as 7 to 5-f, and 

 its bulk as 1,885 to 1 ; which is almoft double that of the 



and the much neareft ftar. Then, putting the number of ftars we call of 



greater impro- between the 6th and 5th magnitude at 450, we (hall have 686 

 firjon of the C °f the 7 th magnitude to combine with them, fo that they may 



two ftars fliould make up a double ftar of the firft clafs, that is to fay, that the 



agree with the ^ ftars fiot be more than #, a f under> Tne f urface f 



phenomena. J , , 



the globe contains 34036131547 circular fpaces, each of 5' m 



diameter ; fo that each of the 686 ftars will have 49615357 of 

 thefe circles in which it might be placed ; but, of all that num- 

 ber, a fingle one would only be the proper fituation in which 

 it could make up a double ftar with one of the 450 given ftars. 

 The odds are ^ ut thefe odds, which are above 75f millions to one againft 

 many millions the compofition of zz Aquarii, are extremely increafed by oui 



to one. 



* The expreflions 2m, 3m, 4m, &c. ftand for ftars at the diftance 

 of 2, 3, 4, &c. times that of Sirius, fuppofed unity, 



foregoing 



