588 ^ PHILOSOPHICAL TRANSACTIONS. [aNNO I789. 



way, let us suppose a cluster to consist of 5000 stars, and that each of them 

 may be put into one of 5000 given places, and have one of 5000 assigned mag- 

 nitudes. Then, without extending our calculation any further, we have five and 

 twenty millions of chances, out of which only one will answer the above im- 

 probable conjecture, while all the rest are against it. When we now remark 

 that this relates only to the given places within the frustrum of a supposed cone, 

 whereas these stars might have been scattered all over the visible space of the 

 heavens ; that they might have been scattered, even within the supposed cone, 

 in a million of places different from the assumed ones, the chance of this appa- 

 rent cluster not being a real one, will be rendered so highly improbable that it 

 ought to be entirely rejected. 



Mr. Michell computes, (Phil. Trans, vol. 57, p. 246,) with respect to the 6 

 brightest stars of the Pleiades only, that the odds are near 500000 to 1, that 

 no 6 stars, out of the number of those which are equal in splendour to the 

 faintest of them, scattered at random in the whole heavens, would be within so 

 small a distance from each other as the Pleiades are. Taking it then for granted 

 that the stars which appear to be gathered together in a group, are in reality thus 

 accumulated, I proceed to prove also that they are nearly of an equal magnitude. 

 . The cluster itself, on account of the small angle it subtends to the eye, we 

 must suppose to be very far removed from us. For, were the stars which com- 

 pose it at the same distance from one another as Sirius is from the sun ; and 

 supposing the cluster to be seen under an angle of 10 minutes, and to contain 

 50 stars in one of its diameters, we should have the mean distance of such stars 

 12 seconds ; and therefore the distance of the cluster from us about 17,00O times 

 greater than the distance of Sirius. Now, since the apparent magnitude of 

 these stars is equal, and their distance from us is also equal, — because we may 

 safely neglect the diameter of the cluster, which, if the centre be 17,000 times 

 the distance of Sirius from us, will give us 17,025 for the farthest, and 17,000 

 wanting 25 for the nearest star of the cluster ; — it follows that we must either 

 give up the idea of a cluster, and recur to the above refuted supposition, or 

 admit theequalitv of the stars that compose these clusters. It is to be remarked 

 that we do not mean entirely to exclude all variety of size ; for the very great 

 distance, and the consequent smallness of the component clustering stars, will 

 not permit us to be extremely precise in the estimation of their magnitudes ; 

 though we have certainly seen enough of them to know that they are contained 

 within pretty narrow limits ; and do not perhaps exceed each other in magnitude 

 more than in some such proportion as one full-grown plant of a certain species 

 may exceed another full-grown plant of the same species. 



If we have drawn proper conclusions relating to the size of stars, we may with 

 still greater safety speak of their relative situations, and affirm that in the same 



