VOL. LXXIX.] PHILOSOPHICAL TRANSACTIONS. 589 



distances from the centre an equal scattering takes place. If this were not the 

 case, the appearance of a cluster could not be uniformly increasing in brightness 

 towards the middle, but would appear nebulous in those parts which were more 

 crowded with stars ; but, as far as we can distinguish, in the clusters of which 

 we speak, every concentric circle maintains an equal degree of compression, as 

 long as the stars are visible ; and when they become too crowded to be distin- 

 guished, an equal brightness takes place, at equal distances from the centre, 

 which is the most luminous part. 



The next step in my argument will be to show that these clusters are of a glo- 

 bular form. This again we rest on the sound doctrine of chances. Here, by 

 way of strength to our argument, we may be allowed to take in all round nebu- 

 lae, though the reasons we have for believing that they consist of stars have not 

 as yet been entered into. For, what I have to say concerning their spherical 

 figure will equally hold good whether they be groups of stars or not. In my 

 catalogues we have, I suppose, not less than 1000 of these round objects. Now 

 whatever may be the shape of a group of stars, or of a nebula, which we would 

 introduce instead of the spherical one, such as a cone, an ellipsis, a spheroid, a 

 circle or a cylinder, it will be evident that out of 1 000 situations, which the 

 axes of such forms may have, there is but one that can answer the phenomenon 

 for which we want to account ; and that is, when those axes are exactly in a line 

 drawn from the object to the place of the observer. Here again we have a mil- 

 lion of chances of which all but one are against any other hypothesis than that 

 which we maintain, and which, for this reason, ought to be admitted. 



The last thing to be inferred from the above related appearances is, that these 

 clusters of stars are more condensed towards the centre than at the surface. If 

 there should be a group of stars in a spherical form, consisting of such as were 

 equally scattered over all the assigned space, it would not appear to be very gra- 

 dually more compressed and brighter in the middle ; much less would it seem to 

 have a bright nucleus in the centre. A spherical cluster of an equal compression 

 within, for that such there are will be seen hereafter, — may be distinguished by 

 the degrees of brightness which take place in going from the centre to the cir- 

 cumference. Thus, when a is the brightness in the centre, it will be 

 V(a* — x^) at any other distance x from the centre. Or, putting a = J, and 

 X = any decimal fraction ; then, in a table of natural sines, where x is the sine, 

 the brightness at x will be expressed by the cosine. Now as a gradual increase 

 of brightness does not agree with the degrees calculated from a supposition of an 

 equal scattering, and as the cluster has been proved to be spherical, it must 

 needs be admitted that there is indeed a greater accumulation towards the centre. 

 And thus, from the above-mentioned appearances, we come to know that there 

 are globular clusters of stars nearly equal in size, which are scattered evenly at 



