434 PHILOSOPHICAL TRANSACTIONS. [aNNO 1767 . 



Besides the brighter stars, it is probable there are many of those of the 

 the smaller magnitudes also that belong to the same system with the sun. 

 Now, if this should be the case, many of them being only fainter on account of 

 their less real magnitude, we may stand the same chance of finding a parallax 

 among some of these, as among the brightest ones, provided we pitch on such as 

 happen to belong to our own system : to direct us with some probability to these, 

 we have the circumstances above-mentioned of their composing larger constella- 

 tions, and their having few stars lying very near them ; and perhaps there may 

 be still a little more reason to suspect that those stars form a part of the same 

 system with ourselves, where, besides these circumstances, there have been 

 observed changes of brightness, &c. among several of them in the same neigh- 

 bourhood, such for instance as the changes which have been observed among 

 several of the stars in the constellations of the Swan, Cassiopeia, &c. We may 

 also venture to add to these, most of those stars that are of a redder hue than 

 the rest, as it is probable that they are a good deal larger, in proportion to 

 their brightness than the whiter stars [see the last note but two] . Many of 

 them also have been observed to have a proper motion of their own, which, with 

 several other concurrent circumstances, tends to make it highly probable that 

 they are some of the nearest to us. 



Having thus endeavoured to establish the probability that the sun is one of 

 a system of stars, placed by themselves in this part of the universe, Mr. M. 

 next inquires into some of the consequences of this hypothesis. Now if this 

 is the case, and we suppose the whole number of stars, which belong to this 

 system only (excluding those which belong to others), to amount to about 1000, 

 we shall find it to be an even chance, that the parallax of the nearest among 

 them does not exceed the parallax of one half that number, in a greater 

 proportion than that of 9 to 1, supposing the earth to be placed in or near the 

 centre of the whole system; nor in a greater proportion than that of about 12 

 to 1, supposing it to be placed very near the edge of the system; for supposing 

 1000 points to be placed within a sphere of any given magnitude, and that they 

 are equally indifferent to every part of that sphere, if we assume any one of 

 these points as a centre, we shall find, according to the known doctrine of chances, 

 that there is an equal degree of probability, whether any one of the rest shall 

 or shall not fall within a sphere described about the point assumed, of about 7 

 ten thousandths of the size of the whole sphere; but the radius of such a 

 sphere is about -j^^. or a little less than -^ of the radius of the whole sphere, that 

 is about ^ of the radius of a sphere of half the size of the greater one ; and therefore 

 a sphere of about 9 times this radius will include half the greater sphere, if 

 its centre be assumed near the centre of the greater sphere, and a sphere of 

 1 2 times this radius will include half the greater sphere, if the point be assumed 

 almost in the surface of it. 



