436 PHILOSOPHIGAL TRANSACTIONS. [aNNO 176?. 



each other, among the 6 stars visible to the naked eye, to be greater than what 

 would subtend an angle, if seen directly from the earth, of about 40 or 50 

 minutes. And consequently the distance between them and the earth would be 

 about 70 times that distance, and their apparent brightness, seen from those 

 that are next to each other, must be about 49OO times as great as it appears to 

 us; but ri of the Pleiades appears not fainter than Sirius in a greater proportion 

 than that of about 100 to 1; this star therefore must appear brighter to the 

 nearest of those 6, which are visible to the naked eye, than Sirius does to us, 

 in the proportion of about 49 to 1. Let us now suppose all the stars belonging 

 to the Pleiades, as well those discoverable with telescopes as those which are 

 visible to the naked eye, to be contained within a sphere, whose apparent 

 diameter at the earth is 2 degrees; and consequently the mean distance of them 

 from a spectator placed somewhere among them, as it might happen, would 

 subtend an angle, when seen directly from the earth, of about 1 degree. Since 

 therefore we have supposed the distances of the stars of our own system to be, 

 at a medium, equal to those of the Pleiades, and consequently their mean 

 distances from the earth to subtend at the Pleiades an angle of 1°, we shall have 

 the distance of the Pleiades about 57 times as great as the mean distance of the 

 stars of our own system from the earth. Hence, if the largest of the stars of 

 our own system should be at this mean distance from us, and Sirius should be the 

 largest, » of the Pleiades must exceed it in the proportion of about 200 to 1 ; for 

 removing Sirius to 57 times his present distance, his light would then be fainter 

 than it is, in the proportion of 3249 to 1, that is, fainter than n of the Pleiades 

 in the proportion of 32.49 to 1 , supposing n of the Pleiades, as above, to afford 

 us 100th part of the light of Sirius; but the magnitude of stars, supposing 

 them equally luminous, and their distance to be given, is as the cube of the 

 square root of their brightness; therefore n of the Pleiades, on this supposition, 

 must be larger than Sirius, in the proportion of the cube of the square root of 

 32.49 (that is 185) to 1. But, according to general, and probably universal analogy, 

 in all those nebulae, in which we discover stars larger than the rest, these stars are 

 placed towards the middle of their respective systems; and if therefore the same 

 thing obtains with regard to our own system, this will make n of the Pleiades 

 still something greater. 



If the distance of the Pleiades is greater than the mean distance of the stars 

 of our own system, in the proportion of about 57 to 1, it would be necessary in 

 order to make stars of the same real magnitude among the Pleiades, equally 

 visible to us with those of our own system, to take in a pencil of rays of a greater 

 diameter than the pupil of the eye, in the same proportion: this, after proper 

 deductions for the loss of light, could not well be effected by an object lens of 

 less than 2 feet aperture. Now Dr. Hooke tells us, in his micographia, that 



