VOL, hVlI.'] PHILOSOPHICAL TRANSACTIONS. 435 



If we assume the stars belonging to our own system to be about 1000; since 

 they are in all respects similar to the sun, excepting perhaps such among them 

 as are liable to frequent changes, and we have nothing to determine us to one 

 magnitude rather than another, we may most reasonably suppose the magnitude 

 of the sun to be a medium among the whole number. On this supposition, he 

 will probably rank, only with the stars of the 4th magnitude; and his light there- 

 fore, if he was removed to the medium distance of the other stars (viz. a 

 distance equal to the radius of the sphere that would include half the stars of 

 our own system) would hardly exceed a 200th part of the light of Sirius; and 

 consequently, if the parallax of Sirius would be about one second, if he was of 

 the same size and native brightness with the sun, it will be an equal chance that 

 the parallax of one half of the stars, belonging to this system, is not less than 

 one second divided by the square root of 200, that is a little more than 4"' ; and 

 it will likewise be an equal chance that the parallax of no one among them 

 exceeds between 9 and 12 times that quantity, or a little more than ^ of a 

 second. 



If, insteatl of 1000 stars, we suppose the whole number, belonging to this 

 system, to be only about 350, the sun will then, if he is of a medium size 

 among them, rank probably with the stars of the 3d magnitude, and his light, 

 at a medium distance, on this hypothesis, would be about a 50th part of that of 

 Sirius. And therefore, according to the reasoning above, we should then find 

 it an equal chance that the parallax of one of these 350 stars would not be less 

 than about 8"'-i-; and there would be the same chance that the parallax of no 

 one among them would be more than between 50"' and about l". In the former 

 supposition of 1000 stars; the apparent magnitude of the sun, when removed to 

 the medium distance, &c. it seems not improbable that the largest star in the 

 system may perhaps exceed the sun, in the proportion of about 1000 to 1 ; and 

 in the latter supposition of 350 stars, &c. that it may perhaps exceed the sun, in 

 the proportion of about 120 to 1. In whatever proportion the diameter of the 

 sun is greater or less than the medium we have taken for it in the suppositions 

 above, in the same proportion will the parallaxes be increased or diminished; and 

 in the inverse triplicate of that proportion must their magnitudes be diminished 

 or increased. 



Let us now examine the circumstances of the Pleiades; and assuming the 

 respective distances of the stars, composing that system, from each other to be, 

 at a medium, equal to those of our own, let us see what will be the consequences 

 of this supposition. Now if the Pleiades do not extend further in the direction 

 of a line drawn between the earth and them, than in a direction at right angles 

 to that line (which, from their composing a system, we have a right to suppose 

 they do not), we can hardly allow the mean distance of those that are next to 



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