402 Prof. Forbes on the evidence for a Physical Connexion 



as well as seemingly near, and may act upon one another by 

 their mutual attractions, after the manner of sun and planet. 

 Such stars are called "physically" double. 



3. Now it is an interesting fact, that long before we had 

 the convincing proof that many binary stars are " physically " 

 as well as "optically" double, which was afforded by the 

 splendid discovery of Sir William Herschel that such stars do 

 in many cases describe orbits round their common centre of 

 gravity, the Rev. John Mitchell, a philosopher of great and 

 original talent, had inferred inductively the probability that 

 such a physical connexion existed, merely from their closeness 

 of apparent position, and without any proof of their exerting 

 a sensible attraction, or other reciprocal influence. Having 

 arrived himself inductively at the conclusion, he endeavoured 

 to put his grounds of belief into a mathematical shape, which 

 should compel the assent of all reasonable persons, by showing 

 the great numerical probability which exists (according to him) 

 against the contrary supposition, namely, that such stars are 

 only "optically," not "physically" double. 



4. Mitchell's argument is contained in a paper, remarkable 

 on many other accounts, entitled " An Inquiry into the pro- 

 bable Magnitude and Parallax of the Fixed Stars from the 

 quantity of Light which they afford to us 9 and the particular 

 circumstances of their situation" printed in the Philosophical 

 Transactions for 1767*. Amongst other results he obtains 

 this one (so often quoted since), that " the odds are near 

 500,000 to 1, that no six stars out of 1500 equal in splendour, 

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

 small a distance from one another as the Pleiades aref." 



5. The principles of reasoning employed in this paper (to 

 which we shall presently revert), and the results contained in 

 it, have been sanctioned by the authority of writers of the 

 very highest eminence, whether on astronomy or on the theory 

 of probabilities ; who, since the time of Mitchell, or for more 

 than eighty years, have adopted them without (so far as I 

 know) a dissentient voice; and the extent to which the prin- 

 ciples of Mitchell have been implicitly admitted by his suc- 

 cessors may be understood from the following statement, rest- 

 ing on the very highest living authorities on sidereal astronomy. 

 M. Struve, director of the Pulkowa Observatory, " calculates 

 the odds at 9570 to 1 against any two stars, from the 1st to 

 the 7th magnitude inclusive, falling (if fortuitously scattered) 

 within 4" of each other. Now the number of such binary 

 combinations actually observed at the date of this calculation 

 was already 91, and many more have been added to the list. 



* Vol. lvii. p. 234. f Ibid. p. 246. 



