S34< MICHELL. 



complement of this quantity to unity will represent tlie probability of 

 the contrary. 



619. Michell obtains the following results on his page 246, 



If now we compute, according to the principles above laid down, 

 what the probability is, that no two stars, in the whole heavens, should 

 have been within so small a distance from each other, as the two stars 

 P Capricorni, to which I shall suppose about 230 stars only to be equal 

 in brightness, we shall find it to be about 80 to 1. 



For an example, where more than two stars are concerned, we may 

 take the six brightest of the Pleiades, and, supj)osing the whole number 

 of those stars, which are equal in splendor to the faintest of these, to 

 be about 1500, we shall find the odds to be near 500000 to 1, that no 

 six stars, out of that number, scattered at random, in the whole hea- 

 vens, would be within so small a distance from each other, as the Plei- 

 ades are. 



Michell ofi ves the details of the calculation in a note. 



620. Laplace alludes to Michell in the Theorie . . . des Proh., 

 page LXiii., and in the Connaissa^ice des Terns for 1815, page 219. 



621. The late Professor Forbes wrote a very interesting criti- 

 cism on Michell's memoir; see the London, Edinhui^gh and Buhlin 

 Philosophical Magazine, for August 181^9 and December 1850. He 

 objects with great justice to Michell's mathematical calculations, 

 and he also altogether distrusts the validity of the inferences 

 drawn from these calculations. 



« 



622. Struve has given some researches on this subject in his 

 Catalogus Kovus Stellarum Duplicium et Midtipliciiim . . . Dorpati, 

 1827, see the pages xxxvii. — XLVIII. Struve's method is very 

 different from Michell's. Let n be the number of stars in a given 

 area S of the celestial surface ; let (/> represent the area of a small 



circle of x" radius. Then Struve takes ^ — - ^ as the chance 



of having a pair of the n stars within the distance x", supposing 

 that the stars are distributed by chance. Let 8 represent the 

 surface beginning from —15'' of declination and extending to the 

 north pole; let n = 10229, and ic = 4 : then Struve finds the above 

 expression to become '007814. 



