MICHELL. 333 



(il8. The part of the memoir with which we are concerned 

 is that in which Michell, from the fact that some stars are very 

 close together, infers the existence of design. His method ^vill be 

 seen from the following extract. He says, page 243, 



Let us then examine what it is jDrobable would have been the least 

 apj)arent distance of any two or more stars, any where in the whole 

 heavens, ui^on the supposition that they had been scattered by mere 

 chance, as it might happen. Now it is manifest, upon this supposition, 

 that every star being as likely to be in any one situation as another, 

 the probability, that any one particular star should happen to be within 

 a certain distance (as for example one degree) of any other given star, 

 would be represented (according to the common way of computing 

 chances) by a fraction, whose numerator would be to it's denominator, 

 as a circle of one degree radius, to a circle, whose racUus is the diameter 

 of a great circle (this last quantity being equal to the whole surface of 



the sphere) that is, by the fraction . ..[^, ^ j or, reducing it to a deci- 



( Oo / D'O ) 



mal form, -000076154 (that is, about 1 in 13131) and the complement 



13130 

 of this to unity, viz. -999923846, or the fraction y^Yqt will represent 



1 1 Ox 



the probability that it would not be so. But, because there is the same 

 chance for any one star to be within the distance of one degree from 

 any given star, as for every other, multiiDlying this fraction into itself 

 as many times as shall be equivalent to the whole number of stars, of 

 not less brightness than those in question, and jDutting oi for this number, 



(-999923846)", or the fraction (^|^)" will represent the probability, 



that no one of the whole number of stars n would be within one de- 

 gree from the proposed given star ; and the complement of this quan- 

 tity to unity will represent the probability, that there would be some 

 one star or more, out of the whole number oi, within the distance of 

 one degree from the given star. And farther, because the same event 

 is equally likely to ha^Dpen to any one star as to any other, and there- 

 fore any one of the whole number of stars 7i might as well have been 

 taken for the given star as any other, we must again repeat the last 

 found chance n times, and consequently the number {('999923846)"}", 



r/13130\")" 

 or the fraction I ( ^kj^. ) [ will represent the probability, that no 



where, in the whole heavens, any two stars, amongst those in question, 

 would be within the distance of one degi-ee from each other; and the 



