between Stars forming Binary or Multiple Groups. 405 



9. Next suppose that there are n other stars in the same 

 category with the given star A, and the independent probability 

 that each shall not be within a degree of it to be that just found, 

 the probability that these n events shall concur, or that no one 

 star shall be within 1° of A, will be expressed by multiplying 



(1 3 1 3*0 \ n 

 — — — ) . 



"And farther," adds Mitchell, "because the same event is 



equally likely to happen to any one star as to any other, and 



therefore any one of the whole number of stars n 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 frac- 



/l 31 30" V* 



tionf ) will represent the probability that nowhere in the 



\13131V i v J 



whole heavens, any two stars amongst those in question would 



be within the distance of one degree from each other; and 



the complement of this quantity to unity will represent the 



probability of the contrary*." 



10. So far as I see, the first part of the argument (in § 8) 

 involves an error, or rather two errors in principle ; the second 

 part (contained in the last paragraph) an error in detail, which 

 vitiates the numerical results arrived at. The last, as being of 

 little consequence if the first be established (which would 

 overthrow the entire calculation), I shall refer for discussion 

 to a note at the end of this paperf- 



11. It is evident that the argument for the physical con- 

 nexion of double stars, derived from the Theory of Chance, 

 depends entirely upon our admission of the primary result, 

 that two given stars cannot be within one degree of one an- 

 other without inferring a reason for it sufficiently powerful to 

 balance the adverse probability of 13131 to 1. AH the rest 

 follows, or may be made to follow, as a matter of course. 



[12.] Let us look at the case straightforwardly. Suppose 

 two luminaries in the heavens, as two dots on a sheet of paper 

 of known dimensions and figure. Is it or is it not common 

 sense to say, that the position of one luminary or one dot being 

 given, the law of " random scattering " can assign any other 

 position in the field as more or less probable or improbable 

 for the second. If one star be in one pole of the heavens, is 

 the most probable position of the second in the opposite pole, 

 or is it 90° from it, or is it 30°, or is it in any assignable 

 position whatever ? 1 think not. Every part of the field, even 

 that close to the star A, is an equally probable allotment for 

 the star B, if we are guided by no predetermining hypothesis 



* Mitchell, pp. 244, 245. f See note A. 



