410 Prof. Forbes on the evidence for a Physical Connexion 



as conformable to Mitchell's fundamental supposition. To 

 express the antecedent improbability (which Mitchell con- 

 founds with an inherent improbability) of two stars falling 

 within 1° of each other, or what is the same thing, of a star 

 falling within a circle 2° in diameter described round the 

 position of any other star as a centre, it is shown in Note A 

 at the end of this paper, that we may imagine as many dice to 

 be thrown at once as there are stars to be considered, and 

 each die to have as many faces as there exist spaces 2° in dia- 

 meter in the whole heavens (which is 13131), then the occur- 

 rence of any doublet in such a throw of dice is equivalent to 

 the duplication of any star by another within 1° of it; and 

 the chance against the occurrence of doublets is (on Mitchell's 

 theory) the chance against the duplication of any star. The 

 chance of throwing a doublet with 100 dice may thus be shown 



2 

 to be about — . If there were only two dice the chance would 



be just . the reciprocal of the number of faces on each*. 



But though there are 13131 different throws for one which is 

 a doublet, there is no more improbability in that than in any 

 other given throw, and therefore, although the appearance of 

 a series of doublets produce a reasonable suspicion of an in- 

 terfering cause, the grounds of that suspicion can by no means 

 be expressed by the numerical antecedent improbability of the 

 event. 



22. A little consideration will show that no event, tolerably 

 complex (such as the distribution of stars^ supposed by chance, 

 or the fall of many dice at once), can occur without the 

 chances, reckoned on the principle of expectation, being per- 

 fectly enormous against it, and giving to it the air of an extra- 

 vagant a -priori improbability. The improbability, for in- 

 stance, of a given deal producing a given hand at whist is so 

 immense, that were we to assume Mitchell's principle, we 

 should be compelled to assign it as the result of an active 

 cause with far more probability than even that found by him 

 for the physical connexion of the six stars of the Pleiades. 



23. A natural but very important error has been made in 

 the use of the term "most probable result." A result which, 

 on the long run of many trials made under the same circum- 

 stances, may be expected to occur oftenest, is truly called the 



* Thus with common dice, having six faces, the number of ways the dice 

 may fall is thirty-six : but six cases give doublets ; the chance of throwing 



doublets is therefore evidently — . 



