between Stars forming Binary or Multiple Groups. 415 



of scattering, the inequalities of dispersion from one square to 

 another due to " accident " are well represented, and can be 

 ascribed to no assignable " cause." 



(2.) In these experiments we observe that the most loaded 

 squares contain from nearly two to more than four times the 

 average number of grains, whilst in four out of five experi- 

 ments one or more squares were vacant. 



(3.) It is quite certain that, had the spaces been smaller 

 and more numerous, the inequalities would have been still 

 greater; for in this form of experiment extent of surface has 

 an equalizing tendency. 



(4.) In all the experiments we observe squares having 

 heavy and light loads very much intermixed. In three cases 

 out of five the heaviest squares are adjacent to others alto- 

 gether blank. 



(5.) If we were to take any one of these experiments, and 

 attempt to calculate the antecedent probability of the grains 

 so arranging themselves on Mitchell's supposition, we should 

 unquestionably find numerical chances far greater against these 

 configurations being the result of accident, than those on which 

 we are told that we form our most certain ordinary judge- 

 ments. Thus if an experimental argument may be admitted, 

 the reasoning of Mitchell and his followers is altogether fal- 

 lacious ; for we find that it would lead to results extravagantly 

 absurd in cases admitting of no doubt. 



27. It will perhaps be said, that though Mitchell's reason- 

 ing was wrong, and his calculations of the chances adverse to 

 any particular arrangement of the stars altogether false and 

 exaggerated, the doctrine of probabilities has other and spe- 

 cial methods applicable to such cases as experiment has here 

 been employed to illustrate. If it be so, they have never been 

 applied to the astronomical question before us, — the question 

 whether the double stars are so " optically" or " physically;" 

 and consequently we are not required to refute investigations 

 which have never been made. The argument which has been 

 now used appears to be sufficient to prove that Mitchell's 

 attempt to express the numerical probability of a causal con- 

 nexion between the pairs of double stars is a complete failure. 

 I think, too, that I have demonstrated that the presumption 

 for such a connexion, which unquestionably arises when the 

 number of close double stars is considerable, arises in the 

 mind in the same way as the belief in the physical connexion 

 of many phenomena of nature which can only be treated in- 

 ductively, and whose ultimate probability is altogether inca- 

 pable of estimation by numbers. I might therefore close my 

 paper here. But I do not think it right to omit a conside- 



