between Stars forming Binary or Multiple Groups. 409 



with which the prints succeeded one another on the surfaces 

 of the sandstone, reproducing group after group of steps in 

 two rows marked by the irregularity of interval characterizing 

 the motion of quadrupeds, furnished an argument, geome- 

 trical no doubt, but incapable of numerical definition, which, 

 when combined with the likeness of the individual marks to the 

 foot-prints of certain animals, raised the evidence to the 

 amount producing conviction. 



19. The arguments and illustrations now adduced to in- 

 validate the conclusion of Mitchell and his followers, that it 

 is possible to assign numerical probabilities for or against the 

 present distribution of the stars, or of any part of them, or even 

 of two or three individual stars especially selected, may I think 

 be reduced to the shape of two main objections to the principle 

 and its primary results, either of which would, I conceive, be 

 fatal to Mitchell's conclusions. I shall state them in the order 

 in which they appear most likely to be at once assented to. I 

 shall first state the objection to the application made of the 

 principle of " random scattering ;" I shall next state an objec- 

 tion to the fundamental definition or implied axiom on which 

 the whole argument is based. 



20. First Objection. — The doubt existing in the mind of 

 a reasonable person, whether an event still future, and which 

 may happen many ways, shall occur in a particular given way, is 

 erroneously considered as equivalent to an inherent improbabi- 

 lity of its happening, or having happened, in that way. 



21. Thus, 10,000 balls numbered consecutively being 

 placed in a bag, the antecedent chance or expectation of draw- 

 ing a given number is ; but it is not the less necessary 



that a specific number be drawn. It was 9999 to 1 that the 

 number 65 (suppose) should not be drawn ; but 65 being de 

 facto the number drawn, every vestige of improbability con- 

 cerning it vanishes. Has not every fall of two common dice 

 an antecedent probability of 17 to 1 against it if the numbers 

 turned up be different*, and 35 to 1 if they be doublets? But 

 have these probabilities any longer a meaning after the dies 

 are cast and the numbers read ? We then see one individual 

 result neither more nor less likely in itself to happen than any 

 other individual result. Now, to apply this to the case of 

 double stars, we must take an illustration already made use off 



* For out of thirty-six possible cases, two cases satisfy the condition ; 

 for instance, three shown by the 1st die and five by the 2nd; or else five 

 by the 1st and three by the 2nd ; in the case of doublets the throw of each 

 die is specifically determined. 



t See note A. 



