SECT. 12.] Randomness and its scientific treatment. 109 



we are looking through regions which are not more thickly 

 occupied but are merely more extensive. The alternative 

 before us, in fact, is this. If the whole volume, so to say, of 

 the starry heavens is tolerably regular in shape, then the 

 arrangement of the stars is not of the random order; if that 

 volume is very irregular in shape, it is possible that the ar 

 rangement within it may be throughout of that order. 



12. (2) When the arrangement in question includes 

 but a comparatively small number of events or objects, it 

 becomes much more difficult to determine whether or not it 

 is to be designated a random one. In fact we have to shift 

 our ground, and to decide not by what has been actually 

 observed but by what we have reason to conclude would be 

 observed if we could continue our observation much longer. 

 This introduces what is called Inverse Probability , viz. the 

 determination of the nature of a cause from the nature of the 

 observed effect; a question which will be fully discussed in 

 a future chapter. But some introductory remarks may be 

 conveniently made here. 



Every problem of Probability, as the subject is here under 

 stood, introduces the conception of an ultimate limit, and 

 therefore presupposes an indefinite possibility of repetition. 

 When we have only a finite number of occurrences before us, 

 direct evidence of the character of their arrangement fails us, 

 and we have to fall back upon the nature of the agency 

 which produces them. And as the number becomes smaller 

 the confidence with which we can estimate the nature of the 

 agency becomes gradually less. 



Begin with an intermediate case. There is a small lawn, 

 sprinkled over with daisies: is this a random arrangement? 

 We feel some confidence that it is so, on mere inspection; 

 meaning by this that (negatively) no trace of any regular 

 pattern can be discerned and (affirmatively) that if we take 



