420 Prof. Forbes on the evidence for a Physical Connexion 



in the nature of things more likely than any other event which 

 could come singly under our notice. If we could form an idea 

 of utter confusion or material chaos, it would not surely be of 

 anything in which uniformity would have a conspicuous share ; 

 it would rather be the most heterogeneous variety in number 

 and paucity 5 bulk and figure, density and rarity. It appears 

 to me to be as arbitrary to assume this uniformity or want of 

 bias, as it would be in attempting to reason about the proper- 

 ties of a mass whose figure is unknown, that it must be a 

 sphere, because, in our ignorance of how it was formed, we 

 can assign no reason why one of its diameters should be 

 greater or less than another. 



35. How then are we to enlarge the idea of " random " so 

 as to meet the case? We must suppose that the dice have 

 been formed out of non-homogeneous matter ; that they are 

 biassed in every possible way; that out of a great number of 

 sets of such dice we are shown the result of the fall of one 

 set only. Here we have no ultimate or ideal distributive 

 tendency of chance to look to, because the result to which 

 many experiments with one set of dice would tend, would not 

 be that of uniformity. The bias is unknown ; it is itself a con- 

 dition of "chance" of a higher order. 



36. Yet notwithstanding, with such dice two consequences 

 follow. (1.) The final result of many throws, each with a 

 different set of such biassed dice, would tend to uniformity, 

 because the chance of the bias would ultimately run through 

 all the possible cases. (2.) The expectation^ or hypothetical 

 probability of a given number turning up at any throw, would 

 be exactly the same as if the dice were known to be un- 

 biassed. 



37. In like manner the experiments with the sieve dropping 

 grains of rice in § 25 can only be considered as in a very limited 

 degree the representation of the phsenomenon of "random scat- 

 tering," though they approach as nearly to Mitchell's theory as 

 any experiment which 1 can imagine ; and therefore it is a case 

 which serves well to discriminate between the two wholly di- 

 stinct objections which I have attempted to establish against 

 this application of the theory of probabilities to the distribution 

 of the stars. Thefirst objection (Art. 20) would apply to the 

 results of that experiment treated by Mitchell's method (as has 

 been explained in its proper place). The second objection 

 (Art. 28) does not apply, because the action of the sieve is not 

 " random scattering" in the extreme sense in which our utter 

 ignorance of causation would require it to be represented. It 

 is only random in respect of subordinate distribution, the me- 

 chanical arrangement is such as to produce a clear and well* 



