SECT. 5.] Randomness and its scientific treatment. 101 



entire accord amongst the various writers as to the assump 

 tions practically to be made in any particular case, and there 

 fore as to the conclusion to be drawn, combined with a very 

 considerable amount of difference as to the axioms and defi 

 nitions to be employed. Thus Mr M. W. Crofton, with the 

 substantial agreement of Mr Woolhouse, laid it down un 

 hesitatingly that &quot;at random&quot; has &quot;a very clear and definite 

 meaning; one which cannot be better conveyed than by Mr 

 Wilson s definition, according to no law ; and in this sense 

 alone I mean to use it.&quot; According to any scientific inter 

 pretation of law I should have said that where there was 

 no law there could be no inference. But ultimate tendency 

 towards equality of distribution is as much taken for granted 

 by Mr Crofton as by any one else: in fact he makes this a 

 deduction from his definition: &quot;As this infinite system of 

 parallels are drawn according to no law, they are as thickly 

 disposed along any part of the [common] perpendicular as 

 along any other&quot; (vn. p. 85). Mr Crofton holds that any 

 kind of unequal distribution would imply law, &quot;If the points 

 [on a plane] tended to become denser in any part of the plane 

 than in another, there must be some law attracting them 

 there&quot; (ib. p. 84). The same view is enforced in his paper 

 on Local Probability (in the Phil. Trans., Vol. 158). Surely 

 if they tend to become equally dense this is just as much 

 a case of regularity or law. 



It may be remarked that wherever any serious practical 

 consequences turn upon duly securing the desired random 

 ness, it is always so contrived that no design or awkwardness 

 or unconscious one-sidedness shall disturb the result. The 

 principal case in point here is of course afforded by games of 

 chance. What we want, when we toss a die, is to secure that 

 all numbers from 1 to 6 shall be equally often represented in 

 the long run, but that no person shall be able to predict the 



