Genesis of the Law of Error. 149 



statement of propositions which I should regard as well 

 established, but for his seeming dissent. 



I. A. (1)-* The origin of the law of error is to be sought in 

 the theory of Probabilities. (2) It is obeyed by random 

 aggregates of variable constituents. Gramesof chance afford 

 the simplest examples. (3) Thus if, a batch of n halls having 

 been taken at random from an immense medley of black and 

 white balls, the number of white balls in the batch is 

 recorded, and the operation is repeated many times, the series 

 of numbers presented by the record will conform to the law- 

 of-error ; more or less approximately according as n is larger, 

 and as the proportion of white to black in the medley is 

 nearer to equality. This correspondence between the bi- 

 nomial series and the law of error was happily employed by 

 Quetelet to illustrate the fulfilment of the law in various 

 kingdoms of nature. In games of chance and organic nature 

 there does not often arise a difficulty which the exact sciences 

 may present; namely, that (4) the aggregation of constituents 

 which is treated as fortuitous is known to be determinate. 

 The most familiar instance is the sequence of decimal places 

 in the evaluation of a natural constant, such as tt |. Each 

 figure is what it is in virtue of determinate law ; and yet the 

 ensemble presents the arrangement which is an outcome of 

 chance. A more important instance is furnished by the 

 distribution of velocities in a molecular chaos ; they obey at 

 once the laws of Dynamics and the laws of Probabilities. 

 The Philosophers J have exercised themselves about this 

 paradox ; but it remains a mystery §. One rule emerges that 

 (5) we should not seek for law (other than statistical uni- 

 formity) as the explanation of chance. We must not do as 

 the fatuous gambler who scrutinizes the records of the roulette 

 table in the hope of eliciting a rule to guide his future stakes, 

 In the weighty words of De Morgan : " No primary considera- 

 tions connected with the subject of Probability can or ought 

 to be received if they depend upon the results of a complicated 

 mathematical analysis ||. To use Dr. Venn's IF phraseology, 



* The passages headed by bracketed numerals in Section I. are referred 

 to in Section II. 



f Op. Venn, ' Logic of Chance,' p. 112 et seq., ed. 3, and Nixon, 

 Journal of the Royal Statistical Society, vol. lxxvi. p. 702 (1913). 



| Rencmvier, Venn, von Kries, etc. 



§ Op. Poincare, " There is here something mysterious inaccessible to 

 tlie mathematician." 



|| Encyclopccdia Metropolitana, vol. ii. : article on the " Theory oi' 

 Probability," S. 1. 



51 ' Empirical Logic.' 



