BAYES. 295 



an event has happened p times and failed ^ times, the probability 

 that its chance at a single trial lies between a and h is 



/■ 



x^ (1 - xy cix 





i)(f{l-xydx 



Bayes does not use this notation ; areas of curves, according to 

 the fashion of his time, occur instead of integrals. Moreover we 

 shall see that there is an important condition implied which we 

 have omitted in the above enunciation, for the sake of brevity: 

 we shall return to this point in Art. 552. 



Bayes also gives rules for obtaining approximate values of the 

 areas which correspond to our integrals. 



542. It will be seen from the title of the first memoir that it 

 was published after the death of Bayes. The Rev. Mr Richard 

 Price is the well known writer, whose name is famous in connexion 

 with politics, science and theology. He begins his letter to 

 Canton thus : 



Dear Sir, I now send you an essay which I have found among the 

 papers of our deceased friend Mr Bayes, and which, in my opinion, has 

 gi-eat merit, and well deserves to be preserved. 



543. The first memoir contains an introductory letter from 

 Price to Canton ; the essay by Bayes follows, in which he begins 

 with a brief demonstration of the general laws of the Theory 

 of Probability, and then establishes his theorem. The enuncia- 

 tions are given of two rules which Bayes proposed for finding 

 approximate values of the areas which to him represented our 

 integrals ; the demonstrations are not given. Price himself added 

 An Appendix containing an Application of the foregoing Rides 

 to some particular Cases. 



The second memoir contains Bayes's demonstration of his prin- 

 cipal rule for approximation ; and some investigations by Price 

 which also relate to the subject of approximation. 



544. Bayes begins, as we have said, with a brief demonstra- 

 tion of the general laws of the Theory of Probability ; this part of 

 his essay is excessively obscure, and contrasts most unfavourably 

 with the treatment of the same subject by De Moivre. 



