[ "3 ] 



These principles, which we have laid down above, may be like- 

 wife applied, as is manifeft, to determine the probability of the dc- 

 cifions in courts of appeal ; where the fame queftion is fucceffively 

 tried before different tribunals. 



And here I cannot avoid obferving, that Dr. Waring's method 

 of determining the refulting probability, where different arguments 

 are contradictory, is erroneous. Let P, fays he, be = the probabi- 

 lity refulting from the arguments in fupport of the fad, and Q_ = 

 the probability refulting from all the arguments againfl: the fad; 

 then the probability of all the arguments for the fad will be P — Q_, 

 if P be greater than Q,-, or againft it = Q7— P, if Q,be greater than 

 P. See Principles of Human Knowledge, § 10. Now, according to 

 thefe principles, if two witneffes of equal veracity fliould con- 

 tradid each other, the difference between the probabilities for and 

 againft the fad would be = 0, that is, the fad would be imijoffiblc; 

 which evidently cannot be a true inference. But in reality, in 

 this cafe, there would be an equal chance for the truth and falfhood 

 of the fad ; for let the odds that each witnefs tells truth be the 

 ratio of a to 3, then the odds refulting that the fad is true, 

 will be the ratio oi ab to b a^ and the refulting probability = 



ah _ j^ 

 ab -\r ab 



Again, if againft a propofition which is abfolutely certain, there 



fiiould occur an argument for the truth of which there was an 



Vol. VII. P even 



