152 Mr. TOZER, ON THE FORCE OF TESTIMONY 



reason be afforded for thinking that one rather than another has occurred, h = h,; and therefore 



— disappears from the formula. 



If anion'' the events, the belief in which may have prompted the allegation, no reason be 

 shewn why one rather than another should be believed, 6 =fc,; and the multiplier of (1 - n)v be- 

 26-6 



Similarly, if no reason be shewn why the witness in attempting to deceive should make any 



particular allegation rather than another, 2:=r- — - - =r;; — — = 1. 



And lastly, if in the case of a witness both deceived and intending to deceive, if there be no 

 reason why the probability that he would allege any one fact should differ from the probability that 



he would believe any other, a = h; and the multiplier of (1 - ?<) (l - «) becomes 1 1 - = j . 



With these hypotheses we therefore have 



i2A;Pj= {l-u)v + {\ -u)M+(l -ii){l-v) (l - ° ). 

 Ill V .^CE — aj 



And with the same assumptions, 



n. 



Pj =Mt, + (1 - u) (1 - V)- 



2a - a 

 And 



] ^, W / U / W / U / V 2a - a/ 



^■^''" ,Wi_,)(i-,),-^ "■ 



\u I \v J z,a - a 



The next material allegation was made by another witness to the effect, that she saw the accused 

 exchange some pills which she had procured for others : the evidence of this fact, as of the former, 

 is contained in the testimony of a single witness; but the antecedent probability of its occurrence 

 is different as we do or do not believe that previously alleged. If then 7r.> be the probability 

 that this allegation is true, 



1 



^3 = . 



p, |A,7ri + A,(l - TT,); 



the previous notation being preserved and adapted as regards the value of its symbols to this 

 particular allegation, 



hi h„ 



2(A + A')' 2(A + /0 



being the probabilities of the occurrence of £, ... £„, on the supposition that the previous fact is 

 true, and 



h\ K 



■2{h + h')" 2(A + A')' 



on the supposition that it is not true. 



Among the means of assigning numerical values to the probabilities of the accuracy and 

 sincerity of a witness, the comparison of the allegations of different witnesses as to immaterial 

 facts is one of the most important. This witness also alleged, that she saw the accused procure 



