IN CASES OF LEGAL EVIDENCE. 153 



the pills for which she substituted others from a surgeon, the surgeon however alleged, that if 

 she had done so, an entry should appear in a book that he produced, which entry did not appear. 

 Let Pi pj be determined as in the value of tti , and let 



e be the probability that the surgeon omitted the entry from design ; 

 / that he did so from neglect ; 

 Q that the fact alleged is true. 

 Then the truth of the allegation is consistent with the non-appearance of the entry ; 

 firstly : if he designed the omission, of which the probability is e ; 



secondly : if he did not design the omission, but neglected to make the entry of this, the pro- 

 bability is (1 - e)/. 

 Again, whatever may have caused the allegation, any hypothesis which excludes its truth 

 may be taken also to exclude the possibility of an entry being made ; and therefore 1 will measure 

 the probability of its not appearing, on every hypothesis but that of the fact having occurred. 



Hence Q = ^^^^^—^-^^^——^—^— . 



''^h,p,{e+fil-e)}^'''P' 



Referring to the expression for tt, the probability of a fact being true, which has no other sup- 

 port than the testimony of one witness, we see that the values of u and v which satisfy the equation 



1 



Pi/i^ 



are those which they would possess if the probability Q were raised by the testimony of this 

 witness alone, and this equation therefore affords the means of correcting the values of those 

 quantities. 



The next independent fact was, that the accused bought As ; it depended for its evidence 

 on the testimony of a single witness ; if therefore tts measure the probability that she did so, 

 TT, will be determined by the formula for tt,; the numerical values being adapted to the particular 

 allegation. 



The witness, who spake to the making of pills, also alleged that she saw some given by the 

 accused to the deceased ; and that she herself took one of them which produced efiFects similar to 

 those produced by Js : as far as this testimony is concerned, the probability that poisonous pills 

 were administered is compounded of the probabilities that any were administered, and that those 

 given, if any were so, were poisonous. In this example it is assumed, that the probability that 

 poisonous pills were given by the accused to the deceased is, as far as the testimony of this 

 particular witness is concerned, the same as the probability that her previous allegation is true, 



or TT,. 



Let then P, be the probability that the accused knowingly possessed poison, 



Pj that she administered it, 



P„ the probability of guilt. 

 Then, as far as these facts are concerned, 



Now each of the facts, whose probabilities are measured by tti, tt^, tfj and tt, afford some 

 probability that each of the facts whose probabilities are measured by P, , P,, is true, and the 

 falsehood of any number of them less than the wiiolc does not render cither /', or P,. 0. The 

 complete expression for each of these quantities will therefore be, 



